Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2013 Article ID 138109 8 pageshttpdxdoiorg1011552013138109
Research ArticleFour-Neutrino Analysis of 15 km Baseline ReactorAntineutrino Oscillations
Sin Kyu Kang12 Yeong-Duk Kim3 Young-Ju Ko4 and Kim Siyeon4
1 School of Liberal Arts Seoul National University of Science and Technology Seoul 139-743 Republic of Korea2 Pittsburgh Particle Physics Astrophysics and Cosmology Center Department of Physics and AstronomyUniversity of Pittsburgh Pittsburgh PA 15260 USA
3Department of Physics Sejong University Seoul 143-747 Republic of Korea4Department of Physics Chung-Ang University Seoul 156-756 Republic of Korea
Correspondence should be addressed to Kim Siyeon siyeoncauackr
Received 7 August 2013 Revised 4 November 2013 Accepted 25 November 2013
Academic Editor Seon-Hee Seo
Copyright copy 2013 Sin Kyu Kang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The masses of sterile neutrinos are not yet known and depending on the orders of magnitudes their existence may explain reactoranomalies or the spectral shape of reactor neutrino events at 15 km baseline detector Here we present four-neutrino analysis ofthe results announced by RENO and Daya Bay which performed the definitive measurements of 120579
13based on the disappearance of
reactor antineutrinos at km order baselines Our results using 3 + 1 scheme include the exclusion curve of Δ1198982
41versus 120579
14and the
adjustment of 12057913due to correlation with 120579
14 The value of 120579
13obtained by RENO and Daya Bay with a three-neutrino oscillation
analysis is included in the 1120590 interval of 12057913allowed by our four-neutrino analysis
1 Introduction
Understanding of the Pontecorvo-Maki-Nakagawa-Sakata(PMNS)matrix [1] is nowmoving to another stage due to thedetermination of the last angle by multidetector observationof reactor neutrinos at Daya Bay [2] and RENO [3] whosesuccess was strongly expected from a series of oscillationexperiments (T2K [4] MINOS [5] and Double Chooz [67]) which all contributed to the forefront of neutrino physics[8] A number of 3] global analyses [9 10] have presentedthe best fit and the allowed ranges of masses and mixingparameters at 90 confidence level (CL) by crediting RENOand Daya Bay for the definitive measurements of sin22120579
13
For instance the best-fit values given in the analysis of Fogliet al [9] are Δ119898
2
21= 75 times 10
minus5 eV2 sin212057912
= 32 times 10minus1
Δ1198982
32= 24 times 10
minus3 eV2 sin212057913
= 28 times 10minus2 and sin2120579
23=
48times10minus1 for normal hierarchyWhile all three mixing angles
are now known to be different from zero the values of the CPviolating phases are completely unknown Although there area number of global analysis which presented consistent values
of masses and mixing parameters [9ndash11] we focus on 12057913and
its associated factors obtained by RENO and Daya BayAlthough the three-neutrino framework is well estab-
lished phenomenologically we do not rule out the existenceof new kinds of neutrinos which are inactive so-calledsterile neutrinos Over the past several years the anomaliesobserved in LSND [12] MiniBooNE [13ndash15] Gallium solarneutrino experiments [16 17] and some reactor experiments[18] have been partly reconciled by the oscillations betweenactive and sterile neutrinos In a previous work we alsoexamined whether the oscillation between sterile neutrinosand active neutrinos is plausible especially when analyzingthe first results released fromDaya Bay and RENO [19]Thereare also other works with similar motivations [20ndash25]
After realizing the impact of the large size of 12057913 both
reactor neutrino experiments have continued and updatedthe far-to-near ratios and sin22120579
13 Daya Bay improved their
measurements and explained the details of the analysisRENO announced an update with an extension until October2012 and modified their results as follows The ratio of theobserved to the expected number of neutrino events at the far
2 Advances in High Energy Physics
detector 119877 = 0929 replaced the former value of 119877 = 0920and sin22120579
13= 0100 replaced the former best fit of sin22120579
13=
0113 [26] The spectral shape was also modified Againwe examine the oscillation between a sterile neutrino andactive neutrinos in order to determinewhether four-neutrinooscillations are preferred to three-neutrino oscillations Thiswork is focused on Δ119898
2
14within the range of O (0001 eV2)
to O (01 eV2) where Δ1198982
14oscillations might have appeared
in the superposition with Δ1198982
13oscillations at far detectors of
O (15 km) baselines Since the mass of the fourth neutrinois unknown it is worth verifying its existence at all availableorders of magnitude which are accessible from differentbaseline sizes For instance the near detector at RENO cansearch reactor antineutrino anomalies withΔ119898
2
14sim O (1 eV2)
[27 28]This paper is organized as follows In Section 2 the
survival probability of electron antineutrinos is presented infour-neutrino oscillation schemeWe exhibit the dependenceof the oscillating aspects on the order of Δ119898
2
41 when reactor
neutrinos in the energy range of 18 to 8MeV are detectedafter travel along a km order baseline In Section 3 thecurves of the four-neutrino oscillations are compared withthe spectral shape of data through October 2012 to searchfor any clues of sterile neutrinos and to see the changes insin22120579
13due to the coexistence with sterile neutrinos Broad
ranges of Δ1198982
41and sin22120579
14remain In the conclusion the
exclusion bounds of sin2212057914
and the best fit of sin2212057913
aresummarized and the consistency between rate-only analysisand shape analysis is discussed
2 Four-Neutrino Analysis ofEvent Rates in Multidetectors
The four-neutrino extension of unitary transformations frommass basis to flavor basis is given in terms of six angles andthree Dirac phases
F = 11987734
(12057934) 11987724
(12057924 1205752) 11987714
(12057914)
sdot 11987723
(12057923) 11987713
(12057913 1205751) 11987712
(12057912 1205753)
(1)
where 119877119894119895(120579119894119895) denotes the rotation of the 119894119895 block by an
angle of 120579119894119895 When a 3 + 1 model is assumed as the minimal
extension the 4-by-4 F is given by
F = (
11988814
0 0 11990414
minus1199041411990424
11988824
0 1198881411990424
minus119888241199041411990434
minus1199042411990434
11988834
119888141198882411990434
minus119888241198883411990414
minus1199042411988834
minus11990434
119888141198882411988834
)
times (
1198801198901
1198801198902
1198801198903
0
1198801205831
1198801205832
1198801205833
0
1198801205911
1198801205912
1198801205913
0
0 0 0 1
)
= (
119888141198801198901
119888141198801198902
119888141198801198903
11990414
sdot sdot sdot sdot sdot sdot sdot sdot sdot 1198881411990424
sdot sdot sdot sdot sdot sdot sdot sdot sdot 119888141198882411990434
sdot sdot sdot sdot sdot sdot sdot sdot sdot 119888141198882411988834
)
(2)
where the PMNS type of a 3-by-3 matrix 119880PMNS with threerows (119880
11989011198801198902
1198801198903) (1198801205831
1198801205832
1198801205833) and (119880
12059111198801205912
1198801205913)
is imbedded The CP phases 1205752and 120575
3introduced in (1) are
omitted for simplicity since they do not affect the electronantineutrino survival probability at the reactor neutrinooscillation
The survival probability of ]119890produced from reactors is
119875Th (]119890997888rarr ]119890) =
10038161003816100381610038161003816100381610038161003816100381610038161003816
4
sum
119895=1
10038161003816100381610038161003816119890119894
10038161003816100381610038161003816
2
exp 119894Δ1198982
1198951119871
2119864]
10038161003816100381610038161003816100381610038161003816100381610038161003816
2
= 1 minus sum
119894lt119895
410038161003816100381610038161003816119890119894
10038161003816100381610038161003816
210038161003816100381610038161003816119890119895
10038161003816100381610038161003816
2
sin2(Δ1198982
119894119895119871
4119864]
)
(3)
where Δ1198982
119894119895denotes the mass-squared difference (119898
2
119894minus
1198982
119895) It can be expressed in terms of combined Δ119898
2
119894119895-driven
oscillations as
119875Th (]119890997888rarr ]119890) = 1 minus 119888
4
141198884
13sin22120579
12sin2 (127Δ119898
2
21
119871
119864)
minus 1198884
14sin22120579
13sin2 (127Δ119898
2
31
119871
119864)
minus 1198882
13sin22120579
14sin2 (127Δ119898
2
41
119871
119864)
minus 1199042
13sin22120579
14sin2 (127Δ119898
2
43
119871
119864)
(4)
where Δ1198982
32asymp Δ119898
2
31and Δ119898
2
42asymp Δ119898
2
41 The size
of 1198984relative to 119898
3is not yet constrained The above
119875Th is understood only within a theoretical frameworksince the energy of the detected neutrinos is not uniquebut is continuously distributed over a certain range Sothe observed quantity is established with a distribution ofneutrino energy spectrum and an energy-dependent crosssection Analyses of neutrino oscillation average accessibleenergies of the neutrinos emerging from the reactors Themeasured probability of survival is
⟨119875⟩ =
int119875Th (119864) 120590tot (119864) 120601 (119864) 119889119864
int120590tot (119864) 120601 (119864) 119889119864
(5)
where 120590tot(119864) is the total cross-section of inverse beta decay(IBD) and 120601(119864) is the neutrino flux distribution from thereactor The total cross section of IBD is given as
120590tot (119864) = 00952(
119864119890radic1198642119890minus 1198982119890
1MeV2) times 10
minus42 cm2 (6)
where 119864119890asymp 119864] minus (119872
119899minus 119872119901) [28 29] The flux distribution
120601(119864) from the four isotopes (U235Pu239U238 and Pu241) atthe reactors is expressed by the following exponential of a fifthorder polynomials of 119864]
120601 (119864]) = exp(
5
sum
119894=0
119891119894119864119894
]) (7)
Advances in High Energy Physics 3
L = 1m 10 100 1000 10000
ND
ND
FDEH1
EH1
ND EH1
EH3
FD EH3
FD EH3
Δm241 = 1 eV
2
Δm241 = 01 eV
2
Δm241 = 001 eV
2
Figure 1 The dependency of ⟨119875⟩ in (5) on Δ1198982
41is presented when
Δ1198982
31= 232 times 10
minus3 eV2 as taken in RENO and Daya Bay Typicalshapes of ⟨119875⟩ versus distance are drawn for comparison with themeasured ratios in the two experiments The amplitudes of Δ119898
2
31
oscillation and Δ1198982
41oscillation are given by sin22120579
13= 010 and
sin2212057914
= 010 respectively as an example
where 1198910
= +457491 times 10 1198911
= minus173774 times 10minus1 1198912
=
minus910302times10minus2 1198913= minus167220times10
minus5 1198914= +172704times10
minus5and 119891
5= minus101048 times 10
minus7 are obtained by fitting the totalflux of the four isotopes with the fission ratio expected at themiddle of the reactor burn up period [30]
The curves in Figure 1 show ⟨119875⟩ as 119871 increases in alogarithmic manner where the three patterns of probabil-ities are shown according to the order of Δ119898
2
41 The first
bump in each curve corresponds to the oscillation due toΔ1198982
41 while the second bump that appears near 1500m
corresponds to the oscillation due to Δ1198982
31 RENO and Daya
Bay were designed to observe the Δ1198982
31-driven oscillations
at far detector (FD) according to three-neutrino analysiswhile additional detector(s) at a closer baseline performs thedetection of neutrinos in the same conditionThe comparisonof the number of neutrino events at FD to the number ofevents at the near detector (ND) is an effective strategy todetermine the disappearance of antineutrinos from reactorsThat is the sin22120579
13is evaluated by the slope of the curve
between ND and FD while their absolute values of eventnumbers do not affect the estimation of the angle 120579
13 Both
experiments used the normalization to adjust the data tosatisfy the boundary condition which is that there is nooscillation effect before the ND From Figure 1 it can beshown that the magnitude of Δ119898
2
41can affect not only the
normalization factor but also the ratio between the FD andND
The six baselines of the near detector (ND) andthe far detector (FD) of RENO are 119871near (meters) =
660 445 302 340 520 746 and 119871 far (meters) = 15601460 1400 1380 1410 1480 while their flux-weighted aver-ages 119871near and 119871far are 4073m and 1443m respectivelyThe baselines of Daya Bay named EH1 EH2 and EH3have lengths of EH1 = 494m EH2 = 554m and EH3 =
1628m respectively so that conventionally EH1 and EH2
are regarded as near detectors while EH3 is regarded as a fardetector
After the first release of results Daya Bay and RENOupdated the far-to-near ratio of neutrino events with addi-tional data Daya Bay reported a ratio of 119877 = 0944 plusmn
0007 (stat) plusmn 0003 (syst) with 119877(EH1) = 0987 plusmn
0004 (stat) plusmn 0003 (syst) [31] RENO also reported anupdate with additional data from March to October in 2012where 119877(FD) = 0929 plusmn 0006 (stat) plusmn 0009 (syst) [26] Theirmeasurements are marked in Figure 1 In three-neutrinoanalysis the far-to-near ratios give the Δ119898
2
31-oscillation
amplitude sin2212057913
= 0089 plusmn 0010 (stat) plusmn 0005 (syst) andsin22120579
13= 0100 plusmn 0010 (stat) plusmn 0015 (syst) in Daya Bay
and RENO respectively On the other hand the far-to-nearratio and the measured-to-expected ratio are understood asa combination of Δ119898
2
31oscillations and Δ119898
2
41oscillations
as shown in Figure 1 For a given value of Δ1198982
41 001 eV2
or 001 eV2 the combination of sin2212057914
and sin2212057913
isdescribed in Figure 2 In the case of RENO the ⟨119875(Δ119898
2
41=
001 eV2)⟩ and ⟨119875(Δ1198982
41= 01 eV2)⟩ curves which pass the
error bars at ND and FD are drawn as blue- (gray-) shadedareas The area where the two shaded areas ND and FDoverlap is the allowed region in sin22120579
13minussin22120579
14space using
rate-only analysisThe corresponding analysis forDaya Bay isshown together in Figure 2 The value of sin22120579
13is in good
agreement with the results released by the two experiments
3 Four-Neutrino Analysis of UpdatedSpectral Shape in RENO
One of RENOrsquos results was the ratio of the observed to theexpected number of antineutrinos in the far detector 119877 =
0929 plusmn 0011 (see [26]) where the observed is simply thenumber of events at FD On the other hand the expectednumber of events at FD can be obtained using severaladjustments of the number of events at ND
119877 equiv[Observed at FD]
[Expected at FD](8)
equiv[No of events at FD]
[No of events at ND]lowast (9)
where the number of events at each detector is normalizedThe normalization of the neutrino fluxes at ND and FDrequires an adjustment between the two individual detectorswhich includes corrections due to DAQ live time detectionefficiency background rate and the distance to each detectorThe numbers of events at FD and ND in (9) have alreadybeen normalized by these correction factors and so we have119877far = 0929 plusmn 0017 and 119877near = 0990 plusmn 0025 as shown inFigure 2The normalization guarantees 119877 = 1 at the center ofthe reactors RENO removes the oscillation effect atNDwhenevaluating the expected number of events at FD by dividingthe denominator of (9) by 0990 which is taken from 119877nearNow
119877 =[No of events at FD]
[No of events at ND] 0990 (10)
4 Advances in High Energy Physics
020
015
010
005
000
020015010005000
sin2(212057914)
sin2(212057913
)
Prob near = 0990 plusmn 0025
Prob far = 0929 plusmn 0011
RENO020
015
010
005
000
020015010005000
sin2(212057914)
sin2(212057913
) Prob near = 0987 plusmn 0005
