CP phase and CP phase and mass hierarchymass hierarchy

Ken-ichi SendaGraduate University for Advanced Studies (SOKENDAI)

&KEKThis talk is based on

K. Hagiwara, N. Okamura, KS PLB 637 266 (2006) (hep-ph/0504061)

K. Hagiwara, N. Okamura, KS hep-ph/0607xxx

What are the merits of detecting T2K off-axis beam in KoreaWhat are the merits of detecting T2K off-axis beam in Korea

LEmij

ij 2

2

The term of matter effect at Korea is

about 3 times large as one at Kamioka!

The term of matter effect is sensitive to the sign of δm213

||016.0cos2sin10.024.0

29508.0~

||sin2sin10.049.0

29511.0~

13

2/1

2

13

2/1

213

MNSrct

e

MNSrct

e

kmLB

kmLA

eeRCTATMe BAP2

sin)1(sinsin4 13222

Contribution of the matter effecteF

SOLMNSRCTATM

SOLRCTe

MNSRCTATM

SOLRCTe

EnGa

EaLB

EaLA

22

coscossintan2

2sin2

2cos4

sinsintan

2sin2

2cos

2122

122

13

||sin

2sin10.049.0

29511.0~ 13

2/1

213

MNSRCT

e kmLA

eeRCTATMe BAP2

sin)1(sinsin4 13222

Normal hierarchy (Δ13> 0): Matter effect enhances the amplitude.

Inverted hierarchy (Δ13 < 0): Matter effect suppresses the amplitude.

Near the oscillation maximum (Δ13 =π)

•The difference of the amplitudes between at Kamioka and at Korea is very large, and its difference obeys the sign of δm2

13.

Both Kamioka and Korea are important

Property of the amplitude

eeRCTATMe BAP2

sin)1(sinsin4 13222

||016.0cos

2sin10.024.0

29508.0~ 13

2/1

2

MNS

RCTe km

LB

The oscillation phase is also sensitive to the sign of Δ13.

sin2 (|Δ13/2| +| Be|) or sin2 (|Δ13/2| - |Be|)

Near the oscillation maximum (Δ13 =π)

•At Kamioka, the term of cos δMNS is dominant in Be.

⇒the sign degeneracy between cos δMNS and Δ13

•At Korea (L > 1000km),

The value of the matter effect term is

comparable with the value of cos δMNS term.

⇒the sign degeneracy 　 can be solved, but the magnitude of the phase shift strongly depends on the value of cos δMNS

Property of the oscillation phase

Analysis methodAnalysis method•Detector size (fiducial volume) Super-Kamiokande : 22.5 kt The detector in Korea : 100 kt

•Exposure time 5 years ( time of T2K running) → 5 ×1021 Proton On Target

•Base line length and off-axis angle Kamioka: L = 295 km off-axis angle: 3.0° Korea: L = 1000km off-axis angle: 0.5°

•Signals Charged Current Quasi Elastic Events …We can reconstruct the neutrino energy and distinghish e events and μ events. bin width: 200MeV 0.4 – 5.0 GeV for -like (SK/Korea)

0.4 – 1.2 GeV for e-like (SK) 0.4 – 2.8 GeV for e-like (Korea)Background Secondary neutrino flux of the νμ 　 primary beam.

Contribution from the π0 is not included.

input parametersinput parameters Solar neutrino

– sin22SOL = 0.84 0.07, m122 = (8.3 0.6) 10-5 eV2

Atmospheric neutrino– sin22 ATM= 0.96-1.00, |m13

2 |= (2.5 0.5) 10-3 eV2

Matter density （ uncertainty : 3%） = 2.8 / 3.0 (g/cm3) (SK/Korea)

22

2

22

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,2

,2

,2

,

2,

2,

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flavor all ,

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:bin:

2

2

01.02sin2sin

2sin2sin2sin

03.00.1

03.00.1

03.00.1

03.0

0.1

inputRCT

fitRCT

solatm solatm

inputSOLATM

fitSOLATM

solatm solatm

inputsolatm

fitsolatm

KrSK

KrSKV

QEflux

e,μi

inputi

inputifitiα

mmm

ff

ff

N

NN

eventnumbers

systematicerrors

parametererrors

expected constraint from future reactorexperiments

Capability to determine the mass hierarchyCapability to determine the mass hierarchy

3σ: sin2 2θRCT > 0.050 (normal hierarchy) or 0.055 (inverted hierarchy)

Normal hierarchy can exclude the fake hierarchy more strongly than the inverted hierarchy. → statistic error.

