Resolving neutrino parameter degeneracy 3rd International Workshop on a Far Detector in Korea for the J-PARC Neutrino Beam Sep. 30 and Oct , 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 ( e  x ) Use reactors as a source of e ( ~3.5 MeV) with a detector 1-2 kms away and look for non-1/r 2 behavior of the e rate Reactor experiments provide the only clean measurement of sin 2 2   : no matter effects, no CP violation, no correlation with other parameters. sin 2 (2  13 )  m 2 13 sin 2 (2  12 )  m 2 12 Negligible for

Accelerators: Appearance (   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: = 0.7 GeV, L = 295 km NO A: = 2.3 GeV, L = 810 km But, the probability P depends on several parameters which may 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 &  m² 23 (  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 Reach Hayato, 2004

But, measuring by appearance channel suffers from degeneracies  Intrinsic ( ,  13 )- degeneracy : (Burguet-Castell et al, 2001) (also: Barger, Marfatia, Whisnant, 2001)  sgn(  m 2 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(  m 2 13 )-degeneracy There are also parameters (      ) with that give the same probabilities (P & P) with  m 2 13 <0  m 2 13 >0

(  23,  /2-  23 )- degeneracy It is sin 2 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 ( eV) IceCube will distinguish   e,  based on the event characteristics:

Flavor composition of astrophysical neutrino sources       e   e p, He...  , K   e   e L=10-30 km L=up to km p, He...  , K   e   e L=10-30 km L=up to 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) = ∑|U  m | 2 |U  m | 2 + m  m’ ∑ Re(U  m U  m’ U  m’ U  m ) cos(  m 2 x/2p) + m  m’ ∑ Im(U  m U  m’ U  m’ U  m ) sin(  m 2 x/2p) =   - 2 m<m’ ∑ Re(U  m U  m’ U  m’ U  m ) 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  m 2 –Use R ≡    e    for astrophysical sources Averaged out !

R neutron beam = P e   / (P ee +P e  ) ~  13 cos  CP, ( to the first order in  13 ) R muon damped = P  / (P  e +P  ) ~  13 cos  CP W. Winter, 2006

R pion beam = (2P  +P e  ) / (2P  e +P ee +2P  +P e  ) ~  13 cos  CP P  e ~ 2  13 2 ± 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) Best-fit

Combining reactor experiment with astrophysical neutrios Assume that reactor exp. (double chooz) measures Sin 2 2  13 and astrophys. source is able to provide the information on a similar time scale as the reactor exp. (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 sin 2 2  13

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 produce certain 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 sources