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