Research Article Four-Neutrino Analysis of 1.5km Baseline ...downloads.hindawi.com/journals/ahep/2013/138109.pdf · and RENO, respectively. On the other hand, the far-to-near ratio

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



)

(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)


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


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


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


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


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)


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


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


000 005 010 015 020000

005

010

015

020RENO (A) Δm2

31 = 283 times 10minus3 eV2

Δm241 = 0039 eV2



000 005 010 015 020000

005

010

015

020



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


[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


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


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




)

(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)


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


41is presented when

Δ1198982

31= 232 times 10


2

31



13= 010 and

sin2212057914


where 1198910

= +457491 times 10 1198911


=


minus5 1198914= +172704times10

minus5and 119891




2

41 The first




31 RENO and Daya






13 Both


2










2

31-oscillation





2


2

41oscillations


41 001 eV2


and sin2212057913


2

41=

001 eV2)⟩ and ⟨119875(Δ1198982



13minussin22120579

14space using


13is in good






[Expected at FD](8)







020

015

010

005

000

020015010005000

sin2(212057914)

sin2(212057913

)



RENO020

015

010

005

000

020015010005000

sin2(212057914)

sin2(212057913



Daya Bay


13and sin22120579




12

11

10

09

082 4 6 8

Far

near


RENO (A)

Δm231 = 283 times 10

minus3 eV2

Δm241 = 0039 eV2

12

11

10

09

082 4 6 8

Far

near


RENO (B)

Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2


14= 0 for Δ119898

2

31= 283 times 10


31= 232 times 10


2



Δ1198982






⟨119875 (FD)⟩

⟨119875 (ND)⟩ (0990)minus1

(11)


2

31 sin22120579


14= 0 The


where sin2212057913

and Δ1198982



31is 000232


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


31 sin22120579

13) is (000283 009) denoted

by A When Δ1198982



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)


Only Δ1198982

41gt Δ119898

2



2

31= 283 times 10


mindof = 048 is at (Δ1198982

41 sin22120579


2

31= 232 times 10


mindof = 106


41 sin22120579



2


for Δ1198982


Δ1198982





2

31and sin22120579

13



41 sin22120579

14) = (0039 eV2 005)

for (A) and (Δ1198982

41 sin22120579

14) = (00078 eV2 0033) for (B)


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)



2

31and Δ119898

2

41) For (A) the 120594

2


2




41 we choose 119898

2


avoiding 1198982


2

41for



13 sin22120579



31= 000283 eV2


31= 000232 eV2 In





13=



2





4 Conclusion


2




2

31 Therefore this



2






2


2


sin2212057914


31=


2

41 sin22120579

14) = (00078 eV2 0054) When we search




31= 000283 eV2

with sin2212057913


2

41 sin22120579

14) = (0039 eV2 0049)


13 sin22120579



2





Acknowledgments



000 005 010 015 020000

005

010

015

020RENO (A) Δm2


Δm241 = 0039 eV2



000 005 010 015 020000

005

010

015

020



Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2

RENO (B)

sin2(212057914)

sin2(212057914)

sin2(212057913) sin

2(212057913)

(0092 0049)(0118 0054)


2-minimum best fits


References






















rarr 120592119890



























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




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


41is presented when

Δ1198982

31= 232 times 10


2

31



13= 010 and

sin2212057914


where 1198910

= +457491 times 10 1198911


=


minus5 1198914= +172704times10

minus5and 119891




2

41 The first




31 RENO and Daya






13 Both


2










2

31-oscillation





2


2

41oscillations


41 001 eV2


and sin2212057913


2

41=

001 eV2)⟩ and ⟨119875(Δ1198982



13minussin22120579

14space using


13is in good






[Expected at FD](8)







020

015

010

005

000

020015010005000

sin2(212057914)

sin2(212057913

)



RENO020

015

010

005

000

020015010005000

sin2(212057914)

sin2(212057913



Daya Bay


13and sin22120579




12

11

10

09

082 4 6 8

Far

near


RENO (A)

Δm231 = 283 times 10

minus3 eV2

Δm241 = 0039 eV2

12

11

10

09

082 4 6 8

Far

near


RENO (B)

Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2


14= 0 for Δ119898

2

31= 283 times 10


31= 232 times 10


2



Δ1198982






⟨119875 (FD)⟩

⟨119875 (ND)⟩ (0990)minus1

(11)


2

31 sin22120579


14= 0 The


where sin2212057913

and Δ1198982



31is 000232


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


31 sin22120579

13) is (000283 009) denoted

by A When Δ1198982



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)


Only Δ1198982

41gt Δ119898

2



2

31= 283 times 10


mindof = 048 is at (Δ1198982

41 sin22120579


2

31= 232 times 10


mindof = 106


41 sin22120579



2


for Δ1198982


Δ1198982





2

31and sin22120579

13



41 sin22120579

14) = (0039 eV2 005)

for (A) and (Δ1198982

41 sin22120579

14) = (00078 eV2 0033) for (B)


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)



2

31and Δ119898

2

41) For (A) the 120594

2


2




41 we choose 119898

2


avoiding 1198982


2

41for



13 sin22120579



31= 000283 eV2


31= 000232 eV2 In





13=



2





4 Conclusion


2




2

31 Therefore this



2






2


2


sin2212057914


31=


2

41 sin22120579

14) = (00078 eV2 0054) When we search




31= 000283 eV2

with sin2212057913


2

41 sin22120579

14) = (0039 eV2 0049)


