Probing the Octant of 23 with very long baseline neutrino

oscillation experiments

G.-L. LinNational Chiao-Tung U.

Taiwan

CYCU Oct. 17 2006

Work done with Y. Umeda

What we know about the neutrino oscillation parameters

Super-K I+II Preliminary

1.910-3 eV2 < m231 < 3.110-3 eV2

sin2223 > 0.93 at 90% CLBest fit: m2

31 = 2.510-3 eV2

sin2223=1

K. Inoue at ICHEP06, Moscow

7.8310-5 eV2 < m212< 8.0110-5 eV2

0.164< sin212< 0.494Best Fit: 7.9210-5 eV2

sin212=0.314

sin2213< 0.124

@2

G.L. Fogli, E. Lisi, A. Marrone and A. PalazzoProgress in Particle and Nuclear Physics 2006

What we don’t know about the neutrino mixing parameter

(a)The sign of m231

LBL+ATM (magnetized iron calorimeter), Very Long Baseline Experiment (matter effect)

(b)The octant of mixing angle 23

LBL+ATM, Very Long Baseline Experiment (matter effect)

(c)The value of mixing angle 13

Reactors, T2K, NOA

(d) The value of CP violation phase

For references on parameter degeneracy in LBL experiments and 3 flavor effects in atmospheric neutrinos, see T. Schwetz in ICHEP06, Moscow

For proposals of very long baseline experiments, seeI. Mocioiu and R. Shrock, Phys. Rev. D 62, 053017 (2000); V. D. Barger,S. Geer, R. Raja and K. Whisnant, Phys. Lett. B485, 379 (2000);V. D. Barger, S. Geer, R. Raja and K. Whisnant, Phys. Rev. D 62, 013004(2000); F. DeJongh, arXiv:hep-ph/0203005 For relating matter effects in survival probability to 23 , see Antusch et al., hep-ph/0404268; D. Choudhury and A. Datta, JHEP07, 058 (2005). For experiments probing 13 and CP violation phase,see K. Inoue and R. Rameika at ICHEP06, Moscow

What I am going to show

Given a known mass hierarchy (with the help ofmagnetized iron calorimeter),and the knowledge on 13, how the mixing angle 23

can be best extracted in the very long baselineneutrino experiments ?

Solid and dashed test 23-min Solid and dotted test 13-max

Solid and dashed test 23 Solid and dotted test 13

The step functions withrc=11.85 g/cm3

rm=4.67 g/cm3

are good approximation.

Freund and Ohlsson hep-ph/9909501

A. M. Dziewonski and D. L. Anderson,Phys. Earth Planet Int. 25, 297 (1981)

Lc

Lm

Lm

Two density begins at L2Lm+Lc=10673 km

L

Max2 emerges at 7000 km

.0,39.0tan

,eV 102.8,0eV 104.2

122

25221

23231

cp

mm

Y. Ashie et al., Phys. Rev. Lett 93, 101801 (2004)J. N. Bahcall, M. C. Gonzalez-Garcia and C. Pena-Garay, JHEP 0408 (2004)

allowed curvesolution 1only :

anyever are thereif for curvessolution 2 :

2sinon depend and

,12cos2cos

13

23232

pP

P

</4

>/4

Chooz bound

+<<- for invertedhierarchy

min

max

+-->> +

An insight from analytic approximations

For a constant medium density:

.2/,2/

.22

with,2cos2sin

,/27.1sin2sin

,/27.1sin2cos,/27.1sin2sin

,4/,4/,2sin,2cos

1,,1,

31231

23131

231

231

2

13231

2

1323131

231

213

2

231

213

231

213

2

1323

2

mme

mme

eFme

me

m

m

mmm

e

AmmAmM

NEGA

mAm

ELmc

ELMbELa

cbacbazy

yzzzyPzyzzyzzyP

0th order in the series expansion ofm2

21/m231

E. K. Akhmedov et al., JHEP 0404, 078 (2004)

The above forms for oscillation probabilitiescan be generalized to the two-density case:

.27.1

with,4

24

,22sinsin2sin

2sincos22cos2cossin2cos

,sin2sin22coscos2cos

with,sincos4

11

2

1

,sincos4

1

.1,,1,

31

213

213

213

213

131313

131313

1313

2222

22

2

cmcm

cm

c

cc

m

mm

mccm

mcmcmcm

cmmccm

e

LE

LE

mML

E

mMzt

zv

zu

tvtuvuz

tvtuz

yzzzyPzyzzyzzyP

J. Bernabeu, S. Palomares-Ruiz, A. Perez and S.T. Pecov,Phys. Lett. B 531, 90 (2002)

3.02cos3.0 ,2cos22cos

,12cos2cos

232323

23232

d

dP

P

Implications

• The sensitivity of muon neutrino survival probability on 23:

• For measurement at the local maximum, no 23 degeneracy in principle. The sensitivity on 23 is completely determined by +. Reasonable sensitivities at L=7000 km and 11000 km.

2323

2cos22cosd

dP

For measurement at the local minimum, min1, - determines the sensitivity on 23 . Sensitivity increases linearly with cos223. Very small sensitivity at 23=/4.

For measurement along min2, - determines the sensitivity on 23 until L=6000 km. Longer than this baseline, both - and + are equally important.

For 9000 km <L<10500 km, there are good sensitivities on 23 even for 23=/4. More importantly, 23 degeneracy is partially lifted.