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Parameter Degeneracy in Neutrino Oscillations (and how to solve it?). INT Program 2010; LBL. Hisakazu Minakata Tokyo Metropolitan University. Purpose of this discussion. To complete n Standard Model (SM + n mass + lepton mixing) measurement of CP phase (KM type) d and q 13 is necessary - PowerPoint PPT Presentation
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Parameter Degeneracy in Neutrino Oscillations (and how to solve it?)
Hisakazu Minakata
Tokyo Metropolitan University
INT Program 2010; LBL ..
Purpose of this discussion
• To complete Standard Model (SM + mass + lepton mixing) measurement of CP phase (KM type) and13is necessary
• It seems that is not so easy to determine them, in particular
• If any theoretical issues involved we shall try to remove them
• One of them is P degeneracy
July 27, 2010 INT Program LBL
P degeneracy
• P degeneracy is the fact that measurement of oscillation probability P and -bar oscillation probability bar-P at an energy (which would determine 13 and actually do NOT lead to a unique solution of 13 and
• Experts may say that they know everything
July 27, 2010 INT Program LBL
Is this true? To what extent?
An example; Intrinsic degeneracy
July 27, 2010 INT Program LBL
P degeneracy is simplest to see by bi-P plot (HM-H.Nunokawa 01)
Is P degeneracy necessarily two-fold?
July 27, 2010 INT Program LBL
Intrinsic degeneracy; S. Uchinami for PhD thesis
But, the answer is NO !People suspect
the answer is YES because
July 27, 2010 INT Program LBL
ParameterDegeneracy;
definition
P degeneracy
• Let us assume that all the mixing parameters besides 13 and are known
• measurement of oscillation probability Pe and bar- oscillation probability bar-Pe at an energy E (which would determine 13 and do NOT lead to unique solution of 13 and
• Easy to solve mathematically: measurement at E=E1 and E2 (or adding more channel) solves the degeneracyJuly 27, 2010 INT Program LBL
Intrinsic degeneracy (Burguet-C. et al. 01)
P degeneracy (continued)
• the mixing parameters besides 13 and are not known so precisely
• Mass hierarchy is not known, and may not be known either at the time of measurement of CP phase
• More solutions of 13 and
•
July 27, 2010 INT Program LBL
Sign m231
degeneracy (HM-Nunokawa 01)
23 octant degeneracy (Fogli-Lisi 96)
July 27, 2010 INT Program LBL
P degeneracy is doubled by unknown mass hierarchy
• You can draw two ellipses from a point in P-Pbar space
• Intrinsic degeneracy
• Doubled by the unknown sign of m2
• 4-fold degeneracy
July 27, 2010 INT Program LBL
A well-defined
framework for P
degeneracy
I use Cervera et al. formula for oscillation probabilities
July 27, 2010 INT Program LBL
You can show 2x2x2=8
P degeneracy; Generalized version
• Similar degeneracy occurs in, in addition to (P, PCP),
• T-conjugate (P=Pe, PT=Pe)
• CPT-conjugate (P, PCPT)
• Golden-silver (PT, PS) channels
July 27, 2010 INT Program LBL
Generally, P degeneracy has simpler structure
July 27, 2010 INT Program LBL
P-degenerac
y as an invariance
of P
P-dege. from symmetry of the probability
July 27, 2010 INT Program LBL
are invariant under transf.
PT and PS are also invariant under the same transformation
(1) P degeneracy obvious (2) Form of the degeneracy solutions are determined by the symmetry
July 27, 2010 INT Program LBL
How to obtain
degeneracy solutions?
An example; intrinsic degeneracy
July 27, 2010 INT Program LBL
An example; intrinsic degeneracy2
July 27, 2010 INT Program LBL
4th-order eq. of s13!
P degeneracy as a re-parametrization invariance
July 27, 2010 INT Program LBL
Degeneracy solutions form network!
July 27, 2010 INT Program LBL
Degeneracy
solutions; how they look like?
13
July 27, 2010 INT Program LBL
II
III
V
July 27, 2010 INT Program LBL
I focus energy dependence; 13
July 27, 2010 INT Program LBL
I focus energy dependence;
July 27, 2010 INT Program LBL
July 27, 2010 INT Program LBL
How to solve P
degeneracy?