Prob far = 0932 plusmn 0009
Daya Bay
Figure 2 Four-neutrino analysis for the observed to expected ratios at both ND and FD of RENO The shaded areas indicate the availablecombination of sin22120579
13and sin22120579
14which is compatible with the ranges of 119877Near and 119877Far released by RENO and Daya Bay Blue (gray) areas
are obtained with Δ1198982
41= 001(01) eV2 The 4] analysis of the far-to-near ratio at Daya Bay is also given for comparison
12
11
10
09
082 4 6 8
Far
near
Neutrino energy (MeV)
RENO (A)
Δm231 = 283 times 10
minus3 eV2
Δm241 = 0039 eV2
12
11
10
09
082 4 6 8
Far
near
Neutrino energy (MeV)
RENO (B)
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
Figure 3 The data and error bars are the reproduction of updated RENO for an extended period until October 2012 The red fits are drawnwith sin22120579
14= 0 for Δ119898
2
31= 283 times 10
minus3 eV2 and for Δ1198982
31= 232 times 10
minus3 eV2 obtained from the analysis in Figure 4 For each case the bluefits are overlaid which are the superposition with Δ119898
2
41= 0039 eV2 oscillation of amplitude sin22120579
14= 0050 and the superposition with
Δ1198982
41= 00078 eV2 oscillation of amplitude sin22120579
14= 0054 respectively obtained from the analysis in Figure 5
In rate-only analysis the ratio of the observed to the expectednumber of events at FD in (8) is just the survival at FD sincethe denominator in (10) is eliminatedThus 119877 coincides with119877far in Figure 2
In spectral shape analysis however the denominatorcannot be neglected since the oscillation effect at ND differsdepending on the neutrino energyThedata points in Figure 3are obtained by the definition of the ratio 119877 given in (8)and (9) per 025MeV bin as the energy varies from 18MeVto 128MeV The data dots and error bars were updatedby including additional data from March to October in2012 officially announced at Neutrino Telescope 2013 [26]
The ratio in (10) is compared with theoretical curves overlaidon the data points The theoretical curves are described by
⟨119875 (FD)⟩
⟨119875 (ND)⟩ (0990)minus1
(11)
where ⟨119875(L)⟩ is given in (4) In Figure 4 the best fitof (Δ119898
2
31 sin22120579
13) is presented when 120579
14= 0 The
point A (000283 eV2 009) indicates the 1205942 minimum
where sin2212057913
and Δ1198982
31are parameters while the point
B (000232 eV2 010) is the minimumwhere Δ1198982
31is 000232
Advances in High Energy Physics 5
00010 001000005000020 0003000015 00070
100
050
020
010
005
002
001
sin22120579
13
Δm231
A (000283 00900)B
(000232 0100)
A 1205942min dof = 096
B 1205942min dof = 132
Figure 4Three-neutrino analysis of the spectral shape updated until October 2012The best fit in (Δ1198982
31 sin22120579
13) is (000283 009) denoted
by A When Δ1198982
31= 000232 eV2 is fixed as taken by RENO the best fit of sin2120579
13is 0100 The 1120590 2120590 and 3120590 exclusion curves are drawn by
solid lines
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(0039 0050)
Δm231 = 283 times 10
minus3 eV2
sin2212057913 = 00900
RENO (A)
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(00078 0033)(0039 0049)
Δm231 = 232 times 10
minus3 eV2
sin2212057913 = 0100
RENO (B)
Figure 5The 1120590 2120590 and 3120590 exclusion curves are drawn by solid lines Apparently a broad range of sin2212057914apparently remains not excluded
Only Δ1198982
41gt Δ119898
2
31is considered and sin22120579
14gt 02 is excluded at 3120590 CL For (A) specified by Δ119898
2
31= 283 times 10
minus3 eV2 the minimum1205942
mindof = 048 is at (Δ1198982
41 sin22120579
14) = (0039 eV2 0050) while for (B) specified by Δ119898
2
31= 232 times 10
minus3 eV2 two minima 1205942
mindof = 106
and 085 are located at (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) and (0039 eV2 0049) respectively
which RENO and Daya Bay used for the fixed value Here-after two cases depending on Δ119898
2
31are discussed one is
for Δ1198982
31= 000283 eV2 marked by 119860 and the other is for
Δ1198982
31= 000232 eV2 marked by B According to the analysis
performed with 12057914
= 0 the red curves for the two valuesof Δ231are overlaid on the spectral data in Figure 3 Figure 5
shows interpretation of the spectral shape in terms of four-neutrino oscillation For given values of Δ
2
31and sin22120579
13
the 1 2 3120590 CL exclusion curves are obtained by convolutionwith the energy resolution of RENO detectors (59radic119864 +
11) Using the best fits (Δ1198982
41 sin22120579
14) = (0039 eV2 005)
for (A) and (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) for (B)
6 Advances in High Energy Physics
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
Δm241 = 0039 eV2
Δm231 = 283 times 10
minus3 eV2
(0092 0049)
00900
RENO (A)
Δm241 = 00078 eV2
Δm231 = 232 times 10
minus3 eV2
(0118 0054)
0100
RENO (B)
Figure 6 The 1120590 2120590 and 3120590 fit of combination of the sin2212057913and sin22120579
14for chosen values of (Δ119898
2
31and Δ119898
2
41) For (A) the 120594
2
mindof of(0092 0049) is 051 For (B) the 120594
2
mindof of (0118 0049) is 096 In both cases the best fit of sin2212057914
= 0 is included in 1120590 region
the blue curves are also added on the spectral data in Figure 3To see a distinct different aspect due to the magnitude ofΔ1198982
41 we choose 119898
2
41= 00078 eV2 for the best fit of (B)
avoiding 1198982
41= 0039 eV2 which is the same as the 119898
2
41for
(A)The solid curves in Figure 6 explain 1120590 2120590 and 3120590 CL of
Δ1205942 in parameters (sin22120579
13 sin22120579
14) of which the best-fits
are found at (0092 0049) for case (A) ofΔ1198982
31= 000283 eV2
and at (0118 0054) for case (B) of Δ1198982
31= 000232 eV2 In
case (B) where the value of Δ1198982
31is the same as the one that
RENO andDaya Bay took for it the best fit of sin2 212057913is 0118
in company with nonzero sin2212057914 The best fit sin22120579
13=
0100with the restriction sin2212057914
= 0 is still within 1120590 regionof four-neutrino analysis Also in case (B) which is specifiedby a rather large Δ119898
2
31compared to the value taken by RENO
and Daya Bay or the value suggested by global analyses thebest fit sin22120579
13= 0090 of three-neutrino analysis is placed
in the region of 1120590 CL This implies no preference betweenthree-neutrino and four-neutrino schemes when the shape inFigure 3 is analyzed in this rough estimation
4 Conclusion
If a fourth type of neutrino has a mass not much largerthan the other three masses the results of reactor neutrinooscillations like RENO Daya Bay and Double Chooz canbe affected by the fourth state For detectors established foroscillations driven by Δ119898
2
31= 000232 eV2 clues about
the fourth neutrino can be perceived only if the order ofΔ1198982
41is not much larger than that of Δ119898
2
31 Therefore this
work examined the possibility of a kind of sterile neutrinoin the range of mass-squared differences below 01 eV2
considering the two announced results of RENO and DayaBay Anomalies of reactor antineutrino oscillations have beenconsidered for the range 01 eV2 lt Δ119898
2
14lt 1 eV2 Thus it is
worth analyzing the absolute flux at the near detector and theratio of the far-to-near flux on a common basis [32]
RENO announced an update of rate-only analysis andthe spectral shape of neutrino events [neutrino telescope]including an observed-to-expected ratio 119877 = 0929 and anoscillation amplitude of sin22120579
13= 0100 We compared the
spectral shape with theoretical curves of the superpositionsof Δ119898
2
41oscillations and Δ119898
2
31oscillations In summary
sin2212057914
gt 02 is excluded at 3120590 CL When Δ1198982
31=
000232 eV2 is fixed the best-fit in four-neutrino parametersis (Δ119898
2
41 sin22120579
14) = (00078 eV2 0054) When we search
the fit of Δ1198982
31along with other parameters of four-neutrino
analysis the best value is obtained Δ1198982
31= 000283 eV2
with sin2212057913
= 0090 from the shape in three-neutrinoanalysis When the parameters are extended to four-neutrinoscheme the best fit is (Δ119898
2
41 sin22120579
14) = (0039 eV2 0049)
As shown in Figure 6 the three-neutrino analysis of RENO(sin22120579
13 sin22120579
14) = (0100 00) is also included within
1120590 CL in four-neutrino analysis Thus it is not yet knownwhether the superposition withΔ119898
2
41oscillations is preferred
to the single Δ1198982
31oscillations at RENO detectors Figure 7
shows that the rate-only analysis and the spectral shapeanalysis are in good agreement within their 1120590 CL range
Acknowledgments
This research was supported by a Chung-Ang Univer-sity Research Scholarship Grant in 2013 and the NationalResearch Foundation of Korea (NRF) Grants funded by the
Advances in High Energy Physics 7
000 005 010 015 020000
005
010
015
020RENO (A) Δm2
31 = 283 times 10minus3 eV2
Δm241 = 0039 eV2
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
000 005 010 015 020000
005
010
015
020
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
RENO (B)
sin2(212057914)
sin2(212057914)
sin2(212057913) sin
2(212057913)
(0092 0049)(0118 0054)
Figure 7 Comparison of rate-only analysis and spectral shape analysis in both (A) and (B) the regions allowed by rate-only analysis areoverlapped in 1120590 range of shape analysis while they do not include the 120594
2-minimum best fits
Korea Government of theMinistry of Education Science andTechnology (MEST) (2011-0014686)
References
[1] Z Maki M Nakagawa and S Sakata ldquoRemarks on the unifiedmodel of elementary particlesrdquo Progress of Theoretical Physicsvol 28 no 5 pp 870ndash880 1962
[2] F P An J Z Bai A B Balantekin et al ldquoObservationof electron-antineutrino disappearance at daya bayrdquo PhysicalReview Letters vol 108 no 17 Article ID 171803 7 pages 2012
[3] J K Ahn S Chebotaryov J H Choi et al ldquoObservationof reactor electron antineutrinos disappearance in the RENOexperimentrdquo Physical Review Letters vol 108 no 19 Article ID191802 6 pages 2012
[4] K Abe N Abgrall Y Ajima et al ldquoIndication of electronneutrino appearance from an accelerator-produced off-axismuon neutrino beamrdquo Physical Review Letters vol 107 no 4Article ID 041801 8 pages 2011
[5] P Adamson D J Auty D S Ayres et al ldquoImproved search formuon-neutrino to electron-neutrino oscillations in MINOSrdquoPhysical Review Letters vol 107 no 18 Article ID 181802 6pages 2011
[6] Y Abe C Aberle T Akiri et al ldquoIndication of reactor 120592119890
disappearance in the double chooz experimentrdquoPhysical ReviewLetters vol 108 no 13 Article ID 131801 7 pages 2012
[7] Y Abe C Aberle J C Anjos et al ldquoReactor electron antineu-trino disappearance in the Double Chooz experimentrdquo PhysicalReview D vol 86 no 5 Article ID 052008 pp 1ndash21 2012
[8] J Beringer J F Arguin R M Barnett1 et al ldquoReview of particlephysicsrdquo Physical Review D vol 86 no 1 Article ID 0100012012
[9] G L Fogli E Lisi A Marrone D Montanino A Palazzo andAM Rotunno ldquoSolar neutrino oscillation parameters after first
KamLAND resultsrdquo Physical Review D vol 67 no 7 Article ID073002 2003
[10] D V Forero M Tortola and J W F Valle ldquoGlobal status ofneutrino oscillation parameters after Neutrino-2012rdquo PhysicalReview D vol 86 no 7 Article ID 073012 8 pages 2012
[11] M C Gonzalez-Garcia M Maltoni J Salvado and T SchwetzldquoGlobal fit to three neutrino mixing critical look at presentprecisionrdquo Journal of High Energy Physics vol 2012 article 1232012
[12] A Aguilar-Arevalo L B Auerbach R L Burman et alldquoEvidence for neutrino oscillations from the observation ofanti-neutrino(electron) appearance in a anti-neutrino(muon)beamrdquo Physical Review D vol 64 no 11 Article ID 112007 22pages 2001
[13] A A Aguilar-Arevalo A O Bazarko and S J Brice ldquoSearch forelectron neutrino appearance at the998779119898
2sim 1 eV2 Scalerdquo Physical
Review Letters vol 98 no 23 Article ID 231801 7 pages 2007[14] A A Aguilar-Arevalo C E Anderson S J Brice et al ldquoEvent
excess in the miniBooNE search for 120592120583
rarr 120592119890oscillationsrdquo
Physical Review Letters vol 105 no 18 Article ID 181801 5pages 2010
[15] A A Aguilar-Arevalo et al ldquoImproved search for 120592120583
rarr 120592119890
Oscillations in the miniBooNE experimentrdquo Physical ReviewLetters vol 110 article 16 Article ID 181801 6 pages 2010
[16] WHampel J Handt G Heusser et al ldquoGALLEX solar neutrinoobservations results for GALLEX IVrdquo Physics Letters B vol 447no 1-2 pp 127ndash133 1999
[17] J N Abdurashitov T J Bowles C Cattadori et al ldquoThe BNO-LNGS joint measurement of the solar neutrino capture ratein71Gardquo Astroparticle Physics vol 25 no 5 pp 349ndash354 2006
[18] B Achkar R Aleksan M Avenier et al ldquoSearch for neutrinooscillations at 15 40 and 95meters from a nuclear power reactorat Bugeyrdquo Nuclear Physics B vol 434 no 3 pp 503ndash532 1995
8 Advances in High Energy Physics
[19] S K Kang Y D Kim Y Ko and K Siyeon ldquoSterile neu-trino analysis of reactor-neutrino oscillationrdquo httparxivorgabs13036173
[20] K Bora D Dutta and P Ghoshal ldquoProbing sterile neutrinoparameters with Double Chooz Daya Bay and RENOrdquo Journalof High Energy Physics vol 2012 article 25 2012
[21] YGao andDMarfatia ldquoMeter-baseline tests of sterile neutrinosat Daya Bayrdquo Physics Letters B vol 723 no 1-3 pp 164ndash167 2013
[22] C Giunti M Laveder Y F Li Q Y Liu and H W LongldquoUpdate of short-baseline electron neutrino and antineutrinodisappearancerdquo Physical Review D vol 86 no 11 Article ID113014 14 pages 2012
[23] J M Conrad C M Ignarra G Karagiorgi M H Shaevitzand J Spitz ldquoSterile neutrino fits to short-baseline neutrinooscillation measurementsrdquo Advances in High Energy Physicsvol 2013 Article ID 163897 26 pages 2013
[24] S N Gninenko ldquoSterile neutrino decay as a common origin forLSNDMiniBooNE and T2K excess eventsrdquo Physical Review Dvol 85 no 5 Article ID 051702 5 pages 2012
[25] J Kopp P A N Machado M Maltoni and T Schwetz ldquoSterileneutrino oscillations the global picturerdquo Journal of High EnergyPhysics vol 2013 article 50 2013
[26] S H Seo ldquoNew results from RENOrdquo in Proceedings of the 15thInternational Workshop on Neutrino Telescopes Venice ItalyMarch 2013
[27] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical Review D vol 83 no 7 Article ID 0730062011
[28] T A Mueller D Lhuillier M Fallot et al ldquoImproved predic-tions of reactor antineutrino spectrardquo Physical Review C vol83 no 5 Article ID 054615 2011
[29] P Vogel and J F Beacom ldquoAngular distribution of neutroninverse beta decay ]
119890+ 119890++ 119899rdquo Physical Review D vol 60 no
5 Article ID 053003 1999[30] P Huber ldquoDetermination of antineutrino spectra from nuclear
reactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2012 Erratum in Physical Review C vol 85 no 2 ArticleID 029901 2012
[31] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013
[32] RENO Collaboration ldquoAbsolute flux of reactor antineutrinosrdquoin preparation
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
2 Advances in High Energy Physics
detector 119877 = 0929 replaced the former value of 119877 = 0920and sin22120579
13= 0100 replaced the former best fit of sin22120579
13=
0113 [26] The spectral shape was also modified Againwe examine the oscillation between a sterile neutrino andactive neutrinos in order to determinewhether four-neutrinooscillations are preferred to three-neutrino oscillations Thiswork is focused on Δ119898
2
14within the range of O (0001 eV2)
to O (01 eV2) where Δ1198982
14oscillations might have appeared
in the superposition with Δ1198982
13oscillations at far detectors of
