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
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
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:
• 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.
Impact of astrophysical neutrinos
→ 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
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