July 27, 2010 INT Program LBL
Varying E at long enough baseline
• Vacuum effect comes in with L/E• Matter effect comes in with aL• Varying E implies to change relative importance
between vacuum and matter effects (varying L not)• powerful for mass hierarchy
a=sqrt{2}GFNea=sqrt{2}GFNe
atmosphericatmospheric
solarsolar
the best way for everything if perfect event reconstruction with 2-3 oscillation periods spanned
the best way for everything if perfect event reconstruction with 2-3 oscillation periods spanned
July 27, 2010 INT Program LBL
Project X: Off-axis NOVA --> VLBL multi-OM type approachProject X: Off-axis NOVA --> VLBL multi-OM type approach
July 27, 2010 INT Program LBL
Practical issues in VLBL approach• In water background at low
energies for high energy beam highly nontrivial -> see next page
• How reliable is the event reconstruction & background rejection algorithm ?
• Energy resolution • Alternative way; ~100 kt scale
Liquid Ar detector => feasible when?
July 27, 2010 INT Program LBL
Background at low E for HE beam
Fanny Dufour@3rd T2KK WSFanny Dufour@3rd T2KK WS
July 27, 2010 INT Program LBL
Varying L
• Matter effect comes in with (aL/2) = ~0.27 and relatively small even at L ~ 1000 km
• By varying L, the trigonometric nature of the oscillations manifests itself (spectrum analysis helps)
• Good for CPV search (w. spectrum analysis)
If a=sqrt{2}GFNe is small If a=sqrt{2}GFNe is small
July 27, 2010 INT Program LBL
Two detector
method is powerful
July 27, 2010 INT Program LBL
Kamioka-Korea 2 detector setting
Why don’t you bring one of the 2 tanks to Korea? (@EPP2010)
Why don’t you bring one of the 2 tanks to Korea? (@EPP2010)
July 27, 2010 INT Program LBL
Original idea: sensitive because dynamism in 2nd oscillation maximum
July 27, 2010 INT Program LBL
Spectral information solves intrinsic degeneracy
from 1000 page Ishitsuka file
from 1000 page Ishitsuka file
SK momentum resolution ~30 MeV at 1 GeVSK momentum resolution ~30 MeV at 1 GeV
T2KT2K T2KKT2KK
2 detector method powerful!2 detector method powerful!
Ishitsuka-Kajita-HM-Nunokawa 05
July 27, 2010 INT Program LBL
Two-detector setting is powerful
• With the same input parameter and Korean detector of 0.54 Mt the sign-m2 degeneracy is NOT completely resolved
T2KKT2KK Korea onlyKorea only
July 27, 2010 INT Program LBL
T2KK vs. T2K II Comparison T2KK vs. T2K II Comparison Total mass of the detectors = 0.54 Mton fid. mass4 years neutrino beam + 4 years anti-neutrino beam
Total mass of the detectors = 0.54 Mton fid. mass4 years neutrino beam + 4 years anti-neutrino beam
3 (thick)3 (thick) 2 (thin)2 (thin)
Mass hierarchyMass hierarchy CP violation (sin≠0)CP violation (sin≠0)
hep-ph/0504026
T2K
T2KK
July 27, 2010 INT Program LBL
Relative cross section error does matter
• Identical 2 detector setting robust to larger systematic error • It gives conservative lower bounds on sensitivity estimate
of mass hierarchy and CP
Barger et al. 07
Barger et al. 07
T2K IIT2K II
T2KKT2KK
July 27, 2010 INT Program LBL
T2KK can solve 23 degeneracy in situ
T2K-II + phase II reactorT2KK=0 assumed
sin
2 2
13
sin2 23
sin
2 2
13
> 32~3
T2KK 2(rough)
T2KK has better sensitivityat sin2 213 < 0.06~0.07 .
hep-ph/0601258
July 27, 2010 INT Program LBL
Conclusion
• Global overview of P degeneracy is given
• In some cases, P degeneracy can be understood by the symmetry argument
• More generically it is an invariance under discrete mapping of mixing parameters whose explicit form should be obtained by solving equations
• Sign-m2 and 23 octant degeneracies are robust against spectrum analysis
• Some ideas are discussed on how to solve P degeneracy
Another example; sign-m2 degeneracy
July 27, 2010 INT Program LBL
Another example; sign-m2 degeneracy2
July 27, 2010 INT Program LBL
Another example; sign-m2 degeneracy3
July 27, 2010 INT Program LBL
July 27, 2010 INT Program LBL
Neutrino factory
July 27, 2010 INT Program LBL
Nufact
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