CP-phase dependence of neutrino oscillation probability in matter

梅 (ume) 田 (da) 義 (yoshi) 章 (aki)with Lin Guey-Lin ( 林　貴林 )

National Chiao-Tung University in Taiwan( 臺灣國立交通大學 )

We calculate neutrino oscillation probability in the framework of three neutrinos.

The latest data is used.

Matter density profile of the earth is approximated by step functions.

The oscillation probability of Pe and P are related to the angle sin2213 and sin2223.

CP-phase dependence of Pe are shown as a function of baseline length L.

Contents • Status of neutrino oscillation• Formalism of three flavor neutrino oscillation• sin2213 and sin2223 dependence of transition probability (CP=0)• cp dependence of transition probability are shown

Solar neutrino

In the core of the sun, the protons will be iron after many fusion steps.Electron neutrinos made in these process, are much less than SM prediction.

core=100g/cm3

surface=0.01g/cm3

many oscillations

EarthSun

SK, e from 8B → 8B* + e+ + e is 40.6% of the SM prediction. (E>5MeV, 20000 events)

SNO (E>6MeV, neutrino from 8B) CC: e + D → p + p + e NC: x + D → x + n + p ES: x + e → x + e Pure D2O phase: Nov.99 – May.01 3He phase: n + 3He → p + 3H +(0.76MeV)Salt phase: Jul.01- Sep.03, n + 35Cl → 36Cl+ (8.6MeV)

Gallium experiments like SAGE and GALLEX /GNO(E>0.23MeV, neutrino from pp, 7B and 8B)neutrinos are detected by the process e + 71Ga →e+ 71Ge

pp-chain

spectrum of solar neutrino

SNO Cherenkov light

atmospheric neutrino Data MC

FC single-ring -like (SK) 1619 2105.8

(In MC, neutrino oscillation is not

assumed)

The energy of neutrino <25GeV

L-dependence can be studied by

measuring zenith angle

In the vacuum, the neutrino oscillation is the function of L/E.

Feb.2004, SK show the L/E plot.

K2K experiment (KEK to Kamioka, 250km)12GeV pp collider →aluminum target → pion → neutrinomeasure the number of , energy, direction at KEK → measure at Kamioka

Fix the baseline length L, measure the neutrino energy dependence.Number of events are not so much.mixing angle → not so sensitivem31

2 → sensitive

KamLAND (nuclear reactor)measure e+ and n (anti- + p →e+ + n )agree with solar neutrino parameter, m21

2=8.3×10-5eV2, sin2212=0.83L/E plot are shown last summer.

CHOOZ (nuclear reactor)Electron neutrino deficit was not measured.sin2213 is constrained.

There are 6 parameters

m21, m31, sin2212, sin2223, sin2213, cp

3- allowed region of oscillation parameters

7.4×103 ≤ m212 ≤ 9.2×103 (best fit 8.2×105, from solar + reactor)

1.9×103 ≤ m312 ≤ 3.0×103 (best fit 2.4×103, from SK)

27.9° ≤ 12 ≤ 37.3° (best fit 32.0°, from solar + reactor)

sin2213 ≤ 0.18 (from atmospheric, K2K, CHOOZ)

sin2223 ≥ 0.9 (from SK)

J.N. Bahcall et. al, hep-ph/0406294

SK collaboration hep-ex/0404034

Best fit value of m212 , m31

2, 12

sin2213=0.1, sin2223=1, cp=0 will be used.

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The relation of ne, nm, nt to the mass eigenstate

Feynman diagram of coherent forward elastic scattering

The step functions withc=11.85 g/cm3

m=4.67 g/cm3

are good approximation.

Freund and Ohlsson hep-ph/9909501

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If we approximate the density profile of the earth by three step functions,mantle → core → mantle, probability PS|2 is

with density profile … calculate non-perturbatively, density is approximated by many step functionsconstant density … calculate non-perturbatively, use constant densityperturbative result … O((m21

2/m312)2) , constant density

for the lowest order,

If m312 < 0, Pe~0.

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m231 dependence of Pe for L=9300km (Fermi – Kamioka)

sin2213=0.1, sin2223=1.0, cp=0, m221=8.2×105, 12=32.0o

sin2213=0.1, sin2223=1We assume that the energy bin for the measurement is 5.5GeV-6.5GeV.

We make a contour plot of Pe and P in 13-23 plane.

5.5GeV≤ E ≤ 6.5GeV

sin2213 ≤ 0.10 sin2223 ≥ 0.92

The contours of Pe and P are orthogonal.

P is not symmetricbetween >45o and <45o.

CP-phase dependence of Pe is shown.

For L=9300km, CP-phase dependence → small,sin2213 and sin2223 dependence → largesin2213 and sin2223 can be fixed by L=9300km.

For L = 1000km and 5000kmCP-phase dependence → large

sin2213=0.1sin2223=112=32o

m213=2.4×103

m213=8.2×105

Check of the calculation. = m212/m31

2.Akhmedov at el., JHEP 04 (2004) 078

L=8500km, MaxMin has minimum. (MaxMin = 0.01)

L=5000km, MaxMin has maximum (MaxMin = 0.065)

CP-phase dependence of P is small.

L=1000km and L=9300km, CP-phase dependence is negligible.

L=5000km, CP-phase dependence can be seen at around 5GeV.

Summary• We relate the measurement of Pe and P to sin2213 and sin2223.• The contour graph of Pe and P are orthogonal in 13-23 plane.

• CP-phase dependence are shown for L=1000, 5000 and 9300km.• The CP-phase effects are small for L=9300km.

Thus sin2213 and sin2223 dependence can be determined without the effects of CP-phase.• (Pe)max – (Pe)min has maximum at around L=5000km. It is about 0.065.• P is not sensitive to CP-phase.