O (15 km) baselines Since the mass of the fourth neutrinois unknown it is worth verifying its existence at all availableorders of magnitude which are accessible from differentbaseline sizes For instance the near detector at RENO cansearch reactor antineutrino anomalies withΔ119898
2
14sim O (1 eV2)
[27 28]This paper is organized as follows In Section 2 the
survival probability of electron antineutrinos is presented infour-neutrino oscillation schemeWe exhibit the dependenceof the oscillating aspects on the order of Δ119898
2
41 when reactor
neutrinos in the energy range of 18 to 8MeV are detectedafter travel along a km order baseline In Section 3 thecurves of the four-neutrino oscillations are compared withthe spectral shape of data through October 2012 to searchfor any clues of sterile neutrinos and to see the changes insin22120579
13due to the coexistence with sterile neutrinos Broad
ranges of Δ1198982
41and sin22120579
14remain In the conclusion the
exclusion bounds of sin2212057914
and the best fit of sin2212057913
aresummarized and the consistency between rate-only analysisand shape analysis is discussed
2 Four-Neutrino Analysis ofEvent Rates in Multidetectors
The four-neutrino extension of unitary transformations frommass basis to flavor basis is given in terms of six angles andthree Dirac phases
F = 11987734
(12057934) 11987724
(12057924 1205752) 11987714
(12057914)
sdot 11987723
(12057923) 11987713
(12057913 1205751) 11987712
(12057912 1205753)
(1)
where 119877119894119895(120579119894119895) denotes the rotation of the 119894119895 block by an
angle of 120579119894119895 When a 3 + 1 model is assumed as the minimal
extension the 4-by-4 F is given by
F = (
11988814
0 0 11990414
minus1199041411990424
11988824
0 1198881411990424
minus119888241199041411990434
minus1199042411990434
11988834
119888141198882411990434
minus119888241198883411990414
minus1199042411988834
minus11990434
119888141198882411988834
)
times (
1198801198901
1198801198902
1198801198903
0
1198801205831
1198801205832
1198801205833
0
1198801205911
1198801205912
1198801205913
0
0 0 0 1
)
= (
119888141198801198901
119888141198801198902
119888141198801198903
11990414
sdot sdot sdot sdot sdot sdot sdot sdot sdot 1198881411990424
sdot sdot sdot sdot sdot sdot sdot sdot sdot 119888141198882411990434
sdot sdot sdot sdot sdot sdot sdot sdot sdot 119888141198882411988834
)
(2)
where the PMNS type of a 3-by-3 matrix 119880PMNS with threerows (119880
11989011198801198902
1198801198903) (1198801205831
1198801205832
1198801205833) and (119880
12059111198801205912
1198801205913)
is imbedded The CP phases 1205752and 120575
3introduced in (1) are
omitted for simplicity since they do not affect the electronantineutrino survival probability at the reactor neutrinooscillation
The survival probability of ]119890produced from reactors is
119875Th (]119890997888rarr ]119890) =
10038161003816100381610038161003816100381610038161003816100381610038161003816
4
sum
119895=1
10038161003816100381610038161003816119890119894
10038161003816100381610038161003816
2
exp 119894Δ1198982
1198951119871
2119864]
10038161003816100381610038161003816100381610038161003816100381610038161003816
2
= 1 minus sum
119894lt119895
410038161003816100381610038161003816119890119894
10038161003816100381610038161003816
210038161003816100381610038161003816119890119895
10038161003816100381610038161003816
2
sin2(Δ1198982
119894119895119871
4119864]
)
(3)
where Δ1198982
119894119895denotes the mass-squared difference (119898
2
119894minus
1198982
119895) It can be expressed in terms of combined Δ119898
2
119894119895-driven
oscillations as
119875Th (]119890997888rarr ]119890) = 1 minus 119888
4
141198884
13sin22120579
12sin2 (127Δ119898
2
21
119871
119864)
minus 1198884
14sin22120579
13sin2 (127Δ119898
2
31
119871
119864)
minus 1198882
13sin22120579
14sin2 (127Δ119898
2
41
119871
119864)
minus 1199042
13sin22120579
14sin2 (127Δ119898
2
43
119871
119864)
(4)
where Δ1198982
32asymp Δ119898
2
31and Δ119898
2
42asymp Δ119898
2
41 The size
of 1198984relative to 119898
3is not yet constrained The above
119875Th is understood only within a theoretical frameworksince the energy of the detected neutrinos is not uniquebut is continuously distributed over a certain range Sothe observed quantity is established with a distribution ofneutrino energy spectrum and an energy-dependent crosssection Analyses of neutrino oscillation average accessibleenergies of the neutrinos emerging from the reactors Themeasured probability of survival is
⟨119875⟩ =
int119875Th (119864) 120590tot (119864) 120601 (119864) 119889119864
int120590tot (119864) 120601 (119864) 119889119864
(5)
where 120590tot(119864) is the total cross-section of inverse beta decay(IBD) and 120601(119864) is the neutrino flux distribution from thereactor The total cross section of IBD is given as
120590tot (119864) = 00952(
119864119890radic1198642119890minus 1198982119890
1MeV2) times 10
minus42 cm2 (6)
where 119864119890asymp 119864] minus (119872
119899minus 119872119901) [28 29] The flux distribution
120601(119864) from the four isotopes (U235Pu239U238 and Pu241) atthe reactors is expressed by the following exponential of a fifthorder polynomials of 119864]
120601 (119864]) = exp(
5
sum
119894=0
119891119894119864119894
]) (7)
Advances in High Energy Physics 3
L = 1m 10 100 1000 10000
ND
ND
FDEH1
EH1
ND EH1
EH3
FD EH3
FD EH3
Δm241 = 1 eV
2
Δm241 = 01 eV
2
Δm241 = 001 eV
2
Figure 1 The dependency of ⟨119875⟩ in (5) on Δ1198982
41is presented when
Δ1198982
31= 232 times 10
minus3 eV2 as taken in RENO and Daya Bay Typicalshapes of ⟨119875⟩ versus distance are drawn for comparison with themeasured ratios in the two experiments The amplitudes of Δ119898
2
31
oscillation and Δ1198982
41oscillation are given by sin22120579
13= 010 and
sin2212057914
= 010 respectively as an example
where 1198910
= +457491 times 10 1198911
= minus173774 times 10minus1 1198912
=
minus910302times10minus2 1198913= minus167220times10
minus5 1198914= +172704times10
minus5and 119891
5= minus101048 times 10
minus7 are obtained by fitting the totalflux of the four isotopes with the fission ratio expected at themiddle of the reactor burn up period [30]
The curves in Figure 1 show ⟨119875⟩ as 119871 increases in alogarithmic manner where the three patterns of probabil-ities are shown according to the order of Δ119898
2
41 The first
bump in each curve corresponds to the oscillation due toΔ1198982
41 while the second bump that appears near 1500m
corresponds to the oscillation due to Δ1198982
31 RENO and Daya
Bay were designed to observe the Δ1198982
31-driven oscillations
at far detector (FD) according to three-neutrino analysiswhile additional detector(s) at a closer baseline performs thedetection of neutrinos in the same conditionThe comparisonof the number of neutrino events at FD to the number ofevents at the near detector (ND) is an effective strategy todetermine the disappearance of antineutrinos from reactorsThat is the sin22120579
13is evaluated by the slope of the curve
between ND and FD while their absolute values of eventnumbers do not affect the estimation of the angle 120579
13 Both
experiments used the normalization to adjust the data tosatisfy the boundary condition which is that there is nooscillation effect before the ND From Figure 1 it can beshown that the magnitude of Δ119898
2
41can affect not only the
normalization factor but also the ratio between the FD andND
The six baselines of the near detector (ND) andthe far detector (FD) of RENO are 119871near (meters) =
660 445 302 340 520 746 and 119871 far (meters) = 15601460 1400 1380 1410 1480 while their flux-weighted aver-ages 119871near and 119871far are 4073m and 1443m respectivelyThe baselines of Daya Bay named EH1 EH2 and EH3have lengths of EH1 = 494m EH2 = 554m and EH3 =
1628m respectively so that conventionally EH1 and EH2
are regarded as near detectors while EH3 is regarded as a fardetector
After the first release of results Daya Bay and RENOupdated the far-to-near ratio of neutrino events with addi-tional data Daya Bay reported a ratio of 119877 = 0944 plusmn
0007 (stat) plusmn 0003 (syst) with 119877(EH1) = 0987 plusmn
0004 (stat) plusmn 0003 (syst) [31] RENO also reported anupdate with additional data from March to October in 2012where 119877(FD) = 0929 plusmn 0006 (stat) plusmn 0009 (syst) [26] Theirmeasurements are marked in Figure 1 In three-neutrinoanalysis the far-to-near ratios give the Δ119898
2
31-oscillation
amplitude sin2212057913
= 0089 plusmn 0010 (stat) plusmn 0005 (syst) andsin22120579
13= 0100 plusmn 0010 (stat) plusmn 0015 (syst) in Daya Bay
and RENO respectively On the other hand the far-to-nearratio and the measured-to-expected ratio are understood asa combination of Δ119898
2
31oscillations and Δ119898
2
41oscillations
as shown in Figure 1 For a given value of Δ1198982
41 001 eV2
or 001 eV2 the combination of sin2212057914
and sin2212057913
isdescribed in Figure 2 In the case of RENO the ⟨119875(Δ119898
2
41=
001 eV2)⟩ and ⟨119875(Δ1198982
41= 01 eV2)⟩ curves which pass the
error bars at ND and FD are drawn as blue- (gray-) shadedareas The area where the two shaded areas ND and FDoverlap is the allowed region in sin22120579
13minussin22120579
14space using
rate-only analysisThe corresponding analysis forDaya Bay isshown together in Figure 2 The value of sin22120579
13is in good
agreement with the results released by the two experiments
3 Four-Neutrino Analysis of UpdatedSpectral Shape in RENO
One of RENOrsquos results was the ratio of the observed to theexpected number of antineutrinos in the far detector 119877 =
0929 plusmn 0011 (see [26]) where the observed is simply thenumber of events at FD On the other hand the expectednumber of events at FD can be obtained using severaladjustments of the number of events at ND
119877 equiv[Observed at FD]
[Expected at FD](8)
equiv[No of events at FD]
[No of events at ND]lowast (9)
where the number of events at each detector is normalizedThe normalization of the neutrino fluxes at ND and FDrequires an adjustment between the two individual detectorswhich includes corrections due to DAQ live time detectionefficiency background rate and the distance to each detectorThe numbers of events at FD and ND in (9) have alreadybeen normalized by these correction factors and so we have119877far = 0929 plusmn 0017 and 119877near = 0990 plusmn 0025 as shown inFigure 2The normalization guarantees 119877 = 1 at the center ofthe reactors RENO removes the oscillation effect atNDwhenevaluating the expected number of events at FD by dividingthe denominator of (9) by 0990 which is taken from 119877nearNow
119877 =[No of events at FD]
[No of events at ND] 0990 (10)
4 Advances in High Energy Physics
020
015
010
005
000
020015010005000
sin2(212057914)
sin2(212057913
)
Prob near = 0990 plusmn 0025
Prob far = 0929 plusmn 0011
RENO020
015
010
005
000
020015010005000
sin2(212057914)
sin2(212057913
) Prob near = 0987 plusmn 0005
Prob far = 0932 plusmn 0009
Daya Bay
Figure 2 Four-neutrino analysis for the observed to expected ratios at both ND and FD of RENO The shaded areas indicate the availablecombination of sin22120579
13and sin22120579
14which is compatible with the ranges of 119877Near and 119877Far released by RENO and Daya Bay Blue (gray) areas
are obtained with Δ1198982
41= 001(01) eV2 The 4] analysis of the far-to-near ratio at Daya Bay is also given for comparison
12
11
10
09
082 4 6 8
Far
near
Neutrino energy (MeV)
RENO (A)
Δm231 = 283 times 10
minus3 eV2
Δm241 = 0039 eV2
12
11
10
09
082 4 6 8
Far
near
Neutrino energy (MeV)
RENO (B)
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
Figure 3 The data and error bars are the reproduction of updated RENO for an extended period until October 2012 The red fits are drawnwith sin22120579
14= 0 for Δ119898
2
31= 283 times 10
minus3 eV2 and for Δ1198982
31= 232 times 10
minus3 eV2 obtained from the analysis in Figure 4 For each case the bluefits are overlaid which are the superposition with Δ119898
2
41= 0039 eV2 oscillation of amplitude sin22120579
14= 0050 and the superposition with
Δ1198982
41= 00078 eV2 oscillation of amplitude sin22120579
14= 0054 respectively obtained from the analysis in Figure 5
In rate-only analysis the ratio of the observed to the expectednumber of events at FD in (8) is just the survival at FD sincethe denominator in (10) is eliminatedThus 119877 coincides with119877far in Figure 2
In spectral shape analysis however the denominatorcannot be neglected since the oscillation effect at ND differsdepending on the neutrino energyThedata points in Figure 3are obtained by the definition of the ratio 119877 given in (8)and (9) per 025MeV bin as the energy varies from 18MeVto 128MeV The data dots and error bars were updatedby including additional data from March to October in2012 officially announced at Neutrino Telescope 2013 [26]
The ratio in (10) is compared with theoretical curves overlaidon the data points The theoretical curves are described by
⟨119875 (FD)⟩
⟨119875 (ND)⟩ (0990)minus1
(11)
where ⟨119875(L)⟩ is given in (4) In Figure 4 the best fitof (Δ119898
2
31 sin22120579
13) is presented when 120579
14= 0 The
point A (000283 eV2 009) indicates the 1205942 minimum
where sin2212057913
and Δ1198982
31are parameters while the point
B (000232 eV2 010) is the minimumwhere Δ1198982
31is 000232
Advances in High Energy Physics 5
00010 001000005000020 0003000015 00070
100
050
020
010
005
002
001
sin22120579
13
Δm231
A (000283 00900)B
(000232 0100)
A 1205942min dof = 096
B 1205942min dof = 132
Figure 4Three-neutrino analysis of the spectral shape updated until October 2012The best fit in (Δ1198982
31 sin22120579
13) is (000283 009) denoted
by A When Δ1198982
31= 000232 eV2 is fixed as taken by RENO the best fit of sin2120579
13is 0100 The 1120590 2120590 and 3120590 exclusion curves are drawn by
solid lines
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(0039 0050)
Δm231 = 283 times 10
minus3 eV2
sin2212057913 = 00900
RENO (A)
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(00078 0033)(0039 0049)
Δm231 = 232 times 10
minus3 eV2
sin2212057913 = 0100
RENO (B)
Figure 5The 1120590 2120590 and 3120590 exclusion curves are drawn by solid lines Apparently a broad range of sin2212057914apparently remains not excluded
Only Δ1198982
41gt Δ119898
2
31is considered and sin22120579
14gt 02 is excluded at 3120590 CL For (A) specified by Δ119898
2
31= 283 times 10
minus3 eV2 the minimum1205942
mindof = 048 is at (Δ1198982
41 sin22120579
14) = (0039 eV2 0050) while for (B) specified by Δ119898
2
31= 232 times 10
minus3 eV2 two minima 1205942
mindof = 106
and 085 are located at (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) and (0039 eV2 0049) respectively
which RENO and Daya Bay used for the fixed value Here-after two cases depending on Δ119898
2
31are discussed one is
for Δ1198982
31= 000283 eV2 marked by 119860 and the other is for
Δ1198982
31= 000232 eV2 marked by B According to the analysis
performed with 12057914
= 0 the red curves for the two valuesof Δ231are overlaid on the spectral data in Figure 3 Figure 5
shows interpretation of the spectral shape in terms of four-neutrino oscillation For given values of Δ
2
31and sin22120579
13
the 1 2 3120590 CL exclusion curves are obtained by convolutionwith the energy resolution of RENO detectors (59radic119864 +
11) Using the best fits (Δ1198982
41 sin22120579
14) = (0039 eV2 005)
for (A) and (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) for (B)
6 Advances in High Energy Physics
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
Δm241 = 0039 eV2
