Transcript q 13

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
q13
Why is it so interesting ?
 Relatively large q13 opens the possibility to observe
generic 3-flavor effects including CP violation and
mass hierarchy.
the key parameter for next generation of neutrino
oscillation experiments.

q13 << 1
hint for some flavor symmetry
How to measure q13
• Reactors: Disappearance (nenx)
Negligible for
2
Dm132 L
2
2 Dm12 L
P(n e  n e )  1  sin 2q13 sin
 sin 2q12 sin
4E
4E
2
2
Dm312 L 

and sin 2 2q13  103
4 En
2
Use reactors as a source of ne (<En>~3.5 MeV) with a detector 1-2 kms away
and look for non-1/r2 behavior of the ne rate
sin2(2q13)
sin2(2q12)
Dm213
Dm212
Reactor experiments provide the only clean measurement of sin22q13:
no matter effects, no CP violation, no correlation with other parameters.
• Accelerators: Appearance (nmne)
Dm132 L
P(n m  n e )  sin q 23 sin 2q13 sin
 not small terms ( CP , sign(Dm132 ))
4E
2
2
2
Use fairly pure, accelerator produced nm beam with a detector
traveling a long distance from the source and look for
the appearance of ne events
T2K: <En> = 0.7 GeV, L = 295 km
NOnA: <En> = 2.3 GeV, L = 810 km
But, the probability P depends on several parameters which
may be correlated with q13
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
n
energy : ~700 MeV
 ~2,200 nm interactions/yr
at SK for OA 2.5°
GOALS :
(i) measure q13 (ne appearance)
(ii) q23 & Dm²23 (nm disappearance)
To achieve the goals
•
•
•
•
High statistics by a high intense n beam
Tune En at the oscillation maximum
Off-Axis n beam
Narrow band beam to reduce BG
Sub-GeV n beam for Water Cherenkov
0.75MW JHF 50GeV-PS
Super-Kamiokande
4MW Super JHF
Hyper-Kamiokande
Hayato, n2004
T2K Sensitivity Reach
But, measuring q13 by n m  n e appearance
channel suffers from degeneracies
 Intrinsic (, q13)-degeneracy : (Burguet-Castell et al, 2001)
(also: Barger, Marfatia, Whisnant, 2001)
 sgn(Dm213)-degeneracy : (Minakata, Nunokawa, 2001)
 (q23, /2-q23)-degeneracy : (Fogli, Lisi, 1996)
Intrinsic (, q13)-degeneracy
The parameters (, q13 ) can give the same probabilities as another
pair of parameters (*, q*13 ) for fixed values of the other parameters
Ambiguity reduces to (, -)
sgn(Dm213)-degeneracy
There are also parameters (*, q*13 ) with Dm213 <0
the same probabilities (P & P) with Dm213 >0
that give
(q23, /2-q23)-degeneracy
It is sin2 2 q23 determined by nm survival measurement,
So q23 can not distinguished from /2-q23
Yasuda 03
Altogether
8-fold degeneracy
Breaking of degeneracies
 several possibilities to resolve the degeneracies are known:
• combining information from detectors at different
baselines
• using additional oscillation chanels (ne  nt )
• spectral information (wideband beam)
• adding information on q13 from a reactor experiment
• adding information from atmospheric neutrino
experiments
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 q13 in
Korea is different from SK.
T2KK solves 8-fold degeneracy
(Kajita et al., 06)
Impact of astrophysical neutrinos
• Detection of astrophysical neutrinos
• Icecube
O(km) long muon tracks
telescope
• IceCube will distinguish nm, ne, nt based on the event
characteristics:
 nm  m produce long muon tracks
Good angular resolution, but limited energy resolution


ne → e produce EM showers
Good energy resolution, poor angular momentum
nt  t  nt produce double-bang’ events
at high energy.
One shower when t is produced, another
when it decays: n spectra in AGN range
( 1013 - 1016 eV)
Flavor composition of astrophysical neutrino sources
p,
He ...
 ±, K±
L=10-30
km
n
m
e±
n
n
m
e
L=up to 13000
km
 Flavor ratio: ( Fe : Fm : Ft )
 Neutron beam source: (1:0:0) ~ TeV.
HE proton be converted to a HE neutron
(p + g → n + +). Neutrinos are produced
from the neutron decays.
(1:0.4:0.4) at telescope
 Pion beam source: (1:2:0) ~ PeV
(+ → … → e+ + nm+ ne+ nm).
The four leptons share equally the energy of
the pion.
(1:1:1) at telescope
mnm
enmne
 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 +
2
m  m’∑ Re(UmUm’Um’Um) cos(Dm x/2p) +
2 x/2p)
∑
Im(U
U
U
U
)
sin(Dm
m  m’
m m’ m’ m
=  - 2
m<m’∑
Re(UmUm’Um’Um)
Averaged out !
• 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 Dm2
– Use R ≡Fm/(FeFt) for astrophysical sources
• R
neutron beam
= Pem / (Pee+Pet)
~ 0.26 + 0.30 q13 cos CP, (to the first
• R muon damped = Pmm / (Pme+Pmt)
~ 0.66 - 0.52 q13 cos CP
W. Winter, 2006
order in q13 )
• R
pion beam
= (2Pmm +Pem) / (2Pme+Pee+2Pmt+Pet)
~ 0.50 - 0.14 q13 cos CP
• Pme~ 2q132 ± 0.09 q13 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
Sin22q13 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 sin22q13
Impact on (q23, /2-q23)-degeneracy
Astrophysical source may help
to resolve it
Summary
• T2K is next generation neutrino LBL experiment
and will measure q13 through appearance
nm  ne channel
• Measuring q13 will suffer from parameter
degeneracy (8-fold)
• Astrophysical neutrinos with high energy are
complementary to resolve degeneracy.
Appearance channels: nm
ne
(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)
 Complicated, but all interesting information
there: q13, CP, mass hierarchy (via A)
Astrophysical sources
• Astrophysical neutrino sources produce
certain flavor ratios of neutrinos (ne:nm:nt):
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 = fm/(feft)
(conservative, since in future also flavors!?)