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Measuring CP Measuring CP violating phase from violating phase from
long baseline neutrino long baseline neutrino experimentsexperiments
Naotoshi OkamuraNaotoshi Okamura
(YITP, Kyoto Univ.)(YITP, Kyoto Univ.)
ICFP2005ICFP2005
Oct. 07, ’05 @ NCUOct. 07, ’05 @ NCU
planplan short reviewshort review
until nowuntil now between CP phase and the othersbetween CP phase and the others
8 fold ambiguity effect of matter
delete, 3m : mixing, mass, matter how to delete Yet Another Problem, error
one example summary
short reviewshort review
parameters (3flavor)parameters (3flavor)
neutrino massesneutrino masses mm11 m m2 2 m m33
flavor mixing anglesflavor mixing angles 12 12 23 23 1313
CP phaseCP phase
Majorana phasesMajorana phases 11 22
neutrino physicsneutrino physics7/9 parameters7/9 parameters
neutrino oscillationneutrino oscillation
squared-differencessquared-differences mm22
1212 mm221313 (m2
3-m21)
flavor mixing anglesflavor mixing angles 12 12 23 23 1313
CP phaseCP phase
Majorana phasesMajorana phases nothingnothing
6 parameters6 parameters
until todayuntil today Solar Neutrino (SK, SNO, KamLAND(reactor))Solar Neutrino (SK, SNO, KamLAND(reactor))
ee ! ! ee (anti- (anti-ee !! anti- anti-ee)) Atmospheric Neutrino (SK, K2K(LBL))Atmospheric Neutrino (SK, K2K(LBL))
!! (anti-(anti- !! anti- anti- ) ) Reactor Neutrino (CHOOZ, PaloVarde)Reactor Neutrino (CHOOZ, PaloVarde)
anti-anti-ee !! anti- anti-ee
only survival probability & 2-flavor analysis
E
LmP
4sin2sin1
222
even function of and m2
Discard : LSNDDiscard : LSND
notationsnotations
222
222
kmGeV
eV2.534
2
ijij
ijijij
mmm
LE
mL
E
m
mass squared difference
ijij
ie
ijije
ccsU
esU
scsU
cos ,
sin ,
13233
133
13122
independent parameters
atm1323
sun12
rct13
sin
sin
sin
cs
s
srelation to experiments
321
321
321
UUU
UUU
UUU eee
MNS matrix
categorizecategorize
solar, matter effect helpssolar, matter effect helps
fullfull100%100%fullfull100%100%
122 2sin 2
12m(12<45) (>0)
atmospheric, even function
halfhalf50%50%halfhalf50%50%
232 2sin 2
13m(23<>45) (<>0)
unknown, will be measured
nonnon0%0%nonnon0%0%
132 2sin MNS(<0.16) (no)
3 ambiguity3 ambiguity
232 2sin value of value of 2323 (octant) (octant)
2 fold ambiguity2 fold ambiguity
MNS13 , unobserved parametersunobserved parameters2 fold ambiguity2 fold ambiguity
213m
sign of sign of mm221313
2 fold ambiguity2 fold ambiguity
“best fit” is 23 =45 : no octant ambiguity
CP phase CP phase and and
the othersthe others
CP phase and mixingCP phase and mixing sin,cos phase CP measuring MNSMNS
12132
13122
2233
1312132122
2233
1222
2
2
21222
2
2
2
sin2
sinsin2
sin4
sinsin2
sin2
sin42
2sin4
2sin4
UUUU
UUUU
UUUUP
flavor changing case P( ! e) : realistic mode in near future.
combination of mixing angles and CP phase
Ue3 : unknown, important to measure CP phase
CP phase vs. mixing CP phase vs. mixing anglesangles
L = 295 km, without matter effect
combination of mixing angles and CP phase
If we do not know the value of 13, we cannot determine the CP phase.
0.16 0.10
e.g.
CP phase and mass CP phase and mass hierarchyhierarchy
2sin4sin 122
21210
PPPP
e
13MNS13332222112
133322132
MNS1
1322
330
sincos
sin22
sin4
2sin4
JUUUUUUUUP
UUUUJP
UUP
eeee
ee
e
sin,cos phase CP measuring MNSMNS
combination of “sign of 13” and “cos”
even odd
CP phase and matterCP phase and matter
232323
13213
1313
12
212
1212
~
1~
2sin22
~
m
a
a
m
Disturbed by the matter effect.
213
212
22
mam
EGa F
Combination of mixing angles and CP phase. Mixing angles are changed by matter effect.
If we do not know the matter profile correctly, we cannot estimate the CP phase, correctly.