Δm231 = 283 times 10
minus3 eV2
(0092 0049)
00900
RENO (A)
Δm241 = 00078 eV2
Δm231 = 232 times 10
minus3 eV2
(0118 0054)
0100
RENO (B)
Figure 6 The 1120590 2120590 and 3120590 fit of combination of the sin2212057913and sin22120579
14for chosen values of (Δ119898
2
31and Δ119898
2
41) For (A) the 120594
2
mindof of(0092 0049) is 051 For (B) the 120594
2
mindof of (0118 0049) is 096 In both cases the best fit of sin2212057914
= 0 is included in 1120590 region
the blue curves are also added on the spectral data in Figure 3To see a distinct different aspect due to the magnitude ofΔ1198982
41 we choose 119898
2
41= 00078 eV2 for the best fit of (B)
avoiding 1198982
41= 0039 eV2 which is the same as the 119898
2
41for
(A)The solid curves in Figure 6 explain 1120590 2120590 and 3120590 CL of
Δ1205942 in parameters (sin22120579
13 sin22120579
14) of which the best-fits
are found at (0092 0049) for case (A) ofΔ1198982
31= 000283 eV2
and at (0118 0054) for case (B) of Δ1198982
31= 000232 eV2 In
case (B) where the value of Δ1198982
31is the same as the one that
RENO andDaya Bay took for it the best fit of sin2 212057913is 0118
in company with nonzero sin2212057914 The best fit sin22120579
13=
0100with the restriction sin2212057914
= 0 is still within 1120590 regionof four-neutrino analysis Also in case (B) which is specifiedby a rather large Δ119898
2
31compared to the value taken by RENO
and Daya Bay or the value suggested by global analyses thebest fit sin22120579
13= 0090 of three-neutrino analysis is placed
in the region of 1120590 CL This implies no preference betweenthree-neutrino and four-neutrino schemes when the shape inFigure 3 is analyzed in this rough estimation
4 Conclusion
If a fourth type of neutrino has a mass not much largerthan the other three masses the results of reactor neutrinooscillations like RENO Daya Bay and Double Chooz canbe affected by the fourth state For detectors established foroscillations driven by Δ119898
2
31= 000232 eV2 clues about
the fourth neutrino can be perceived only if the order ofΔ1198982
41is not much larger than that of Δ119898
2
31 Therefore this
work examined the possibility of a kind of sterile neutrinoin the range of mass-squared differences below 01 eV2
considering the two announced results of RENO and DayaBay Anomalies of reactor antineutrino oscillations have beenconsidered for the range 01 eV2 lt Δ119898
2
14lt 1 eV2 Thus it is
worth analyzing the absolute flux at the near detector and theratio of the far-to-near flux on a common basis [32]
RENO announced an update of rate-only analysis andthe spectral shape of neutrino events [neutrino telescope]including an observed-to-expected ratio 119877 = 0929 and anoscillation amplitude of sin22120579
13= 0100 We compared the
spectral shape with theoretical curves of the superpositionsof Δ119898
2
41oscillations and Δ119898
2
31oscillations In summary
sin2212057914
gt 02 is excluded at 3120590 CL When Δ1198982
31=
000232 eV2 is fixed the best-fit in four-neutrino parametersis (Δ119898
2
41 sin22120579
14) = (00078 eV2 0054) When we search
the fit of Δ1198982
31along with other parameters of four-neutrino
analysis the best value is obtained Δ1198982
31= 000283 eV2
with sin2212057913
= 0090 from the shape in three-neutrinoanalysis When the parameters are extended to four-neutrinoscheme the best fit is (Δ119898
2
41 sin22120579
14) = (0039 eV2 0049)
As shown in Figure 6 the three-neutrino analysis of RENO(sin22120579
13 sin22120579
14) = (0100 00) is also included within
1120590 CL in four-neutrino analysis Thus it is not yet knownwhether the superposition withΔ119898
2
41oscillations is preferred
to the single Δ1198982
31oscillations at RENO detectors Figure 7
shows that the rate-only analysis and the spectral shapeanalysis are in good agreement within their 1120590 CL range
Acknowledgments
This research was supported by a Chung-Ang Univer-sity Research Scholarship Grant in 2013 and the NationalResearch Foundation of Korea (NRF) Grants funded by the
Advances in High Energy Physics 7
000 005 010 015 020000
005
010
015
020RENO (A) Δm2
31 = 283 times 10minus3 eV2
Δm241 = 0039 eV2
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
000 005 010 015 020000
005
010
015
020
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
RENO (B)
sin2(212057914)
sin2(212057914)
sin2(212057913) sin
2(212057913)
(0092 0049)(0118 0054)
Figure 7 Comparison of rate-only analysis and spectral shape analysis in both (A) and (B) the regions allowed by rate-only analysis areoverlapped in 1120590 range of shape analysis while they do not include the 120594
2-minimum best fits
Korea Government of theMinistry of Education Science andTechnology (MEST) (2011-0014686)
References
[1] Z Maki M Nakagawa and S Sakata ldquoRemarks on the unifiedmodel of elementary particlesrdquo Progress of Theoretical Physicsvol 28 no 5 pp 870ndash880 1962
[2] F P An J Z Bai A B Balantekin et al ldquoObservationof electron-antineutrino disappearance at daya bayrdquo PhysicalReview Letters vol 108 no 17 Article ID 171803 7 pages 2012
[3] J K Ahn S Chebotaryov J H Choi et al ldquoObservationof reactor electron antineutrinos disappearance in the RENOexperimentrdquo Physical Review Letters vol 108 no 19 Article ID191802 6 pages 2012
[4] K Abe N Abgrall Y Ajima et al ldquoIndication of electronneutrino appearance from an accelerator-produced off-axismuon neutrino beamrdquo Physical Review Letters vol 107 no 4Article ID 041801 8 pages 2011
[5] P Adamson D J Auty D S Ayres et al ldquoImproved search formuon-neutrino to electron-neutrino oscillations in MINOSrdquoPhysical Review Letters vol 107 no 18 Article ID 181802 6pages 2011
[6] Y Abe C Aberle T Akiri et al ldquoIndication of reactor 120592119890
disappearance in the double chooz experimentrdquoPhysical ReviewLetters vol 108 no 13 Article ID 131801 7 pages 2012
[7] Y Abe C Aberle J C Anjos et al ldquoReactor electron antineu-trino disappearance in the Double Chooz experimentrdquo PhysicalReview D vol 86 no 5 Article ID 052008 pp 1ndash21 2012
[8] J Beringer J F Arguin R M Barnett1 et al ldquoReview of particlephysicsrdquo Physical Review D vol 86 no 1 Article ID 0100012012
[9] G L Fogli E Lisi A Marrone D Montanino A Palazzo andAM Rotunno ldquoSolar neutrino oscillation parameters after first
KamLAND resultsrdquo Physical Review D vol 67 no 7 Article ID073002 2003
[10] D V Forero M Tortola and J W F Valle ldquoGlobal status ofneutrino oscillation parameters after Neutrino-2012rdquo PhysicalReview D vol 86 no 7 Article ID 073012 8 pages 2012
[11] M C Gonzalez-Garcia M Maltoni J Salvado and T SchwetzldquoGlobal fit to three neutrino mixing critical look at presentprecisionrdquo Journal of High Energy Physics vol 2012 article 1232012
[12] A Aguilar-Arevalo L B Auerbach R L Burman et alldquoEvidence for neutrino oscillations from the observation ofanti-neutrino(electron) appearance in a anti-neutrino(muon)beamrdquo Physical Review D vol 64 no 11 Article ID 112007 22pages 2001
[13] A A Aguilar-Arevalo A O Bazarko and S J Brice ldquoSearch forelectron neutrino appearance at the998779119898
2sim 1 eV2 Scalerdquo Physical
Review Letters vol 98 no 23 Article ID 231801 7 pages 2007[14] A A Aguilar-Arevalo C E Anderson S J Brice et al ldquoEvent
excess in the miniBooNE search for 120592120583
rarr 120592119890oscillationsrdquo
Physical Review Letters vol 105 no 18 Article ID 181801 5pages 2010
[15] A A Aguilar-Arevalo et al ldquoImproved search for 120592120583
rarr 120592119890
Oscillations in the miniBooNE experimentrdquo Physical ReviewLetters vol 110 article 16 Article ID 181801 6 pages 2010
[16] WHampel J Handt G Heusser et al ldquoGALLEX solar neutrinoobservations results for GALLEX IVrdquo Physics Letters B vol 447no 1-2 pp 127ndash133 1999
[17] J N Abdurashitov T J Bowles C Cattadori et al ldquoThe BNO-LNGS joint measurement of the solar neutrino capture ratein71Gardquo Astroparticle Physics vol 25 no 5 pp 349ndash354 2006
[18] B Achkar R Aleksan M Avenier et al ldquoSearch for neutrinooscillations at 15 40 and 95meters from a nuclear power reactorat Bugeyrdquo Nuclear Physics B vol 434 no 3 pp 503ndash532 1995
8 Advances in High Energy Physics
[19] S K Kang Y D Kim Y Ko and K Siyeon ldquoSterile neu-trino analysis of reactor-neutrino oscillationrdquo httparxivorgabs13036173
[20] K Bora D Dutta and P Ghoshal ldquoProbing sterile neutrinoparameters with Double Chooz Daya Bay and RENOrdquo Journalof High Energy Physics vol 2012 article 25 2012
[21] YGao andDMarfatia ldquoMeter-baseline tests of sterile neutrinosat Daya Bayrdquo Physics Letters B vol 723 no 1-3 pp 164ndash167 2013
[22] C Giunti M Laveder Y F Li Q Y Liu and H W LongldquoUpdate of short-baseline electron neutrino and antineutrinodisappearancerdquo Physical Review D vol 86 no 11 Article ID113014 14 pages 2012
[23] J M Conrad C M Ignarra G Karagiorgi M H Shaevitzand J Spitz ldquoSterile neutrino fits to short-baseline neutrinooscillation measurementsrdquo Advances in High Energy Physicsvol 2013 Article ID 163897 26 pages 2013
[24] S N Gninenko ldquoSterile neutrino decay as a common origin forLSNDMiniBooNE and T2K excess eventsrdquo Physical Review Dvol 85 no 5 Article ID 051702 5 pages 2012
[25] J Kopp P A N Machado M Maltoni and T Schwetz ldquoSterileneutrino oscillations the global picturerdquo Journal of High EnergyPhysics vol 2013 article 50 2013
[26] S H Seo ldquoNew results from RENOrdquo in Proceedings of the 15thInternational Workshop on Neutrino Telescopes Venice ItalyMarch 2013
[27] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical Review D vol 83 no 7 Article ID 0730062011
[28] T A Mueller D Lhuillier M Fallot et al ldquoImproved predic-tions of reactor antineutrino spectrardquo Physical Review C vol83 no 5 Article ID 054615 2011
[29] P Vogel and J F Beacom ldquoAngular distribution of neutroninverse beta decay ]
119890+ 119890++ 119899rdquo Physical Review D vol 60 no
5 Article ID 053003 1999[30] P Huber ldquoDetermination of antineutrino spectra from nuclear
reactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2012 Erratum in Physical Review C vol 85 no 2 ArticleID 029901 2012
[31] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013
[32] RENO Collaboration ldquoAbsolute flux of reactor antineutrinosrdquoin preparation
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Advances in High Energy Physics 3
L = 1m 10 100 1000 10000
ND
ND
FDEH1
EH1
ND EH1
EH3
FD EH3
FD EH3
Δm241 = 1 eV
2
Δm241 = 01 eV
2
Δm241 = 001 eV
2
Figure 1 The dependency of ⟨119875⟩ in (5) on Δ1198982
41is presented when
Δ1198982
31= 232 times 10
minus3 eV2 as taken in RENO and Daya Bay Typicalshapes of ⟨119875⟩ versus distance are drawn for comparison with themeasured ratios in the two experiments The amplitudes of Δ119898
2
31
oscillation and Δ1198982
41oscillation are given by sin22120579
13= 010 and
sin2212057914
= 010 respectively as an example
where 1198910
= +457491 times 10 1198911
= minus173774 times 10minus1 1198912
=
minus910302times10minus2 1198913= minus167220times10
minus5 1198914= +172704times10
minus5and 119891
5= minus101048 times 10
minus7 are obtained by fitting the totalflux of the four isotopes with the fission ratio expected at themiddle of the reactor burn up period [30]
The curves in Figure 1 show ⟨119875⟩ as 119871 increases in alogarithmic manner where the three patterns of probabil-ities are shown according to the order of Δ119898
2
41 The first
bump in each curve corresponds to the oscillation due toΔ1198982
41 while the second bump that appears near 1500m
corresponds to the oscillation due to Δ1198982
31 RENO and Daya
Bay were designed to observe the Δ1198982
31-driven oscillations
at far detector (FD) according to three-neutrino analysiswhile additional detector(s) at a closer baseline performs thedetection of neutrinos in the same conditionThe comparisonof the number of neutrino events at FD to the number ofevents at the near detector (ND) is an effective strategy todetermine the disappearance of antineutrinos from reactorsThat is the sin22120579
13is evaluated by the slope of the curve
between ND and FD while their absolute values of eventnumbers do not affect the estimation of the angle 120579
13 Both
experiments used the normalization to adjust the data tosatisfy the boundary condition which is that there is nooscillation effect before the ND From Figure 1 it can beshown that the magnitude of Δ119898
2
41can affect not only the
normalization factor but also the ratio between the FD andND
The six baselines of the near detector (ND) andthe far detector (FD) of RENO are 119871near (meters) =
660 445 302 340 520 746 and 119871 far (meters) = 15601460 1400 1380 1410 1480 while their flux-weighted aver-ages 119871near and 119871far are 4073m and 1443m respectivelyThe baselines of Daya Bay named EH1 EH2 and EH3have lengths of EH1 = 494m EH2 = 554m and EH3 =
1628m respectively so that conventionally EH1 and EH2
are regarded as near detectors while EH3 is regarded as a fardetector
After the first release of results Daya Bay and RENOupdated the far-to-near ratio of neutrino events with addi-tional data Daya Bay reported a ratio of 119877 = 0944 plusmn
0007 (stat) plusmn 0003 (syst) with 119877(EH1) = 0987 plusmn
0004 (stat) plusmn 0003 (syst) [31] RENO also reported anupdate with additional data from March to October in 2012where 119877(FD) = 0929 plusmn 0006 (stat) plusmn 0009 (syst) [26] Theirmeasurements are marked in Figure 1 In three-neutrinoanalysis the far-to-near ratios give the Δ119898
2
31-oscillation
amplitude sin2212057913
= 0089 plusmn 0010 (stat) plusmn 0005 (syst) andsin22120579
13= 0100 plusmn 0010 (stat) plusmn 0015 (syst) in Daya Bay
and RENO respectively On the other hand the far-to-nearratio and the measured-to-expected ratio are understood asa combination of Δ119898
2
31oscillations and Δ119898
2
41oscillations
as shown in Figure 1 For a given value of Δ1198982
41 001 eV2
or 001 eV2 the combination of sin2212057914
and sin2212057913
isdescribed in Figure 2 In the case of RENO the ⟨119875(Δ119898
2
41=
001 eV2)⟩ and ⟨119875(Δ1198982
41= 01 eV2)⟩ curves which pass the
error bars at ND and FD are drawn as blue- (gray-) shadedareas The area where the two shaded areas ND and FDoverlap is the allowed region in sin22120579
13minussin22120579
14space using
rate-only analysisThe corresponding analysis forDaya Bay isshown together in Figure 2 The value of sin22120579
13is in good
agreement with the results released by the two experiments
3 Four-Neutrino Analysis of UpdatedSpectral Shape in RENO
One of RENOrsquos results was the ratio of the observed to theexpected number of antineutrinos in the far detector 119877 =
0929 plusmn 0011 (see [26]) where the observed is simply thenumber of events at FD On the other hand the expectednumber of events at FD can be obtained using severaladjustments of the number of events at ND
119877 equiv[Observed at FD]
[Expected at FD](8)
equiv[No of events at FD]
[No of events at ND]lowast (9)
where the number of events at each detector is normalizedThe normalization of the neutrino fluxes at ND and FDrequires an adjustment between the two individual detectorswhich includes corrections due to DAQ live time detectionefficiency background rate and the distance to each detectorThe numbers of events at FD and ND in (9) have alreadybeen normalized by these correction factors and so we have119877far = 0929 plusmn 0017 and 119877near = 0990 plusmn 0025 as shown inFigure 2The normalization guarantees 119877 = 1 at the center ofthe reactors RENO removes the oscillation effect atNDwhenevaluating the expected number of events at FD by dividingthe denominator of (9) by 0990 which is taken from 119877nearNow
