Resolving neutrino parameter degeneracy

3rd International Workshop on a Far Detector in Korea for the J-PARC Neutrino Beam

Sep. 30 and Oct. 1 2007, Univ. of Tokyo, Hongo

Sin Kyu Kang

Seoul National University of Technology

Determination of

Relatively large opens the possibility to

observe generic 3-flavor effects including CP violation and mass hierarchy.

<< 1 hint for some flavor symmetry

Why is it so interesting ?

the key parameter for next generation of neutrino oscillation experiments.

How to measure 13

• Reactors: Disappearance (ex)

Use reactors as a source of e (<E>~3.5 MeV) with a detector 1-2 kms awayand look for non-1/r2 behavior of the e rate

Reactor experiments provide the only clean measurement of sin22: no matter effects, no CP violation, no correlation with other parameters.

sin2(213)

m213

sin2(212)

m212

2 22 2 2 213 12

13 12( ) 1 sin 2 sin sin 2 sin4 4e e

m L m LP

E E

Negligible for

313

2231 102sin and

24

E

Lm

• Accelerators: Appearance (e) 2

2 2 2 21323 13 13( ) sin sin 2 sin not small terms ( , ( ))

4e CP

m LP sign m

E

Use fairly pure, accelerator produced beam with a detector traveling a long distance from the source and look for

the appearance of e events

T2K: <E> = 0.7 GeV, L = 295 km NOA: <E> = 2.3 GeV, L = 810 km

But, the probability P depends on several parameters whichmay be correlated with

T2K experiment

JPARC : 40 GeV PS 0.75 MW for phase I 4 MW for phase II

~2.5° off axis with respect to SK

Peak energy : ~700 MeV

~2,200 nm interactions/yr at SK for OA 2.5°

GOALS : (i) measure 13 (e appearance)

(ii) 23 & m²23 ( disappearance)

• High statistics by a high intense beam• Tune E at the oscillation maximum• Narrow band beam to reduce BG• Sub-GeV beam for Water Cherenkov

0.75MW JHF 50GeV-PS

Off-Axis beam

Super-Kamiokande

To achieve the goals

4MW Super JHF

Hyper-Kamiokande

T2K Sensitivity ReachH

ayat

o,

2004

But, measuring by appearance channel suffers from degeneracies

13 e

Intrinsic (, 13)-degeneracy : (Burguet-Castell et al, 2001)

(also: Barger, Marfatia, Whisnant, 2001) sgn(m2

13)-degeneracy : (Minakata, Nunokawa, 2001)

(23, /2-23)-degeneracy : (Fogli, Lisi, 1996)

Intrinsic (, 13)-degeneracy

The parameters (, 13 ) can give the same probabilities

as another pair of parameters (, ) for fixed values

of the other parameters

Ambiguity reduces to (, -)

sgn(m213)-degeneracy

There are also parameters ( ) with

that give

the same probabilities (P & P) with

m213 <0

m213 >0

(23, /2-23)-degeneracy

It is sin2 2 23 determined by survival measurement,So 23 can not distinguished from /2-23

Yasuda 03

Altogether 8-fold degeneracy

Breaking of degeneracies

• combining information from detectors at different baselines• using additional oscillation chanels (e )• spectral information (wideband beam)• adding information on 13 from a reactor experiment• adding information from atmospheric neutrino experiments

several possibilities to resolve the degeneracies are known:

Breaking neutrino parameter degeneracy at T2KK

• There are two merits of measuring T2K beam in Korea (Hagiwara et al.)

(a) The contribution from become large.

It is useful to determine the sign of

(b) The correlation between CP phase and 13 in

Korea is different from SK.

T2KK solves 8-fold degeneracy (Kajita et al., 06)

Impact of astrophysical neutrinos

• Detection of astrophysical neutrinos telescope

• Icecube

O(km) long muon tracks

→ produce long muon tracks Good angular resolution, but limited energy resolution

e → e produce EM showers Good energy resolution, poor angular momentum

→→ produce double-bang’ events at high energy. One shower when is produced, another

when it decays: spectra in AGN range ( 1013 - 1016 eV)

• IceCube will distinguish e, based on the event characteristics:

Flavor composition of astrophysical neutrino sources

ee

p, He ...

, K

e

e

L=10-30 km

L=up to 13000 km

p, He ...

, K

e

e

L=10-30 km

L=up to 13000 km

Flavor ratio: (e : : )

Neutron beam source: (1:0:0) ~ TeV. HE proton be converted to a HE neutron (p + → n + +). Neutrinos are produced from the neutron decays. (1:0.4:0.4) at telescope

Pion beam source: (1:2:0) ~ PeV (+ → … → e+ + + e+ ). The four leptons share equally the energy of the pion. (1:1:1) at telescope

Muon damped source: (0:1:0) from pion decays with muon absorption. dN/dE ~E-2, eg., from GRB, ~ GeV

• Oscillating probability over a very long travel: P( →, x) = ∑|Um|2|Um|2 + m m’∑ Re(UmUm’Um’Um) cos(m2 x/2p) + m m’∑ Im(UmUm’Um’Um) sin(m2 x/2p)

= - 2 m<m’∑ Re(UmUm’Um’Um)

• The predicted flavor composition at the earth depends on the mixing parameters including CP phase and CP-even part of the mixng only.– No dependence on m2

– Use R ≡e for astrophysical sources

Averaged out !

• R neutron beam = Pe/ (Pee+Pe) ~ 0.26 + 0.30 13 cos CP, (to the first order in 13 )

• R muon damped = P/ (Pe+P) ~ 0.66 - 0.52 13 cos CP

W. Winter, 2006

• R pion beam = (2P +Pe) / (2Pe+Pee+2P+Pe)

~ 0.50 - 0.14 13 cos CP

• Pe~ 2132 ± 0.09 13 sin CP : terr. neutrino beam

Can we obtain useful information on oscilaltion parameters from measuring R ?

Very difficult due to low statistics and no spectral information

But, complementary to the one of Reactor exp. and neutrino beams.

(Winter,06)(Winter,06) Best-fit

Combining reactor experiment with astrophysical neutrios

Assume that reactor exp.(double chooz) measuresSin2213 and astrophys.source is able to providethe information on a similar time scaleas the reactor exp.

(Winter,06)(Winter,06)

Impact on mass hierarchy

• Astrophysical source may help mass hierarchy measurement at superbeam: 20% prec. good

thanks to the fact that mass hierarchy sensitivity is affected by the correlations with cp and

sin2213

Impact on (23, /2-23)-degeneracy

Astrophysical source may help to resolve it

Summary

• T2K is next generation neutrino LBL experiment and will measure 13 through appearance

e channel

• Measuring 13 will suffer from parameter degeneracy (8-fold)

• Astrophysical neutrinos with high energy are complementary to resolve degeneracy.

Appearance channels: e

Complicated, but all interesting information there: 13, CP, mass hierarchy (via A)

(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)

• Astrophysical neutrino sources producecertain flavor ratios of neutrinos (e::):Neutron decays: (1:0:0)Muon damped sources: (0:1:0)Pion decays: (1:2:0)

• These ratios are changed through averaged neutrino oscillations:Only CP-conserving effects remaining ~ cos CP

• Measure muon track to shower ratio at neutrino telescope: R = /(e)(conservative, since in future also flavors!?)

Astrophysical sourcesAstrophysical sources