13 sin22120579



2





Acknowledgments



000 005 010 015 020000

005

010

015

020RENO (A) Δm2


Δm241 = 0039 eV2



000 005 010 015 020000

005

010

015

020



Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2

RENO (B)

sin2(212057914)

sin2(212057914)

sin2(212057913) sin

2(212057913)

(0092 0049)(0118 0054)


2-minimum best fits


References






















rarr 120592119890



























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




020

015

010

005

000

020015010005000

sin2(212057914)

sin2(212057913

)



RENO020

015

010

005

000

020015010005000

sin2(212057914)

sin2(212057913



Daya Bay


13and sin22120579




12

11

10

09

082 4 6 8

Far

near


RENO (A)

Δm231 = 283 times 10

minus3 eV2

Δm241 = 0039 eV2

12

11

10

09

082 4 6 8

Far

near


RENO (B)

Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2


14= 0 for Δ119898

2

31= 283 times 10


31= 232 times 10


2



Δ1198982






⟨119875 (FD)⟩

⟨119875 (ND)⟩ (0990)minus1

(11)


2

31 sin22120579


14= 0 The


where sin2212057913

and Δ1198982



31is 000232


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


31 sin22120579

13) is (000283 009) denoted

by A When Δ1198982



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)


Only Δ1198982

41gt Δ119898

2



2

31= 283 times 10


mindof = 048 is at (Δ1198982

41 sin22120579


2

31= 232 times 10


mindof = 106


41 sin22120579



2


for Δ1198982


Δ1198982





2

31and sin22120579

13



41 sin22120579

14) = (0039 eV2 005)

for (A) and (Δ1198982

41 sin22120579

14) = (00078 eV2 0033) for (B)


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)



2

31and Δ119898

2

41) For (A) the 120594

2


2




41 we choose 119898

2


avoiding 1198982


2

41for



13 sin22120579



31= 000283 eV2


31= 000232 eV2 In





13=



2





4 Conclusion


2




2

31 Therefore this



2






2


2


sin2212057914


31=


2

41 sin22120579

14) = (00078 eV2 0054) When we search




31= 000283 eV2

with sin2212057913


2

41 sin22120579

14) = (0039 eV2 0049)


13 sin22120579



2





Acknowledgments



000 005 010 015 020000

005

010

015

020RENO (A) Δm2


Δm241 = 0039 eV2



000 005 010 015 020000

005

010

015

020



Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2

RENO (B)

sin2(212057914)

sin2(212057914)

sin2(212057913) sin

2(212057913)

(0092 0049)(0118 0054)


2-minimum best fits


References






















rarr 120592119890



























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




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


31 sin22120579

13) is (000283 009) denoted

by A When Δ1198982



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)


Only Δ1198982

41gt Δ119898

2



2

31= 283 times 10


mindof = 048 is at (Δ1198982

41 sin22120579


2

31= 232 times 10


mindof = 106


41 sin22120579



2


for Δ1198982


Δ1198982





2

31and sin22120579

13



41 sin22120579

14) = (0039 eV2 005)

for (A) and (Δ1198982

41 sin22120579

14) = (00078 eV2 0033) for (B)


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)



2

31and Δ119898

2

41) For (A) the 120594

2


2




41 we choose 119898

2


avoiding 1198982


2

41for



13 sin22120579



31= 000283 eV2


31= 000232 eV2 In





13=



2





4 Conclusion


2




2

31 Therefore this



2






2


2


sin2212057914


31=


2

41 sin22120579

14) = (00078 eV2 0054) When we search




31= 000283 eV2

with sin2212057913


2

41 sin22120579

14) = (0039 eV2 0049)


13 sin22120579



2





Acknowledgments



000 005 010 015 020000

005

010

015

020RENO (A) Δm2


Δm241 = 0039 eV2



000 005 010 015 020000

005

010

015

020



Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2

RENO (B)

sin2(212057914)

sin2(212057914)

sin2(212057913) sin

2(212057913)

(0092 0049)(0118 0054)


2-minimum best fits


References






















rarr 120592119890



























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




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)



2

31and Δ119898

2

41) For (A) the 120594

2


2




41 we choose 119898

2


avoiding 1198982


2

41for



13 sin22120579



31= 000283 eV2


31= 000232 eV2 In





13=



2





4 Conclusion


2




2

31 Therefore this



2






2


2


sin2212057914


31=


2

41 sin22120579

14) = (00078 eV2 0054) When we search




31= 000283 eV2

with sin2212057913


2

41 sin22120579

14) = (0039 eV2 0049)


13 sin22120579



2





Acknowledgments



000 005 010 015 020000

005

010

015

020RENO (A) Δm2


Δm241 = 0039 eV2



000 005 010 015 020000

005

010

015

020



Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2

RENO (B)

sin2(212057914)

sin2(212057914)

sin2(212057913) sin

2(212057913)

(0092 0049)(0118 0054)


2-minimum best fits


References






















rarr 120592119890



























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




000 005 010 015 020000

005

010

015

020RENO (A) Δm2


Δm241 = 0039 eV2



000 005 010 015 020000

005

010

015

020



Δm231 = 232 times 10

minus3 eV2

Δm241 = 00078 eV2

RENO (B)

sin2(212057914)

sin2(212057914)

sin2(212057913) sin

2(212057913)

(0092 0049)(0118 0054)


2-minimum best fits


References






















rarr 120592119890



























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics

























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Documents

Research Article Four-Neutrino Analysis of 1.5km Baseline ...downloads.hindawi.com/journals/ahep/2013/138109.pdf · and RENO, respectively. On the other hand, the far-to-near ratio