119877 =[No of events at FD]
[No of events at ND] 0990 (10)
4 Advances in High Energy Physics
020
015
010
005
000
020015010005000
sin2(212057914)
sin2(212057913
)
Prob near = 0990 plusmn 0025
Prob far = 0929 plusmn 0011
RENO020
015
010
005
000
020015010005000
sin2(212057914)
sin2(212057913
) Prob near = 0987 plusmn 0005
Prob far = 0932 plusmn 0009
Daya Bay
Figure 2 Four-neutrino analysis for the observed to expected ratios at both ND and FD of RENO The shaded areas indicate the availablecombination of sin22120579
13and sin22120579
14which is compatible with the ranges of 119877Near and 119877Far released by RENO and Daya Bay Blue (gray) areas
are obtained with Δ1198982
41= 001(01) eV2 The 4] analysis of the far-to-near ratio at Daya Bay is also given for comparison
12
11
10
09
082 4 6 8
Far
near
Neutrino energy (MeV)
RENO (A)
Δm231 = 283 times 10
minus3 eV2
Δm241 = 0039 eV2
12
11
10
09
082 4 6 8
Far
near
Neutrino energy (MeV)
RENO (B)
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
Figure 3 The data and error bars are the reproduction of updated RENO for an extended period until October 2012 The red fits are drawnwith sin22120579
14= 0 for Δ119898
2
31= 283 times 10
minus3 eV2 and for Δ1198982
31= 232 times 10
minus3 eV2 obtained from the analysis in Figure 4 For each case the bluefits are overlaid which are the superposition with Δ119898
2
41= 0039 eV2 oscillation of amplitude sin22120579
14= 0050 and the superposition with
Δ1198982
41= 00078 eV2 oscillation of amplitude sin22120579
14= 0054 respectively obtained from the analysis in Figure 5
In rate-only analysis the ratio of the observed to the expectednumber of events at FD in (8) is just the survival at FD sincethe denominator in (10) is eliminatedThus 119877 coincides with119877far in Figure 2
In spectral shape analysis however the denominatorcannot be neglected since the oscillation effect at ND differsdepending on the neutrino energyThedata points in Figure 3are obtained by the definition of the ratio 119877 given in (8)and (9) per 025MeV bin as the energy varies from 18MeVto 128MeV The data dots and error bars were updatedby including additional data from March to October in2012 officially announced at Neutrino Telescope 2013 [26]
The ratio in (10) is compared with theoretical curves overlaidon the data points The theoretical curves are described by
⟨119875 (FD)⟩
⟨119875 (ND)⟩ (0990)minus1
(11)
where ⟨119875(L)⟩ is given in (4) In Figure 4 the best fitof (Δ119898
2
31 sin22120579
13) is presented when 120579
14= 0 The
point A (000283 eV2 009) indicates the 1205942 minimum
where sin2212057913
and Δ1198982
31are parameters while the point
B (000232 eV2 010) is the minimumwhere Δ1198982
31is 000232
Advances in High Energy Physics 5
00010 001000005000020 0003000015 00070
100
050
020
010
005
002
001
sin22120579
13
Δm231
A (000283 00900)B
(000232 0100)
A 1205942min dof = 096
B 1205942min dof = 132
Figure 4Three-neutrino analysis of the spectral shape updated until October 2012The best fit in (Δ1198982
31 sin22120579
13) is (000283 009) denoted
by A When Δ1198982
31= 000232 eV2 is fixed as taken by RENO the best fit of sin2120579
13is 0100 The 1120590 2120590 and 3120590 exclusion curves are drawn by
solid lines
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(0039 0050)
Δm231 = 283 times 10
minus3 eV2
sin2212057913 = 00900
RENO (A)
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(00078 0033)(0039 0049)
Δm231 = 232 times 10
minus3 eV2
sin2212057913 = 0100
RENO (B)
Figure 5The 1120590 2120590 and 3120590 exclusion curves are drawn by solid lines Apparently a broad range of sin2212057914apparently remains not excluded
Only Δ1198982
41gt Δ119898
2
31is considered and sin22120579
14gt 02 is excluded at 3120590 CL For (A) specified by Δ119898
2
31= 283 times 10
minus3 eV2 the minimum1205942
mindof = 048 is at (Δ1198982
41 sin22120579
14) = (0039 eV2 0050) while for (B) specified by Δ119898
2
31= 232 times 10
minus3 eV2 two minima 1205942
mindof = 106
and 085 are located at (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) and (0039 eV2 0049) respectively
which RENO and Daya Bay used for the fixed value Here-after two cases depending on Δ119898
2
31are discussed one is
for Δ1198982
31= 000283 eV2 marked by 119860 and the other is for
Δ1198982
31= 000232 eV2 marked by B According to the analysis
performed with 12057914
= 0 the red curves for the two valuesof Δ231are overlaid on the spectral data in Figure 3 Figure 5
shows interpretation of the spectral shape in terms of four-neutrino oscillation For given values of Δ
2
31and sin22120579
13
the 1 2 3120590 CL exclusion curves are obtained by convolutionwith the energy resolution of RENO detectors (59radic119864 +
11) Using the best fits (Δ1198982
41 sin22120579
14) = (0039 eV2 005)
for (A) and (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) for (B)
6 Advances in High Energy Physics
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
Δm241 = 0039 eV2
Δm231 = 283 times 10
minus3 eV2
(0092 0049)
00900
RENO (A)
Δm241 = 00078 eV2
Δm231 = 232 times 10
minus3 eV2
(0118 0054)
0100
RENO (B)
Figure 6 The 1120590 2120590 and 3120590 fit of combination of the sin2212057913and sin22120579
14for chosen values of (Δ119898
2
31and Δ119898
2
41) For (A) the 120594
2
mindof of(0092 0049) is 051 For (B) the 120594
2
mindof of (0118 0049) is 096 In both cases the best fit of sin2212057914
= 0 is included in 1120590 region
the blue curves are also added on the spectral data in Figure 3To see a distinct different aspect due to the magnitude ofΔ1198982
41 we choose 119898
2
41= 00078 eV2 for the best fit of (B)
avoiding 1198982
41= 0039 eV2 which is the same as the 119898
2
41for
(A)The solid curves in Figure 6 explain 1120590 2120590 and 3120590 CL of
Δ1205942 in parameters (sin22120579
13 sin22120579
14) of which the best-fits
are found at (0092 0049) for case (A) ofΔ1198982
31= 000283 eV2
and at (0118 0054) for case (B) of Δ1198982
31= 000232 eV2 In
case (B) where the value of Δ1198982
31is the same as the one that
RENO andDaya Bay took for it the best fit of sin2 212057913is 0118
in company with nonzero sin2212057914 The best fit sin22120579
13=
0100with the restriction sin2212057914
= 0 is still within 1120590 regionof four-neutrino analysis Also in case (B) which is specifiedby a rather large Δ119898
2
31compared to the value taken by RENO
and Daya Bay or the value suggested by global analyses thebest fit sin22120579
13= 0090 of three-neutrino analysis is placed
in the region of 1120590 CL This implies no preference betweenthree-neutrino and four-neutrino schemes when the shape inFigure 3 is analyzed in this rough estimation
4 Conclusion
If a fourth type of neutrino has a mass not much largerthan the other three masses the results of reactor neutrinooscillations like RENO Daya Bay and Double Chooz canbe affected by the fourth state For detectors established foroscillations driven by Δ119898
2
31= 000232 eV2 clues about
the fourth neutrino can be perceived only if the order ofΔ1198982
41is not much larger than that of Δ119898
2
31 Therefore this
work examined the possibility of a kind of sterile neutrinoin the range of mass-squared differences below 01 eV2
considering the two announced results of RENO and DayaBay Anomalies of reactor antineutrino oscillations have beenconsidered for the range 01 eV2 lt Δ119898
2
14lt 1 eV2 Thus it is
worth analyzing the absolute flux at the near detector and theratio of the far-to-near flux on a common basis [32]
RENO announced an update of rate-only analysis andthe spectral shape of neutrino events [neutrino telescope]including an observed-to-expected ratio 119877 = 0929 and anoscillation amplitude of sin22120579
13= 0100 We compared the
spectral shape with theoretical curves of the superpositionsof Δ119898
2
41oscillations and Δ119898
2
31oscillations In summary
sin2212057914
gt 02 is excluded at 3120590 CL When Δ1198982
31=
000232 eV2 is fixed the best-fit in four-neutrino parametersis (Δ119898
2
41 sin22120579
14) = (00078 eV2 0054) When we search
the fit of Δ1198982
31along with other parameters of four-neutrino
analysis the best value is obtained Δ1198982
31= 000283 eV2
with sin2212057913
= 0090 from the shape in three-neutrinoanalysis When the parameters are extended to four-neutrinoscheme the best fit is (Δ119898
2
41 sin22120579
14) = (0039 eV2 0049)
As shown in Figure 6 the three-neutrino analysis of RENO(sin22120579
13 sin22120579
14) = (0100 00) is also included within
1120590 CL in four-neutrino analysis Thus it is not yet knownwhether the superposition withΔ119898
2
41oscillations is preferred
to the single Δ1198982
31oscillations at RENO detectors Figure 7
shows that the rate-only analysis and the spectral shapeanalysis are in good agreement within their 1120590 CL range
Acknowledgments
This research was supported by a Chung-Ang Univer-sity Research Scholarship Grant in 2013 and the NationalResearch Foundation of Korea (NRF) Grants funded by the
Advances in High Energy Physics 7
000 005 010 015 020000
005
010
015
020RENO (A) Δm2
31 = 283 times 10minus3 eV2
Δm241 = 0039 eV2
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
000 005 010 015 020000
005
010
015
020
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
RENO (B)
sin2(212057914)
sin2(212057914)
sin2(212057913) sin
2(212057913)
(0092 0049)(0118 0054)
Figure 7 Comparison of rate-only analysis and spectral shape analysis in both (A) and (B) the regions allowed by rate-only analysis areoverlapped in 1120590 range of shape analysis while they do not include the 120594
2-minimum best fits
Korea Government of theMinistry of Education Science andTechnology (MEST) (2011-0014686)
References
[1] Z Maki M Nakagawa and S Sakata ldquoRemarks on the unifiedmodel of elementary particlesrdquo Progress of Theoretical Physicsvol 28 no 5 pp 870ndash880 1962
[2] F P An J Z Bai A B Balantekin et al ldquoObservationof electron-antineutrino disappearance at daya bayrdquo PhysicalReview Letters vol 108 no 17 Article ID 171803 7 pages 2012
[3] J K Ahn S Chebotaryov J H Choi et al ldquoObservationof reactor electron antineutrinos disappearance in the RENOexperimentrdquo Physical Review Letters vol 108 no 19 Article ID191802 6 pages 2012
[4] K Abe N Abgrall Y Ajima et al ldquoIndication of electronneutrino appearance from an accelerator-produced off-axismuon neutrino beamrdquo Physical Review Letters vol 107 no 4Article ID 041801 8 pages 2011
[5] P Adamson D J Auty D S Ayres et al ldquoImproved search formuon-neutrino to electron-neutrino oscillations in MINOSrdquoPhysical Review Letters vol 107 no 18 Article ID 181802 6pages 2011
[6] Y Abe C Aberle T Akiri et al ldquoIndication of reactor 120592119890
disappearance in the double chooz experimentrdquoPhysical ReviewLetters vol 108 no 13 Article ID 131801 7 pages 2012
[7] Y Abe C Aberle J C Anjos et al ldquoReactor electron antineu-trino disappearance in the Double Chooz experimentrdquo PhysicalReview D vol 86 no 5 Article ID 052008 pp 1ndash21 2012
[8] J Beringer J F Arguin R M Barnett1 et al ldquoReview of particlephysicsrdquo Physical Review D vol 86 no 1 Article ID 0100012012
[9] G L Fogli E Lisi A Marrone D Montanino A Palazzo andAM Rotunno ldquoSolar neutrino oscillation parameters after first
KamLAND resultsrdquo Physical Review D vol 67 no 7 Article ID073002 2003
[10] D V Forero M Tortola and J W F Valle ldquoGlobal status ofneutrino oscillation parameters after Neutrino-2012rdquo PhysicalReview D vol 86 no 7 Article ID 073012 8 pages 2012
[11] M C Gonzalez-Garcia M Maltoni J Salvado and T SchwetzldquoGlobal fit to three neutrino mixing critical look at presentprecisionrdquo Journal of High Energy Physics vol 2012 article 1232012
[12] A Aguilar-Arevalo L B Auerbach R L Burman et alldquoEvidence for neutrino oscillations from the observation ofanti-neutrino(electron) appearance in a anti-neutrino(muon)beamrdquo Physical Review D vol 64 no 11 Article ID 112007 22pages 2001
[13] A A Aguilar-Arevalo A O Bazarko and S J Brice ldquoSearch forelectron neutrino appearance at the998779119898
2sim 1 eV2 Scalerdquo Physical
Review Letters vol 98 no 23 Article ID 231801 7 pages 2007[14] A A Aguilar-Arevalo C E Anderson S J Brice et al ldquoEvent
excess in the miniBooNE search for 120592120583
rarr 120592119890oscillationsrdquo
Physical Review Letters vol 105 no 18 Article ID 181801 5pages 2010
[15] A A Aguilar-Arevalo et al ldquoImproved search for 120592120583
rarr 120592119890
Oscillations in the miniBooNE experimentrdquo Physical ReviewLetters vol 110 article 16 Article ID 181801 6 pages 2010
[16] WHampel J Handt G Heusser et al ldquoGALLEX solar neutrinoobservations results for GALLEX IVrdquo Physics Letters B vol 447no 1-2 pp 127ndash133 1999
[17] J N Abdurashitov T J Bowles C Cattadori et al ldquoThe BNO-LNGS joint measurement of the solar neutrino capture ratein71Gardquo Astroparticle Physics vol 25 no 5 pp 349ndash354 2006
[18] B Achkar R Aleksan M Avenier et al ldquoSearch for neutrinooscillations at 15 40 and 95meters from a nuclear power reactorat Bugeyrdquo Nuclear Physics B vol 434 no 3 pp 503ndash532 1995
8 Advances in High Energy Physics
[19] S K Kang Y D Kim Y Ko and K Siyeon ldquoSterile neu-trino analysis of reactor-neutrino oscillationrdquo httparxivorgabs13036173
[20] K Bora D Dutta and P Ghoshal ldquoProbing sterile neutrinoparameters with Double Chooz Daya Bay and RENOrdquo Journalof High Energy Physics vol 2012 article 25 2012
[21] YGao andDMarfatia ldquoMeter-baseline tests of sterile neutrinosat Daya Bayrdquo Physics Letters B vol 723 no 1-3 pp 164ndash167 2013
[22] C Giunti M Laveder Y F Li Q Y Liu and H W LongldquoUpdate of short-baseline electron neutrino and antineutrinodisappearancerdquo Physical Review D vol 86 no 11 Article ID113014 14 pages 2012
[23] J M Conrad C M Ignarra G Karagiorgi M H Shaevitzand J Spitz ldquoSterile neutrino fits to short-baseline neutrinooscillation measurementsrdquo Advances in High Energy Physicsvol 2013 Article ID 163897 26 pages 2013
[24] S N Gninenko ldquoSterile neutrino decay as a common origin forLSNDMiniBooNE and T2K excess eventsrdquo Physical Review Dvol 85 no 5 Article ID 051702 5 pages 2012
[25] J Kopp P A N Machado M Maltoni and T Schwetz ldquoSterileneutrino oscillations the global picturerdquo Journal of High EnergyPhysics vol 2013 article 50 2013
[26] S H Seo ldquoNew results from RENOrdquo in Proceedings of the 15thInternational Workshop on Neutrino Telescopes Venice ItalyMarch 2013
[27] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical Review D vol 83 no 7 Article ID 0730062011
[28] T A Mueller D Lhuillier M Fallot et al ldquoImproved predic-tions of reactor antineutrino spectrardquo Physical Review C vol83 no 5 Article ID 054615 2011
[29] P Vogel and J F Beacom ldquoAngular distribution of neutroninverse beta decay ]
119890+ 119890++ 119899rdquo Physical Review D vol 60 no
5 Article ID 053003 1999[30] P Huber ldquoDetermination of antineutrino spectra from nuclear
reactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2012 Erratum in Physical Review C vol 85 no 2 ArticleID 029901 2012
[31] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013
[32] RENO Collaboration ldquoAbsolute flux of reactor antineutrinosrdquoin preparation
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
4 Advances in High Energy Physics
020
015
010
005
000
020015010005000
sin2(212057914)
sin2(212057913
)
Prob near = 0990 plusmn 0025
Prob far = 0929 plusmn 0011
RENO020
015
010
005
000