CP phase and the othersCP phase and the others
sin,cos
phase CP measuring
MNSMNS
313
13
sin
unknown:
eU
hierarchy mass
ofsign 213m
matter effectdisturb
3m3m
mixing anglesmass hierarchy
matter effect
mixing anglemixing angle
13121321222
3
2
2
1322
3
2
31222
2
2
2
sinsin2
sin2
sin42
2sin14
2sin141
UU
UUUUP
213
21232 mmUU ee
flavor conserving case insensitive : slightly depend on CP phase, via MNS elements. P(e ! e) : independent of CP
Reactor experiments are independent of CP phase
KASKA, DayaBay, Double Chooz, and so on.
2m2m
mixing anglesmass hierarchy
matter effect
mass hierarchy 1mass hierarchy 1
221213
132 ,sin2
sin aOGFP e
12MNSrct2
atm2
rct2
MNSrct2
213
atm2
rct2
cos2
sin21sinsin2
sinsin211sinsin4
BAE
aLG
Am
aF
matter effect helps usmatter effect helps us
rct4
sun2atm
2rct
2
rct2
atm2
sunatmrct
cossin112
sinsin
2
cossin12sinsintan
B
A
A>>B
mass hierarchy 2mass hierarchy 2
12MNSrct2
atm2
rct2 cos
2sin21sinsin A
E
aL
2
cossin12sinsintan rct2
atm2
sunatmrct A
We can determine mass hierarchy independently,We can determine mass hierarchy independently, if matter effect is large.if matter effect is large.
13
3
2/1
rct2
sun
atm 0.32sin
10.0
0.92
2sin
tan
1km980
cmgL
When L/E is fixed at oscillation maximum,
L>1000 km : matter effect term dominateL>1000 km : matter effect term dominateL<1000 km : CP phase term dominateL<1000 km : CP phase term dominate
neutrino worldneutrino world
CERNCERN
FNALFNALJ-PARCJ-PARC
J-PARC – SK ( 300km)J-PARC – SK ( 300km)and and
– – Korea (1000km)Korea (1000km)
1m1m
mixing anglesmass hierarchy
matter effect
matter effectmatter effect
matter effect disturbs CP phase measurement.matter effect disturbs CP phase measurement.
helps to determine the mass hierarchy.helps to determine the mass hierarchy. makes difference between makes difference between and anti-and anti-
If we know the matter profile “preciselyprecisely””, matter effect will not be a big problem.
Cheer UP!! Geologist !!
0m0m
mixing anglesmass hierarchy
matter effect
CP phase and the othersCP phase and the others
sin,cos
phase CP measuring
MNSMNS
313
13
sin
unknown:
eU
hierarchy mass
ofsign 213m
matter effectdisturbGeologistGeologist
reactorreactor 1000km1000km
Japan && KoreaJapan && Korea »»one exampleone example»»
way to CP phaseway to CP phasehep-ph/0504061, with K.Hagiwara, K.i.Sendahep-ph/0504061, with K.Hagiwara, K.i.Senda
TTokaimura-okaimura-toto--KKamioka amioka (T2K)(T2K)
J-PARC (http://j-parc.jp/index.html)J-PARC (http://j-parc.jp/index.html)
50 GeV Proton Synchrotron1021 POT/year
Intensity of neutrino O(2) higher than K2K
SK (http://www-sk.icrr.u-tokyo.ac.jp/index.html)SK (http://www-sk.icrr.u-tokyo.ac.jp/index.html)50Kton water Cherenkov detectorfiducial volume : 22.5Kton good e/ identification cannot measure the charge
LL=295 km=295 km
Neutrinos will go to Neutrinos will go to KoreaKorea
OAB : cone, umbrellaL=295km, =2.0-3.0
L=1000-1200km, =1.0-4.0
2.5@SK
S-KoreaS-Korea
Super-KSuper-K
J-PARCJ-PARC
today’s choicetoday’s choicefor hierarchy, angle and place.
3.0@SK
truetrue : “normal” : “normal”fitfit : “inverted” : “inverted”
true : sin2213= 0.1 free : fit = 0.0 free
two distance is better two distance is better than onethan oneSK only Korea only Combine
•SK only • bad• no matter
•Combine• Better !!
BAD
•Korea only• not bad • w/o reactor, difficult
true : sin2213 = 0.06, CP : n£90o
fit : sin2213 = horizontal, CP : freely
SO,SO
GOOD
CP phaseCP phase
We can determine CP phase more, if Ue3 is measured.
Ue3:freely
normal hierarchy
summarysummary CP Phase vs. 3mCP Phase vs. 3m
mixing angles, mass hierarchy, matter effectmixing angles, mass hierarchy, matter effect mixing angle (Ue3:unkown)mixing angle (Ue3:unkown)
reactor experiment reactor experiment mass hierarchymass hierarchy
1000km is turning distance.1000km is turning distance.
matter effectmatter effect not so bad guy. helps us.not so bad guy. helps us. Cheers UP!! Geologist !!Cheers UP!! Geologist !!
Japan-Korea experimentJapan-Korea experiment
13
3
2/1
rct2
sun
atm 0.32sin
10.0
0.92
2sin
tan
1km980
cmgL
!eand !
Thank you Thank you for your attentionfor your attention