Capability depends on CP phase strongly. ← Contribution of the phase shift !

13

2/1

2

2/1

2

1313

2sin10.0cos

2sin10.0cos24.0

100048.0

2||

2||

fitRCT

fitMNSinput

RCT

inputMNS

fite

inpute

kmL

BB

3 σ 3 σ

In this analysis, the statistic error is dominant. →Δχ2 is roughly proportional to the detector sizes

and the intensity of the neutrino beam.

•Δχ2 　 is roughly proportional to the volumes.

ex.) sin2 2θRCT = 0.10 &δMNS = 0°

22.5kt & 100kt :Δχ2 ~ 23

100kt & 500kt : Δχ2 ~ 90

•Only Hyper-Kamiokande can not determine the mass hierarchy.The difference between 2 hierarchy patterns is too small at Kamioka.

•Only Korea is not so bad.The constraint from reactor experiments plays the same role of Kamioka.

•Optimal ratio is 0.5:5.5 ~ 2:4

Total fiducial volume: 600kt

Input:normal Fit: Inverted

The mechanism for measuring CP phase The mechanism for measuring CP phase and θand θRCTRCT

LEmij

ij 2

2

||016.0cos2sin10.024.0

29508.0~

||sin2sin10.049.0

29511.0~

13

2/1

2

13

2/1

213

MNSRCT

e

MNSRCT

e

kmLB

kmLA

eeRCTATMe BAP2

sin)1(sinsin4 13222

Amplitude: sin2 θRCT , sin δMNS

2 detector system: The ambiguity can be solved because of the matter effect.

Oscillation phase: cos δMNS

The setup for determination of the mass hierarchy pattern is useful for measurement of CP phase.

Input: normal

Fit : normal

Inverted

δMNS is constrained at least ± 30° 　 at 1 sigma level.

In small θRCT region, the allowed regions for fake hierarchy remain.

Input: inverted

Fit: Inverted

Normal

δMNS is constrained at least ± 30° 　 at 1 sigma level.

In small θRCT region, the allowed regions for fake hierarchy remain.

SummarySummary The matter effect is very important for the T2KK expe

riment. When we detect the off-axis beam 3.0deg by SK and

0.5 deg at L = 1000km by 100kt water cerenkov detector putted in Korea during the T2K experimental period, we can determine the mass hierarchy pattern more than 3 σ C.L!!

(sin2 2θRCT>0.050 (normal), 0.055 (inverted))

We can also constrain the CP phase uniquely by the same measuring condition without using anti-neutrino beam !

To Be Continued…….To Be Continued…….

Fit CP phase and reactor angleFit CP phase and reactor angle

2/1

2

2/1

2

1313

2sin10.0cos

2sin10.0cos24.0

100048.0

2||

2||

fitRCT

inputMNSinput

RCT

inputMNS

fite

inpute

kmL

BB

Fitting CP phase is favored around 0 deg. in order to reduce the phase difference.

When the input hierarchy is normal (inverted), the fitting reactor angle is larger (smaller) than input reactor angle.

The importance of νThe importance of νμ μ eventevent

Without μ eventWith μ event

Importance of μ event Importance of μ event –CP phase-–CP phase-

Where should we detect the off-axis beam in Korea?Where should we detect the off-axis beam in Korea?

3 σ

Input: Normal hierarchy

Fit: Inverted hierarchy

Input : Inverted

Fit : Normal

Best combination: OAB3.0° at Kamioka 　 + OAB 0.5° at L = 1000km in Korea

0.5° off-axis beam: flux cover with the oscillation maximum region in Korea

(1.6 GeV ~ 2.4 GeV)

Input sin2 2θRCT = 0.10 δMNS = 0