020015010005000
sin2(212057914)
sin2(212057913
) Prob near = 0987 plusmn 0005
Prob far = 0932 plusmn 0009
Daya Bay
Figure 2 Four-neutrino analysis for the observed to expected ratios at both ND and FD of RENO The shaded areas indicate the availablecombination of sin22120579
13and sin22120579
14which is compatible with the ranges of 119877Near and 119877Far released by RENO and Daya Bay Blue (gray) areas
are obtained with Δ1198982
41= 001(01) eV2 The 4] analysis of the far-to-near ratio at Daya Bay is also given for comparison
12
11
10
09
082 4 6 8
Far
near
Neutrino energy (MeV)
RENO (A)
Δm231 = 283 times 10
minus3 eV2
Δm241 = 0039 eV2
12
11
10
09
082 4 6 8
Far
near
Neutrino energy (MeV)
RENO (B)
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
Figure 3 The data and error bars are the reproduction of updated RENO for an extended period until October 2012 The red fits are drawnwith sin22120579
14= 0 for Δ119898
2
31= 283 times 10
minus3 eV2 and for Δ1198982
31= 232 times 10
minus3 eV2 obtained from the analysis in Figure 4 For each case the bluefits are overlaid which are the superposition with Δ119898
2
41= 0039 eV2 oscillation of amplitude sin22120579
14= 0050 and the superposition with
Δ1198982
41= 00078 eV2 oscillation of amplitude sin22120579
14= 0054 respectively obtained from the analysis in Figure 5
In rate-only analysis the ratio of the observed to the expectednumber of events at FD in (8) is just the survival at FD sincethe denominator in (10) is eliminatedThus 119877 coincides with119877far in Figure 2
In spectral shape analysis however the denominatorcannot be neglected since the oscillation effect at ND differsdepending on the neutrino energyThedata points in Figure 3are obtained by the definition of the ratio 119877 given in (8)and (9) per 025MeV bin as the energy varies from 18MeVto 128MeV The data dots and error bars were updatedby including additional data from March to October in2012 officially announced at Neutrino Telescope 2013 [26]
The ratio in (10) is compared with theoretical curves overlaidon the data points The theoretical curves are described by
⟨119875 (FD)⟩
⟨119875 (ND)⟩ (0990)minus1
(11)
where ⟨119875(L)⟩ is given in (4) In Figure 4 the best fitof (Δ119898
2
31 sin22120579
13) is presented when 120579
14= 0 The
point A (000283 eV2 009) indicates the 1205942 minimum
where sin2212057913
and Δ1198982
31are parameters while the point
B (000232 eV2 010) is the minimumwhere Δ1198982
31is 000232
Advances in High Energy Physics 5
00010 001000005000020 0003000015 00070
100
050
020
010
005
002
001
sin22120579
13
Δm231
A (000283 00900)B
(000232 0100)
A 1205942min dof = 096
B 1205942min dof = 132
Figure 4Three-neutrino analysis of the spectral shape updated until October 2012The best fit in (Δ1198982
31 sin22120579
13) is (000283 009) denoted
by A When Δ1198982
31= 000232 eV2 is fixed as taken by RENO the best fit of sin2120579
13is 0100 The 1120590 2120590 and 3120590 exclusion curves are drawn by
solid lines
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(0039 0050)
Δm231 = 283 times 10
minus3 eV2
sin2212057913 = 00900
RENO (A)
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(00078 0033)(0039 0049)
Δm231 = 232 times 10
minus3 eV2
sin2212057913 = 0100
RENO (B)
Figure 5The 1120590 2120590 and 3120590 exclusion curves are drawn by solid lines Apparently a broad range of sin2212057914apparently remains not excluded
Only Δ1198982
41gt Δ119898
2
31is considered and sin22120579
14gt 02 is excluded at 3120590 CL For (A) specified by Δ119898
2
31= 283 times 10
minus3 eV2 the minimum1205942
mindof = 048 is at (Δ1198982
41 sin22120579
14) = (0039 eV2 0050) while for (B) specified by Δ119898
2
31= 232 times 10
minus3 eV2 two minima 1205942
mindof = 106
and 085 are located at (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) and (0039 eV2 0049) respectively
which RENO and Daya Bay used for the fixed value Here-after two cases depending on Δ119898
2
31are discussed one is
for Δ1198982
31= 000283 eV2 marked by 119860 and the other is for
Δ1198982
31= 000232 eV2 marked by B According to the analysis
performed with 12057914
= 0 the red curves for the two valuesof Δ231are overlaid on the spectral data in Figure 3 Figure 5
shows interpretation of the spectral shape in terms of four-neutrino oscillation For given values of Δ
2
31and sin22120579
13
the 1 2 3120590 CL exclusion curves are obtained by convolutionwith the energy resolution of RENO detectors (59radic119864 +
11) Using the best fits (Δ1198982
41 sin22120579
14) = (0039 eV2 005)
for (A) and (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) for (B)
6 Advances in High Energy Physics
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
Δm241 = 0039 eV2
Δm231 = 283 times 10
minus3 eV2
(0092 0049)
00900
RENO (A)
Δm241 = 00078 eV2
Δm231 = 232 times 10
minus3 eV2
(0118 0054)
0100
RENO (B)
Figure 6 The 1120590 2120590 and 3120590 fit of combination of the sin2212057913and sin22120579
14for chosen values of (Δ119898
2
31and Δ119898
2
41) For (A) the 120594
2
mindof of(0092 0049) is 051 For (B) the 120594
2
mindof of (0118 0049) is 096 In both cases the best fit of sin2212057914
= 0 is included in 1120590 region
the blue curves are also added on the spectral data in Figure 3To see a distinct different aspect due to the magnitude ofΔ1198982
41 we choose 119898
2
41= 00078 eV2 for the best fit of (B)
avoiding 1198982
41= 0039 eV2 which is the same as the 119898
2
41for
(A)The solid curves in Figure 6 explain 1120590 2120590 and 3120590 CL of
Δ1205942 in parameters (sin22120579
13 sin22120579
14) of which the best-fits
are found at (0092 0049) for case (A) ofΔ1198982
31= 000283 eV2
and at (0118 0054) for case (B) of Δ1198982
31= 000232 eV2 In
case (B) where the value of Δ1198982
31is the same as the one that
RENO andDaya Bay took for it the best fit of sin2 212057913is 0118
in company with nonzero sin2212057914 The best fit sin22120579
13=
0100with the restriction sin2212057914
= 0 is still within 1120590 regionof four-neutrino analysis Also in case (B) which is specifiedby a rather large Δ119898
2
31compared to the value taken by RENO
and Daya Bay or the value suggested by global analyses thebest fit sin22120579
13= 0090 of three-neutrino analysis is placed
in the region of 1120590 CL This implies no preference betweenthree-neutrino and four-neutrino schemes when the shape inFigure 3 is analyzed in this rough estimation
4 Conclusion
If a fourth type of neutrino has a mass not much largerthan the other three masses the results of reactor neutrinooscillations like RENO Daya Bay and Double Chooz canbe affected by the fourth state For detectors established foroscillations driven by Δ119898
2
31= 000232 eV2 clues about
the fourth neutrino can be perceived only if the order ofΔ1198982
41is not much larger than that of Δ119898
2
31 Therefore this
work examined the possibility of a kind of sterile neutrinoin the range of mass-squared differences below 01 eV2
considering the two announced results of RENO and DayaBay Anomalies of reactor antineutrino oscillations have beenconsidered for the range 01 eV2 lt Δ119898
2
14lt 1 eV2 Thus it is
worth analyzing the absolute flux at the near detector and theratio of the far-to-near flux on a common basis [32]
RENO announced an update of rate-only analysis andthe spectral shape of neutrino events [neutrino telescope]including an observed-to-expected ratio 119877 = 0929 and anoscillation amplitude of sin22120579
13= 0100 We compared the
spectral shape with theoretical curves of the superpositionsof Δ119898
2
41oscillations and Δ119898
2
31oscillations In summary
sin2212057914
gt 02 is excluded at 3120590 CL When Δ1198982
31=
000232 eV2 is fixed the best-fit in four-neutrino parametersis (Δ119898
2
41 sin22120579
14) = (00078 eV2 0054) When we search
the fit of Δ1198982
31along with other parameters of four-neutrino
analysis the best value is obtained Δ1198982
31= 000283 eV2
with sin2212057913
= 0090 from the shape in three-neutrinoanalysis When the parameters are extended to four-neutrinoscheme the best fit is (Δ119898
2
41 sin22120579
14) = (0039 eV2 0049)
As shown in Figure 6 the three-neutrino analysis of RENO(sin22120579
13 sin22120579
14) = (0100 00) is also included within
1120590 CL in four-neutrino analysis Thus it is not yet knownwhether the superposition withΔ119898
2
41oscillations is preferred
to the single Δ1198982
31oscillations at RENO detectors Figure 7
shows that the rate-only analysis and the spectral shapeanalysis are in good agreement within their 1120590 CL range
Acknowledgments
This research was supported by a Chung-Ang Univer-sity Research Scholarship Grant in 2013 and the NationalResearch Foundation of Korea (NRF) Grants funded by the
Advances in High Energy Physics 7
000 005 010 015 020000
005
010
015
020RENO (A) Δm2
31 = 283 times 10minus3 eV2
Δm241 = 0039 eV2
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
000 005 010 015 020000
005
010
015
020
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
RENO (B)
sin2(212057914)
sin2(212057914)
sin2(212057913) sin
2(212057913)
(0092 0049)(0118 0054)
Figure 7 Comparison of rate-only analysis and spectral shape analysis in both (A) and (B) the regions allowed by rate-only analysis areoverlapped in 1120590 range of shape analysis while they do not include the 120594
2-minimum best fits
Korea Government of theMinistry of Education Science andTechnology (MEST) (2011-0014686)
References
[1] Z Maki M Nakagawa and S Sakata ldquoRemarks on the unifiedmodel of elementary particlesrdquo Progress of Theoretical Physicsvol 28 no 5 pp 870ndash880 1962
[2] F P An J Z Bai A B Balantekin et al ldquoObservationof electron-antineutrino disappearance at daya bayrdquo PhysicalReview Letters vol 108 no 17 Article ID 171803 7 pages 2012
[3] J K Ahn S Chebotaryov J H Choi et al ldquoObservationof reactor electron antineutrinos disappearance in the RENOexperimentrdquo Physical Review Letters vol 108 no 19 Article ID191802 6 pages 2012
[4] K Abe N Abgrall Y Ajima et al ldquoIndication of electronneutrino appearance from an accelerator-produced off-axismuon neutrino beamrdquo Physical Review Letters vol 107 no 4Article ID 041801 8 pages 2011
[5] P Adamson D J Auty D S Ayres et al ldquoImproved search formuon-neutrino to electron-neutrino oscillations in MINOSrdquoPhysical Review Letters vol 107 no 18 Article ID 181802 6pages 2011
[6] Y Abe C Aberle T Akiri et al ldquoIndication of reactor 120592119890
disappearance in the double chooz experimentrdquoPhysical ReviewLetters vol 108 no 13 Article ID 131801 7 pages 2012
[7] Y Abe C Aberle J C Anjos et al ldquoReactor electron antineu-trino disappearance in the Double Chooz experimentrdquo PhysicalReview D vol 86 no 5 Article ID 052008 pp 1ndash21 2012
[8] J Beringer J F Arguin R M Barnett1 et al ldquoReview of particlephysicsrdquo Physical Review D vol 86 no 1 Article ID 0100012012
[9] G L Fogli E Lisi A Marrone D Montanino A Palazzo andAM Rotunno ldquoSolar neutrino oscillation parameters after first
KamLAND resultsrdquo Physical Review D vol 67 no 7 Article ID073002 2003
[10] D V Forero M Tortola and J W F Valle ldquoGlobal status ofneutrino oscillation parameters after Neutrino-2012rdquo PhysicalReview D vol 86 no 7 Article ID 073012 8 pages 2012
[11] M C Gonzalez-Garcia M Maltoni J Salvado and T SchwetzldquoGlobal fit to three neutrino mixing critical look at presentprecisionrdquo Journal of High Energy Physics vol 2012 article 1232012
[12] A Aguilar-Arevalo L B Auerbach R L Burman et alldquoEvidence for neutrino oscillations from the observation ofanti-neutrino(electron) appearance in a anti-neutrino(muon)beamrdquo Physical Review D vol 64 no 11 Article ID 112007 22pages 2001
[13] A A Aguilar-Arevalo A O Bazarko and S J Brice ldquoSearch forelectron neutrino appearance at the998779119898
2sim 1 eV2 Scalerdquo Physical
Review Letters vol 98 no 23 Article ID 231801 7 pages 2007[14] A A Aguilar-Arevalo C E Anderson S J Brice et al ldquoEvent
excess in the miniBooNE search for 120592120583
rarr 120592119890oscillationsrdquo
Physical Review Letters vol 105 no 18 Article ID 181801 5pages 2010
[15] A A Aguilar-Arevalo et al ldquoImproved search for 120592120583
rarr 120592119890
Oscillations in the miniBooNE experimentrdquo Physical ReviewLetters vol 110 article 16 Article ID 181801 6 pages 2010
[16] WHampel J Handt G Heusser et al ldquoGALLEX solar neutrinoobservations results for GALLEX IVrdquo Physics Letters B vol 447no 1-2 pp 127ndash133 1999
[17] J N Abdurashitov T J Bowles C Cattadori et al ldquoThe BNO-LNGS joint measurement of the solar neutrino capture ratein71Gardquo Astroparticle Physics vol 25 no 5 pp 349ndash354 2006
[18] B Achkar R Aleksan M Avenier et al ldquoSearch for neutrinooscillations at 15 40 and 95meters from a nuclear power reactorat Bugeyrdquo Nuclear Physics B vol 434 no 3 pp 503ndash532 1995
8 Advances in High Energy Physics
[19] S K Kang Y D Kim Y Ko and K Siyeon ldquoSterile neu-trino analysis of reactor-neutrino oscillationrdquo httparxivorgabs13036173
[20] K Bora D Dutta and P Ghoshal ldquoProbing sterile neutrinoparameters with Double Chooz Daya Bay and RENOrdquo Journalof High Energy Physics vol 2012 article 25 2012
[21] YGao andDMarfatia ldquoMeter-baseline tests of sterile neutrinosat Daya Bayrdquo Physics Letters B vol 723 no 1-3 pp 164ndash167 2013
[22] C Giunti M Laveder Y F Li Q Y Liu and H W LongldquoUpdate of short-baseline electron neutrino and antineutrinodisappearancerdquo Physical Review D vol 86 no 11 Article ID113014 14 pages 2012
[23] J M Conrad C M Ignarra G Karagiorgi M H Shaevitzand J Spitz ldquoSterile neutrino fits to short-baseline neutrinooscillation measurementsrdquo Advances in High Energy Physicsvol 2013 Article ID 163897 26 pages 2013
[24] S N Gninenko ldquoSterile neutrino decay as a common origin forLSNDMiniBooNE and T2K excess eventsrdquo Physical Review Dvol 85 no 5 Article ID 051702 5 pages 2012
[25] J Kopp P A N Machado M Maltoni and T Schwetz ldquoSterileneutrino oscillations the global picturerdquo Journal of High EnergyPhysics vol 2013 article 50 2013
[26] S H Seo ldquoNew results from RENOrdquo in Proceedings of the 15thInternational Workshop on Neutrino Telescopes Venice ItalyMarch 2013
[27] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical Review D vol 83 no 7 Article ID 0730062011
[28] T A Mueller D Lhuillier M Fallot et al ldquoImproved predic-tions of reactor antineutrino spectrardquo Physical Review C vol83 no 5 Article ID 054615 2011
[29] P Vogel and J F Beacom ldquoAngular distribution of neutroninverse beta decay ]
119890+ 119890++ 119899rdquo Physical Review D vol 60 no
5 Article ID 053003 1999[30] P Huber ldquoDetermination of antineutrino spectra from nuclear
reactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2012 Erratum in Physical Review C vol 85 no 2 ArticleID 029901 2012
[31] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013
[32] RENO Collaboration ldquoAbsolute flux of reactor antineutrinosrdquoin preparation
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Advances in High Energy Physics 5
00010 001000005000020 0003000015 00070
100
050
020
010
005
002
001
sin22120579
13
Δm231
A (000283 00900)B
(000232 0100)
A 1205942min dof = 096
B 1205942min dof = 132
Figure 4Three-neutrino analysis of the spectral shape updated until October 2012The best fit in (Δ1198982
31 sin22120579
13) is (000283 009) denoted
by A When Δ1198982
31= 000232 eV2 is fixed as taken by RENO the best fit of sin2120579
13is 0100 The 1120590 2120590 and 3120590 exclusion curves are drawn by
solid lines
