Matter Effects on Neutrino Oscillations

By G.-L. LinNCTU

Nov. 20, 04 AS

Outline

• Matter effects and Solar Neutrinos• The world with 13 and matter enhancement

to 13

• Very Long Baseline Neutrino Oscillation Experiments and the Determination of 13 and 23—work in progress with Y. Umeda

10000

00

0010 toreduces ,0 ,0For

with ,

1212

1212

2323

2323

2323122312

2323122312

1212

13

231323122313122312231312

231323131223122313122312

1312131312

3

2

1

cssc

cssc

cscssscccs

scU

Us

ccsccssesscscescssseccsscecssesccc

U

U

ii

ii

i

e

The Neutrino Mixing Matrix

The world without 13 and CHOOZ bound sin2213< 0.1

have we,

at lookingby then,

,00000000

00000000

and ,With

.00000000

0000000

21with

,

123

123231223

1

231

221

ee

ee

e

ee

U

rAU

rAUUUU

rAU

mmU

EH

Hdrdi

ErnGrAmmm eFejiij 22,222 Neutrino-electron coherent scattering

ee

eee

eee

cmscmscmrAsm

E

rAU

mU

Edrdi

scsc

rAU

mmU

Edrdi

212

2211212

221

1212221

212

221

1122

2112

23232323

112

231

22112

21

000

000

21

withdealsy effectivel we

isolated, is Since .;with

,00000000

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21

Solar Neutrino Oscillations and Matter Enhancement

Diagonalization: 1212m

Sun theinsidepoint some :

!4

2cos :Resonance

2cos2sin2tan

0

012012221

12221

12221

12

r

rrAm

rAmm

me

e

m

Wolfenstein, 1978Mikheyev and Smirnov, 1986

Varying electron density in the SunAdiabaticity

Combine Solar Neutrino and KamLAND experiments:

09.007.012

2

256.05.0

221

40.0tan

eV 102.8

mY.-F. Wang in ICHEP04

The World with 13

eee rAUU

mmUU

Edrdi

00000000

0000000

21 1

131

12231

2211213

new mixing! new mixing!

The e oscillation length:

GeVkm 93004

221

EmElosc

For an experiment with the terrestrial beam E a few GeV, one drops . and 2

1212 mU

ee

eee

cmcsm

csmAsm

E

rAU

mU

Edrdi

213

2311313

231

1313231

213

231

113

231

13

0000

0

21

00000000

00000000

21

does not evolve, while e + induced by13 and Ae.

Diagonalization: 1313m

!4

2cos :Resonance

22,2cos

2sin2tan

013013231

13231

13231

13

rrAm

ErnGrArAm

m

me

eFee

m

Earth mantle: =5 g/cm3, Eres6.4 GeV

Earth core: =12 g/cm3, Eres2.7 GeV

! negativefor resonance No

eV 104.2231

23231

m

m

Barger et al., 99Banuls, Barenboim, Bernabeu, 01

Stacey, Physics of the Earth, 77

Freund and Ohlsson 99

m=5 g/cm3

c=12 g/cm3

Very Long Baseline Neutrino Oscillation Experiments

21323113

2223131

31231

231

231

2

13231

13231

13

2313232313

2313232313

1313

1323

11323

2

2

1323

2cos2sinwith

,21,

21

2cos2sin2tan,

0

0000000

21

mAm

AmmAmM

Amm

ccscssccsssc

UUU

UUm

MUU

Edrdi

em

me

me

e

m

mm

mm

mm

m

emm

e

The solution the equation in the constant-density approximation:

In progresswith Y. Umeda

Still treat =0

GeVin km,in ,eVin , ,

.2/27.1sin2sinsin

2/27.1sin2sincos

/27.1sinsin2sin1

4 tosensitivenot ,2sin~

/27.1sinsin2sin

231

231

31231

223

213

2

31231

223

213

2

312

234

132

2323232

312

232

132

ELAm

ELAm

ELAm

ELP

P

ELP

me

me

m

me

m

mm

mme

Use actual Earth density profile for calculation

How long is the “very long” baseline?

3

13

3max

312

res132

312

232

132

g/cm km2tan

1018.512for 1/27.1sin

mantle)(Earth GeV 4.6for 12sin

/27.1sinsin2sin

pLEL

EE

ELP

m

m

mme

Banuls, Barenboim, Bernabeu, 01

km 10200 0,p ,1.02sin

km 11200 0,p ,05.02sinmax

132

max13

2

L

L

Optimized for P(e)1-P() also peaks at E Eres

Gandhi et al., hep-ph/0408361

Simultaneous measurements of P(e) and P(): sensitive to 13 and 23. Are they reallyIndependent?

P(e) studied for L=9300 km—Fermilab to Kamioka.

F. DeJongh, hep-ex/0203005

Consider L=9300 km case for P(e) Pe and P() P

1.02sin

,eV 1024

132

23231

23

m

023

132

45

,1.02sin

In progress with Y. Umeda

023

132

45

,1.02sin

023

23231

45

,eV 102

m

023

23231

45

,eV 102

m

1.02sin

,eV 102

92.02sin

132

23231

232

m

1.02sin

,eV 102

92.02sin

132

23231

232

m

< 0.03

>0.03

w.r.t resonant energy

Issues to be considered:The effect of CPV phase (10%, Gandhi et al., hep-ph/0408361 )Convoluting with the spectrum from the accelerator

. DeJongh, hep-ex/0203005

CC eventsbefore and afteroscillationsSharp cutoff

to avoid background

.2

1

0000

0

21

00000000

00000000

21

00000000

00000000

21with

,

12323

123

213

2311313

231

1313231

213

231

23

123

113

231

1323

123

113

112

231

121323

UUE

Ucmcsm

csmAsmU

E

UrA

Um

UUE

rAUUU

mUUU

EH

Hdrdi

e

e

e

ee

:gives ingDiagonaliz

e

m

mm

mm

mm

m

mm

ee

ee

mm

Amm

ccscssccsssc

UUU

UUm

MUU

EH

mAmAmm

mAmAmM

Um

MU

13231

13231

13

2313232313

2313232313

1313

1323

11323

2

2

1323

213

23113

22231

231

2

213

23113

22231

231

2

113

2

2

13

2cos2sin2tan,

0

with00

00000

21Then

.2cos2sin21

,2cos2sin21

with,00

00000

From the mixing matrix, one derives

GeVin kmin

eVin , ,

.2/27.1sin2sinsin

2/27.1sin2sincos

/27.1sinsin2sin1

2cos2sin

with,/27.1sinsin2sin

231

231

31231

223

213

2

31231

223

213

2

312

234

132

213

23113

22231

2231

312

232

132

EL

Am

ELAm

ELAm

ELP

mAmmM

ELP

me

me

m

me

m

mm

em

mme

on)? now from g(neglectin zeronot is ifWhat

000

21

neutrinos, catmospherifor Hence,.0set can one ,atmospherein oscillatenot does Since

00000000

0000

21

22113

1232

3123

212

123

231

221

212

2211212

2211212

221

212

23

m

Um

UEdr

di

m

rAU

mmcmcsmcsms

UEdr

di

e

eee

Studying GeV neutrinos on Earth