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(0039 0050)
Δm231 = 283 times 10
minus3 eV2
sin2212057913 = 00900
RENO (A)
01000050002000100005
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
Δm241
(00078 0033)(0039 0049)
Δm231 = 232 times 10
minus3 eV2
sin2212057913 = 0100
RENO (B)
Figure 5The 1120590 2120590 and 3120590 exclusion curves are drawn by solid lines Apparently a broad range of sin2212057914apparently remains not excluded
Only Δ1198982
41gt Δ119898
2
31is considered and sin22120579
14gt 02 is excluded at 3120590 CL For (A) specified by Δ119898
2
31= 283 times 10
minus3 eV2 the minimum1205942
mindof = 048 is at (Δ1198982
41 sin22120579
14) = (0039 eV2 0050) while for (B) specified by Δ119898
2
31= 232 times 10
minus3 eV2 two minima 1205942
mindof = 106
and 085 are located at (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) and (0039 eV2 0049) respectively
which RENO and Daya Bay used for the fixed value Here-after two cases depending on Δ119898
2
31are discussed one is
for Δ1198982
31= 000283 eV2 marked by 119860 and the other is for
Δ1198982
31= 000232 eV2 marked by B According to the analysis
performed with 12057914
= 0 the red curves for the two valuesof Δ231are overlaid on the spectral data in Figure 3 Figure 5
shows interpretation of the spectral shape in terms of four-neutrino oscillation For given values of Δ
2
31and sin22120579
13
the 1 2 3120590 CL exclusion curves are obtained by convolutionwith the energy resolution of RENO detectors (59radic119864 +
11) Using the best fits (Δ1198982
41 sin22120579
14) = (0039 eV2 005)
for (A) and (Δ1198982
41 sin22120579
14) = (00078 eV2 0033) for (B)
6 Advances in High Energy Physics
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
Δm241 = 0039 eV2
Δm231 = 283 times 10
minus3 eV2
(0092 0049)
00900
RENO (A)
Δm241 = 00078 eV2
Δm231 = 232 times 10
minus3 eV2
(0118 0054)
0100
RENO (B)
Figure 6 The 1120590 2120590 and 3120590 fit of combination of the sin2212057913and sin22120579
14for chosen values of (Δ119898
2
31and Δ119898
2
41) For (A) the 120594
2
mindof of(0092 0049) is 051 For (B) the 120594
2
mindof of (0118 0049) is 096 In both cases the best fit of sin2212057914
= 0 is included in 1120590 region
the blue curves are also added on the spectral data in Figure 3To see a distinct different aspect due to the magnitude ofΔ1198982
41 we choose 119898
2
41= 00078 eV2 for the best fit of (B)
avoiding 1198982
41= 0039 eV2 which is the same as the 119898
2
41for
(A)The solid curves in Figure 6 explain 1120590 2120590 and 3120590 CL of
Δ1205942 in parameters (sin22120579
13 sin22120579
14) of which the best-fits
are found at (0092 0049) for case (A) ofΔ1198982
31= 000283 eV2
and at (0118 0054) for case (B) of Δ1198982
31= 000232 eV2 In
case (B) where the value of Δ1198982
31is the same as the one that
RENO andDaya Bay took for it the best fit of sin2 212057913is 0118
in company with nonzero sin2212057914 The best fit sin22120579
13=
0100with the restriction sin2212057914
= 0 is still within 1120590 regionof four-neutrino analysis Also in case (B) which is specifiedby a rather large Δ119898
2
31compared to the value taken by RENO
and Daya Bay or the value suggested by global analyses thebest fit sin22120579
13= 0090 of three-neutrino analysis is placed
in the region of 1120590 CL This implies no preference betweenthree-neutrino and four-neutrino schemes when the shape inFigure 3 is analyzed in this rough estimation
4 Conclusion
If a fourth type of neutrino has a mass not much largerthan the other three masses the results of reactor neutrinooscillations like RENO Daya Bay and Double Chooz canbe affected by the fourth state For detectors established foroscillations driven by Δ119898
2
31= 000232 eV2 clues about
the fourth neutrino can be perceived only if the order ofΔ1198982
41is not much larger than that of Δ119898
2
31 Therefore this
work examined the possibility of a kind of sterile neutrinoin the range of mass-squared differences below 01 eV2
considering the two announced results of RENO and DayaBay Anomalies of reactor antineutrino oscillations have beenconsidered for the range 01 eV2 lt Δ119898
2
14lt 1 eV2 Thus it is
worth analyzing the absolute flux at the near detector and theratio of the far-to-near flux on a common basis [32]
RENO announced an update of rate-only analysis andthe spectral shape of neutrino events [neutrino telescope]including an observed-to-expected ratio 119877 = 0929 and anoscillation amplitude of sin22120579
13= 0100 We compared the
spectral shape with theoretical curves of the superpositionsof Δ119898
2
41oscillations and Δ119898
2
31oscillations In summary
sin2212057914
gt 02 is excluded at 3120590 CL When Δ1198982
31=
000232 eV2 is fixed the best-fit in four-neutrino parametersis (Δ119898
2
41 sin22120579
14) = (00078 eV2 0054) When we search
the fit of Δ1198982
31along with other parameters of four-neutrino
analysis the best value is obtained Δ1198982
31= 000283 eV2
with sin2212057913
= 0090 from the shape in three-neutrinoanalysis When the parameters are extended to four-neutrinoscheme the best fit is (Δ119898
2
41 sin22120579
14) = (0039 eV2 0049)
As shown in Figure 6 the three-neutrino analysis of RENO(sin22120579
13 sin22120579
14) = (0100 00) is also included within
1120590 CL in four-neutrino analysis Thus it is not yet knownwhether the superposition withΔ119898
2
41oscillations is preferred
to the single Δ1198982
31oscillations at RENO detectors Figure 7
shows that the rate-only analysis and the spectral shapeanalysis are in good agreement within their 1120590 CL range
Acknowledgments
This research was supported by a Chung-Ang Univer-sity Research Scholarship Grant in 2013 and the NationalResearch Foundation of Korea (NRF) Grants funded by the
Advances in High Energy Physics 7
000 005 010 015 020000
005
010
015
020RENO (A) Δm2
31 = 283 times 10minus3 eV2
Δm241 = 0039 eV2
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
000 005 010 015 020000
005
010
015
020
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
RENO (B)
sin2(212057914)
sin2(212057914)
sin2(212057913) sin
2(212057913)
(0092 0049)(0118 0054)
Figure 7 Comparison of rate-only analysis and spectral shape analysis in both (A) and (B) the regions allowed by rate-only analysis areoverlapped in 1120590 range of shape analysis while they do not include the 120594
2-minimum best fits
Korea Government of theMinistry of Education Science andTechnology (MEST) (2011-0014686)
References
[1] Z Maki M Nakagawa and S Sakata ldquoRemarks on the unifiedmodel of elementary particlesrdquo Progress of Theoretical Physicsvol 28 no 5 pp 870ndash880 1962
[2] F P An J Z Bai A B Balantekin et al ldquoObservationof electron-antineutrino disappearance at daya bayrdquo PhysicalReview Letters vol 108 no 17 Article ID 171803 7 pages 2012
[3] J K Ahn S Chebotaryov J H Choi et al ldquoObservationof reactor electron antineutrinos disappearance in the RENOexperimentrdquo Physical Review Letters vol 108 no 19 Article ID191802 6 pages 2012
[4] K Abe N Abgrall Y Ajima et al ldquoIndication of electronneutrino appearance from an accelerator-produced off-axismuon neutrino beamrdquo Physical Review Letters vol 107 no 4Article ID 041801 8 pages 2011
[5] P Adamson D J Auty D S Ayres et al ldquoImproved search formuon-neutrino to electron-neutrino oscillations in MINOSrdquoPhysical Review Letters vol 107 no 18 Article ID 181802 6pages 2011
[6] Y Abe C Aberle T Akiri et al ldquoIndication of reactor 120592119890
disappearance in the double chooz experimentrdquoPhysical ReviewLetters vol 108 no 13 Article ID 131801 7 pages 2012
[7] Y Abe C Aberle J C Anjos et al ldquoReactor electron antineu-trino disappearance in the Double Chooz experimentrdquo PhysicalReview D vol 86 no 5 Article ID 052008 pp 1ndash21 2012
[8] J Beringer J F Arguin R M Barnett1 et al ldquoReview of particlephysicsrdquo Physical Review D vol 86 no 1 Article ID 0100012012
[9] G L Fogli E Lisi A Marrone D Montanino A Palazzo andAM Rotunno ldquoSolar neutrino oscillation parameters after first
KamLAND resultsrdquo Physical Review D vol 67 no 7 Article ID073002 2003
[10] D V Forero M Tortola and J W F Valle ldquoGlobal status ofneutrino oscillation parameters after Neutrino-2012rdquo PhysicalReview D vol 86 no 7 Article ID 073012 8 pages 2012
[11] M C Gonzalez-Garcia M Maltoni J Salvado and T SchwetzldquoGlobal fit to three neutrino mixing critical look at presentprecisionrdquo Journal of High Energy Physics vol 2012 article 1232012
[12] A Aguilar-Arevalo L B Auerbach R L Burman et alldquoEvidence for neutrino oscillations from the observation ofanti-neutrino(electron) appearance in a anti-neutrino(muon)beamrdquo Physical Review D vol 64 no 11 Article ID 112007 22pages 2001
[13] A A Aguilar-Arevalo A O Bazarko and S J Brice ldquoSearch forelectron neutrino appearance at the998779119898
2sim 1 eV2 Scalerdquo Physical
Review Letters vol 98 no 23 Article ID 231801 7 pages 2007[14] A A Aguilar-Arevalo C E Anderson S J Brice et al ldquoEvent
excess in the miniBooNE search for 120592120583
rarr 120592119890oscillationsrdquo
Physical Review Letters vol 105 no 18 Article ID 181801 5pages 2010
[15] A A Aguilar-Arevalo et al ldquoImproved search for 120592120583
rarr 120592119890
Oscillations in the miniBooNE experimentrdquo Physical ReviewLetters vol 110 article 16 Article ID 181801 6 pages 2010
[16] WHampel J Handt G Heusser et al ldquoGALLEX solar neutrinoobservations results for GALLEX IVrdquo Physics Letters B vol 447no 1-2 pp 127ndash133 1999
[17] J N Abdurashitov T J Bowles C Cattadori et al ldquoThe BNO-LNGS joint measurement of the solar neutrino capture ratein71Gardquo Astroparticle Physics vol 25 no 5 pp 349ndash354 2006
[18] B Achkar R Aleksan M Avenier et al ldquoSearch for neutrinooscillations at 15 40 and 95meters from a nuclear power reactorat Bugeyrdquo Nuclear Physics B vol 434 no 3 pp 503ndash532 1995
8 Advances in High Energy Physics
[19] S K Kang Y D Kim Y Ko and K Siyeon ldquoSterile neu-trino analysis of reactor-neutrino oscillationrdquo httparxivorgabs13036173
[20] K Bora D Dutta and P Ghoshal ldquoProbing sterile neutrinoparameters with Double Chooz Daya Bay and RENOrdquo Journalof High Energy Physics vol 2012 article 25 2012
[21] YGao andDMarfatia ldquoMeter-baseline tests of sterile neutrinosat Daya Bayrdquo Physics Letters B vol 723 no 1-3 pp 164ndash167 2013
[22] C Giunti M Laveder Y F Li Q Y Liu and H W LongldquoUpdate of short-baseline electron neutrino and antineutrinodisappearancerdquo Physical Review D vol 86 no 11 Article ID113014 14 pages 2012
[23] J M Conrad C M Ignarra G Karagiorgi M H Shaevitzand J Spitz ldquoSterile neutrino fits to short-baseline neutrinooscillation measurementsrdquo Advances in High Energy Physicsvol 2013 Article ID 163897 26 pages 2013
[24] S N Gninenko ldquoSterile neutrino decay as a common origin forLSNDMiniBooNE and T2K excess eventsrdquo Physical Review Dvol 85 no 5 Article ID 051702 5 pages 2012
[25] J Kopp P A N Machado M Maltoni and T Schwetz ldquoSterileneutrino oscillations the global picturerdquo Journal of High EnergyPhysics vol 2013 article 50 2013
[26] S H Seo ldquoNew results from RENOrdquo in Proceedings of the 15thInternational Workshop on Neutrino Telescopes Venice ItalyMarch 2013
[27] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical Review D vol 83 no 7 Article ID 0730062011
[28] T A Mueller D Lhuillier M Fallot et al ldquoImproved predic-tions of reactor antineutrino spectrardquo Physical Review C vol83 no 5 Article ID 054615 2011
[29] P Vogel and J F Beacom ldquoAngular distribution of neutroninverse beta decay ]
119890+ 119890++ 119899rdquo Physical Review D vol 60 no
5 Article ID 053003 1999[30] P Huber ldquoDetermination of antineutrino spectra from nuclear
reactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2012 Erratum in Physical Review C vol 85 no 2 ArticleID 029901 2012
[31] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013
[32] RENO Collaboration ldquoAbsolute flux of reactor antineutrinosrdquoin preparation
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
6 Advances in High Energy Physics
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
1000050001000050001000050001
1000
0500
0100
0050
0010
0005
0001
sin22120579
14
sin2212057913
Δm241 = 0039 eV2
Δm231 = 283 times 10
minus3 eV2
(0092 0049)
00900
RENO (A)
Δm241 = 00078 eV2
Δm231 = 232 times 10
minus3 eV2
(0118 0054)
0100
RENO (B)
Figure 6 The 1120590 2120590 and 3120590 fit of combination of the sin2212057913and sin22120579
14for chosen values of (Δ119898
2
31and Δ119898
2
41) For (A) the 120594
2
mindof of(0092 0049) is 051 For (B) the 120594
2
mindof of (0118 0049) is 096 In both cases the best fit of sin2212057914
= 0 is included in 1120590 region
the blue curves are also added on the spectral data in Figure 3To see a distinct different aspect due to the magnitude ofΔ1198982
41 we choose 119898
2
41= 00078 eV2 for the best fit of (B)
avoiding 1198982
41= 0039 eV2 which is the same as the 119898
2
41for
(A)The solid curves in Figure 6 explain 1120590 2120590 and 3120590 CL of
Δ1205942 in parameters (sin22120579
13 sin22120579
14) of which the best-fits
are found at (0092 0049) for case (A) ofΔ1198982
31= 000283 eV2
and at (0118 0054) for case (B) of Δ1198982
31= 000232 eV2 In
case (B) where the value of Δ1198982
31is the same as the one that
RENO andDaya Bay took for it the best fit of sin2 212057913is 0118
in company with nonzero sin2212057914 The best fit sin22120579
13=
0100with the restriction sin2212057914
= 0 is still within 1120590 regionof four-neutrino analysis Also in case (B) which is specifiedby a rather large Δ119898
2
31compared to the value taken by RENO
and Daya Bay or the value suggested by global analyses thebest fit sin22120579
13= 0090 of three-neutrino analysis is placed
in the region of 1120590 CL This implies no preference betweenthree-neutrino and four-neutrino schemes when the shape inFigure 3 is analyzed in this rough estimation
4 Conclusion
If a fourth type of neutrino has a mass not much largerthan the other three masses the results of reactor neutrinooscillations like RENO Daya Bay and Double Chooz canbe affected by the fourth state For detectors established foroscillations driven by Δ119898
2
31= 000232 eV2 clues about
the fourth neutrino can be perceived only if the order ofΔ1198982
41is not much larger than that of Δ119898
2
31 Therefore this
work examined the possibility of a kind of sterile neutrinoin the range of mass-squared differences below 01 eV2
considering the two announced results of RENO and DayaBay Anomalies of reactor antineutrino oscillations have beenconsidered for the range 01 eV2 lt Δ119898
2
14lt 1 eV2 Thus it is
worth analyzing the absolute flux at the near detector and theratio of the far-to-near flux on a common basis [32]
RENO announced an update of rate-only analysis andthe spectral shape of neutrino events [neutrino telescope]including an observed-to-expected ratio 119877 = 0929 and anoscillation amplitude of sin22120579
13= 0100 We compared the
spectral shape with theoretical curves of the superpositionsof Δ119898
2
41oscillations and Δ119898
2
31oscillations In summary
sin2212057914
gt 02 is excluded at 3120590 CL When Δ1198982
31=
000232 eV2 is fixed the best-fit in four-neutrino parametersis (Δ119898
2
41 sin22120579
14) = (00078 eV2 0054) When we search
the fit of Δ1198982
31along with other parameters of four-neutrino
analysis the best value is obtained Δ1198982
31= 000283 eV2
with sin2212057913
= 0090 from the shape in three-neutrinoanalysis When the parameters are extended to four-neutrinoscheme the best fit is (Δ119898
2
41 sin22120579
14) = (0039 eV2 0049)
As shown in Figure 6 the three-neutrino analysis of RENO(sin22120579
13 sin22120579
14) = (0100 00) is also included within
1120590 CL in four-neutrino analysis Thus it is not yet knownwhether the superposition withΔ119898
2
41oscillations is preferred
to the single Δ1198982
31oscillations at RENO detectors Figure 7
shows that the rate-only analysis and the spectral shapeanalysis are in good agreement within their 1120590 CL range
Acknowledgments
This research was supported by a Chung-Ang Univer-sity Research Scholarship Grant in 2013 and the NationalResearch Foundation of Korea (NRF) Grants funded by the
Advances in High Energy Physics 7
000 005 010 015 020000
005
010
015
020RENO (A) Δm2
31 = 283 times 10minus3 eV2
Δm241 = 0039 eV2
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
000 005 010 015 020000
005
010
015
020
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
RENO (B)
sin2(212057914)
sin2(212057914)
sin2(212057913) sin
2(212057913)
(0092 0049)(0118 0054)
Figure 7 Comparison of rate-only analysis and spectral shape analysis in both (A) and (B) the regions allowed by rate-only analysis areoverlapped in 1120590 range of shape analysis while they do not include the 120594
2-minimum best fits
Korea Government of theMinistry of Education Science andTechnology (MEST) (2011-0014686)
References
[1] Z Maki M Nakagawa and S Sakata ldquoRemarks on the unifiedmodel of elementary particlesrdquo Progress of Theoretical Physicsvol 28 no 5 pp 870ndash880 1962
[2] F P An J Z Bai A B Balantekin et al ldquoObservationof electron-antineutrino disappearance at daya bayrdquo PhysicalReview Letters vol 108 no 17 Article ID 171803 7 pages 2012
[3] J K Ahn S Chebotaryov J H Choi et al ldquoObservationof reactor electron antineutrinos disappearance in the RENOexperimentrdquo Physical Review Letters vol 108 no 19 Article ID191802 6 pages 2012
[4] K Abe N Abgrall Y Ajima et al ldquoIndication of electronneutrino appearance from an accelerator-produced off-axismuon neutrino beamrdquo Physical Review Letters vol 107 no 4Article ID 041801 8 pages 2011
[5] P Adamson D J Auty D S Ayres et al ldquoImproved search formuon-neutrino to electron-neutrino oscillations in MINOSrdquoPhysical Review Letters vol 107 no 18 Article ID 181802 6pages 2011
[6] Y Abe C Aberle T Akiri et al ldquoIndication of reactor 120592119890
disappearance in the double chooz experimentrdquoPhysical ReviewLetters vol 108 no 13 Article ID 131801 7 pages 2012
[7] Y Abe C Aberle J C Anjos et al ldquoReactor electron antineu-trino disappearance in the Double Chooz experimentrdquo PhysicalReview D vol 86 no 5 Article ID 052008 pp 1ndash21 2012
[8] J Beringer J F Arguin R M Barnett1 et al ldquoReview of particlephysicsrdquo Physical Review D vol 86 no 1 Article ID 0100012012
[9] G L Fogli E Lisi A Marrone D Montanino A Palazzo andAM Rotunno ldquoSolar neutrino oscillation parameters after first
KamLAND resultsrdquo Physical Review D vol 67 no 7 Article ID073002 2003
[10] D V Forero M Tortola and J W F Valle ldquoGlobal status ofneutrino oscillation parameters after Neutrino-2012rdquo PhysicalReview D vol 86 no 7 Article ID 073012 8 pages 2012
[11] M C Gonzalez-Garcia M Maltoni J Salvado and T SchwetzldquoGlobal fit to three neutrino mixing critical look at presentprecisionrdquo Journal of High Energy Physics vol 2012 article 1232012
[12] A Aguilar-Arevalo L B Auerbach R L Burman et alldquoEvidence for neutrino oscillations from the observation ofanti-neutrino(electron) appearance in a anti-neutrino(muon)beamrdquo Physical Review D vol 64 no 11 Article ID 112007 22pages 2001
[13] A A Aguilar-Arevalo A O Bazarko and S J Brice ldquoSearch forelectron neutrino appearance at the998779119898
2sim 1 eV2 Scalerdquo Physical
Review Letters vol 98 no 23 Article ID 231801 7 pages 2007[14] A A Aguilar-Arevalo C E Anderson S J Brice et al ldquoEvent
excess in the miniBooNE search for 120592120583
rarr 120592119890oscillationsrdquo
Physical Review Letters vol 105 no 18 Article ID 181801 5pages 2010
[15] A A Aguilar-Arevalo et al ldquoImproved search for 120592120583
rarr 120592119890
Oscillations in the miniBooNE experimentrdquo Physical ReviewLetters vol 110 article 16 Article ID 181801 6 pages 2010
[16] WHampel J Handt G Heusser et al ldquoGALLEX solar neutrinoobservations results for GALLEX IVrdquo Physics Letters B vol 447no 1-2 pp 127ndash133 1999
[17] J N Abdurashitov T J Bowles C Cattadori et al ldquoThe BNO-LNGS joint measurement of the solar neutrino capture ratein71Gardquo Astroparticle Physics vol 25 no 5 pp 349ndash354 2006
[18] B Achkar R Aleksan M Avenier et al ldquoSearch for neutrinooscillations at 15 40 and 95meters from a nuclear power reactorat Bugeyrdquo Nuclear Physics B vol 434 no 3 pp 503ndash532 1995
8 Advances in High Energy Physics
[19] S K Kang Y D Kim Y Ko and K Siyeon ldquoSterile neu-trino analysis of reactor-neutrino oscillationrdquo httparxivorgabs13036173
[20] K Bora D Dutta and P Ghoshal ldquoProbing sterile neutrinoparameters with Double Chooz Daya Bay and RENOrdquo Journalof High Energy Physics vol 2012 article 25 2012
[21] YGao andDMarfatia ldquoMeter-baseline tests of sterile neutrinosat Daya Bayrdquo Physics Letters B vol 723 no 1-3 pp 164ndash167 2013
[22] C Giunti M Laveder Y F Li Q Y Liu and H W LongldquoUpdate of short-baseline electron neutrino and antineutrinodisappearancerdquo Physical Review D vol 86 no 11 Article ID113014 14 pages 2012
[23] J M Conrad C M Ignarra G Karagiorgi M H Shaevitzand J Spitz ldquoSterile neutrino fits to short-baseline neutrinooscillation measurementsrdquo Advances in High Energy Physicsvol 2013 Article ID 163897 26 pages 2013
[24] S N Gninenko ldquoSterile neutrino decay as a common origin forLSNDMiniBooNE and T2K excess eventsrdquo Physical Review Dvol 85 no 5 Article ID 051702 5 pages 2012
[25] J Kopp P A N Machado M Maltoni and T Schwetz ldquoSterileneutrino oscillations the global picturerdquo Journal of High EnergyPhysics vol 2013 article 50 2013
[26] S H Seo ldquoNew results from RENOrdquo in Proceedings of the 15thInternational Workshop on Neutrino Telescopes Venice ItalyMarch 2013
[27] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical Review D vol 83 no 7 Article ID 0730062011
[28] T A Mueller D Lhuillier M Fallot et al ldquoImproved predic-tions of reactor antineutrino spectrardquo Physical Review C vol83 no 5 Article ID 054615 2011
[29] P Vogel and J F Beacom ldquoAngular distribution of neutroninverse beta decay ]
119890+ 119890++ 119899rdquo Physical Review D vol 60 no
5 Article ID 053003 1999[30] P Huber ldquoDetermination of antineutrino spectra from nuclear
reactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2012 Erratum in Physical Review C vol 85 no 2 ArticleID 029901 2012
[31] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013
[32] RENO Collaboration ldquoAbsolute flux of reactor antineutrinosrdquoin preparation
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Advances in High Energy Physics 7
000 005 010 015 020000
005
010
015
020RENO (A) Δm2
31 = 283 times 10minus3 eV2
Δm241 = 0039 eV2
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
000 005 010 015 020000
005
010
015
020
Prob far = 0929 plusmn 0011
Prob near = 0990 plusmn 0025
Δm231 = 232 times 10
minus3 eV2
Δm241 = 00078 eV2
RENO (B)
sin2(212057914)
sin2(212057914)
sin2(212057913) sin
2(212057913)
(0092 0049)(0118 0054)
Figure 7 Comparison of rate-only analysis and spectral shape analysis in both (A) and (B) the regions allowed by rate-only analysis areoverlapped in 1120590 range of shape analysis while they do not include the 120594
2-minimum best fits
Korea Government of theMinistry of Education Science andTechnology (MEST) (2011-0014686)
References
[1] Z Maki M Nakagawa and S Sakata ldquoRemarks on the unifiedmodel of elementary particlesrdquo Progress of Theoretical Physicsvol 28 no 5 pp 870ndash880 1962
[2] F P An J Z Bai A B Balantekin et al ldquoObservationof electron-antineutrino disappearance at daya bayrdquo PhysicalReview Letters vol 108 no 17 Article ID 171803 7 pages 2012
[3] J K Ahn S Chebotaryov J H Choi et al ldquoObservationof reactor electron antineutrinos disappearance in the RENOexperimentrdquo Physical Review Letters vol 108 no 19 Article ID191802 6 pages 2012
[4] K Abe N Abgrall Y Ajima et al ldquoIndication of electronneutrino appearance from an accelerator-produced off-axismuon neutrino beamrdquo Physical Review Letters vol 107 no 4Article ID 041801 8 pages 2011
[5] P Adamson D J Auty D S Ayres et al ldquoImproved search formuon-neutrino to electron-neutrino oscillations in MINOSrdquoPhysical Review Letters vol 107 no 18 Article ID 181802 6pages 2011
[6] Y Abe C Aberle T Akiri et al ldquoIndication of reactor 120592119890
disappearance in the double chooz experimentrdquoPhysical ReviewLetters vol 108 no 13 Article ID 131801 7 pages 2012
[7] Y Abe C Aberle J C Anjos et al ldquoReactor electron antineu-trino disappearance in the Double Chooz experimentrdquo PhysicalReview D vol 86 no 5 Article ID 052008 pp 1ndash21 2012
[8] J Beringer J F Arguin R M Barnett1 et al ldquoReview of particlephysicsrdquo Physical Review D vol 86 no 1 Article ID 0100012012
[9] G L Fogli E Lisi A Marrone D Montanino A Palazzo andAM Rotunno ldquoSolar neutrino oscillation parameters after first
KamLAND resultsrdquo Physical Review D vol 67 no 7 Article ID073002 2003
[10] D V Forero M Tortola and J W F Valle ldquoGlobal status ofneutrino oscillation parameters after Neutrino-2012rdquo PhysicalReview D vol 86 no 7 Article ID 073012 8 pages 2012
[11] M C Gonzalez-Garcia M Maltoni J Salvado and T SchwetzldquoGlobal fit to three neutrino mixing critical look at presentprecisionrdquo Journal of High Energy Physics vol 2012 article 1232012
[12] A Aguilar-Arevalo L B Auerbach R L Burman et alldquoEvidence for neutrino oscillations from the observation ofanti-neutrino(electron) appearance in a anti-neutrino(muon)beamrdquo Physical Review D vol 64 no 11 Article ID 112007 22pages 2001
[13] A A Aguilar-Arevalo A O Bazarko and S J Brice ldquoSearch forelectron neutrino appearance at the998779119898
2sim 1 eV2 Scalerdquo Physical
Review Letters vol 98 no 23 Article ID 231801 7 pages 2007[14] A A Aguilar-Arevalo C E Anderson S J Brice et al ldquoEvent
excess in the miniBooNE search for 120592120583
rarr 120592119890oscillationsrdquo
Physical Review Letters vol 105 no 18 Article ID 181801 5pages 2010
[15] A A Aguilar-Arevalo et al ldquoImproved search for 120592120583
rarr 120592119890
Oscillations in the miniBooNE experimentrdquo Physical ReviewLetters vol 110 article 16 Article ID 181801 6 pages 2010
[16] WHampel J Handt G Heusser et al ldquoGALLEX solar neutrinoobservations results for GALLEX IVrdquo Physics Letters B vol 447no 1-2 pp 127ndash133 1999
[17] J N Abdurashitov T J Bowles C Cattadori et al ldquoThe BNO-LNGS joint measurement of the solar neutrino capture ratein71Gardquo Astroparticle Physics vol 25 no 5 pp 349ndash354 2006
[18] B Achkar R Aleksan M Avenier et al ldquoSearch for neutrinooscillations at 15 40 and 95meters from a nuclear power reactorat Bugeyrdquo Nuclear Physics B vol 434 no 3 pp 503ndash532 1995
8 Advances in High Energy Physics
[19] S K Kang Y D Kim Y Ko and K Siyeon ldquoSterile neu-trino analysis of reactor-neutrino oscillationrdquo httparxivorgabs13036173
[20] K Bora D Dutta and P Ghoshal ldquoProbing sterile neutrinoparameters with Double Chooz Daya Bay and RENOrdquo Journalof High Energy Physics vol 2012 article 25 2012
[21] YGao andDMarfatia ldquoMeter-baseline tests of sterile neutrinosat Daya Bayrdquo Physics Letters B vol 723 no 1-3 pp 164ndash167 2013
[22] C Giunti M Laveder Y F Li Q Y Liu and H W LongldquoUpdate of short-baseline electron neutrino and antineutrinodisappearancerdquo Physical Review D vol 86 no 11 Article ID113014 14 pages 2012
[23] J M Conrad C M Ignarra G Karagiorgi M H Shaevitzand J Spitz ldquoSterile neutrino fits to short-baseline neutrinooscillation measurementsrdquo Advances in High Energy Physicsvol 2013 Article ID 163897 26 pages 2013
[24] S N Gninenko ldquoSterile neutrino decay as a common origin forLSNDMiniBooNE and T2K excess eventsrdquo Physical Review Dvol 85 no 5 Article ID 051702 5 pages 2012
[25] J Kopp P A N Machado M Maltoni and T Schwetz ldquoSterileneutrino oscillations the global picturerdquo Journal of High EnergyPhysics vol 2013 article 50 2013
[26] S H Seo ldquoNew results from RENOrdquo in Proceedings of the 15thInternational Workshop on Neutrino Telescopes Venice ItalyMarch 2013
[27] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical Review D vol 83 no 7 Article ID 0730062011
[28] T A Mueller D Lhuillier M Fallot et al ldquoImproved predic-tions of reactor antineutrino spectrardquo Physical Review C vol83 no 5 Article ID 054615 2011
[29] P Vogel and J F Beacom ldquoAngular distribution of neutroninverse beta decay ]
119890+ 119890++ 119899rdquo Physical Review D vol 60 no
5 Article ID 053003 1999[30] P Huber ldquoDetermination of antineutrino spectra from nuclear
reactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2012 Erratum in Physical Review C vol 85 no 2 ArticleID 029901 2012
[31] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013
[32] RENO Collaboration ldquoAbsolute flux of reactor antineutrinosrdquoin preparation
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
8 Advances in High Energy Physics
[19] S K Kang Y D Kim Y Ko and K Siyeon ldquoSterile neu-trino analysis of reactor-neutrino oscillationrdquo httparxivorgabs13036173
[20] K Bora D Dutta and P Ghoshal ldquoProbing sterile neutrinoparameters with Double Chooz Daya Bay and RENOrdquo Journalof High Energy Physics vol 2012 article 25 2012
[21] YGao andDMarfatia ldquoMeter-baseline tests of sterile neutrinosat Daya Bayrdquo Physics Letters B vol 723 no 1-3 pp 164ndash167 2013
[22] C Giunti M Laveder Y F Li Q Y Liu and H W LongldquoUpdate of short-baseline electron neutrino and antineutrinodisappearancerdquo Physical Review D vol 86 no 11 Article ID113014 14 pages 2012
[23] J M Conrad C M Ignarra G Karagiorgi M H Shaevitzand J Spitz ldquoSterile neutrino fits to short-baseline neutrinooscillation measurementsrdquo Advances in High Energy Physicsvol 2013 Article ID 163897 26 pages 2013
[24] S N Gninenko ldquoSterile neutrino decay as a common origin forLSNDMiniBooNE and T2K excess eventsrdquo Physical Review Dvol 85 no 5 Article ID 051702 5 pages 2012
[25] J Kopp P A N Machado M Maltoni and T Schwetz ldquoSterileneutrino oscillations the global picturerdquo Journal of High EnergyPhysics vol 2013 article 50 2013
[26] S H Seo ldquoNew results from RENOrdquo in Proceedings of the 15thInternational Workshop on Neutrino Telescopes Venice ItalyMarch 2013
[27] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical Review D vol 83 no 7 Article ID 0730062011
[28] T A Mueller D Lhuillier M Fallot et al ldquoImproved predic-tions of reactor antineutrino spectrardquo Physical Review C vol83 no 5 Article ID 054615 2011
[29] P Vogel and J F Beacom ldquoAngular distribution of neutroninverse beta decay ]
119890+ 119890++ 119899rdquo Physical Review D vol 60 no
5 Article ID 053003 1999[30] P Huber ldquoDetermination of antineutrino spectra from nuclear
reactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2012 Erratum in Physical Review C vol 85 no 2 ArticleID 029901 2012
[31] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013
[32] RENO Collaboration ldquoAbsolute flux of reactor antineutrinosrdquoin preparation
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of