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Parameter Degeneracy in Neutrino Oscillations (and how to solve it?)

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

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Parameter Degeneracy in Neutrino Oscillations (and how to solve it?)

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  1. Parameter Degeneracy in Neutrino Oscillations (and how to solve it?) INT Program 2010; LBL .. Hisakazu Minakata Tokyo Metropolitan University

  2. Purpose of this discussion • To complete n Standard Model (SM + n mass + lepton mixing) measurement of CP phase (KM type) dandq13is necessary • It seems that is not so easy to determine them, in particular d • If any theoretical issues involved we shall try to remove them • One of them is P degeneracy INT Program LBL

  3. P degeneracy • P degeneracy is the fact that measurement of n oscillation probability P and n-bar oscillation probability bar-P at an energy (which would determine q13 and d) actually do NOT lead to a unique solution of q13 and d • Experts may say that they know everything Is this true? To what extent? INT Program LBL

  4. An example; Intrinsic degeneracy P degeneracy is simplest to see by bi-P plot (HM-H.Nunokawa 01) INT Program LBL

  5. Is P degeneracy necessarily two-fold? But, the answer is NO ! People suspect the answer is YES because Intrinsic degeneracy; S. Uchinami for PhD thesis INT Program LBL

  6. Parameter Degeneracy; definition INT Program LBL

  7. P degeneracy • Let us assume that all the mixing parameters besides q13 and dare known • measurement of n oscillation probability Pmeand bar-n oscillation probability bar-Pmeat an energy E (which would determine q13 and d) do NOT lead to unique solution of q13 and d • Easy to solve mathematically: measurement at E=E1 and E2 (or adding more channel) solves the degeneracy Intrinsic degeneracy (Burguet-C. et al. 01) INT Program LBL

  8. P degeneracy (continued) • the mixing parameters besides q13 and d are not known so precisely • Mass hierarchy is not known, and may not be known either at the time of measurement of CP phase d • More solutions of q13 and d: Sign Dm231 degeneracy (HM-Nunokawa 01) q23octant degeneracy (Fogli-Lisi 96) INT Program LBL

  9. 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 INT Program LBL

  10. A well-defined framework for P degeneracy INT Program LBL

  11. I use Cervera et al. formula for n oscillation probabilities You can show 2x2x2=8 INT Program LBL

  12. P degeneracy; Generalized version • Similar degeneracy occurs in, in addition to (P, PCP), • T-conjugate (P=Pme, PT=Pem) • CPT-conjugate (P, PCPT) • Golden-silver (PT, PS) channels Generally, P degeneracy has simpler structure INT Program LBL

  13. P-degeneracy as an invariance of P INT Program LBL

  14. P-dege. from symmetry of the probability 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 INT Program LBL

  15. How to obtain degeneracy solutions? INT Program LBL

  16. An example; intrinsic degeneracy INT Program LBL

  17. An example; intrinsic degeneracy2 4th-order eq. of s13! INT Program LBL

  18. P degeneracy as a re-parametrization invariance Degeneracy solutions form network! INT Program LBL

  19. Degeneracy solutions; how they look like? INT Program LBL

  20. q13 II III V INT Program LBL

  21. d INT Program LBL

  22. I focus energy dependence; q13 INT Program LBL

  23. I focus energy dependence; d INT Program LBL

  24. How to solve P degeneracy? INT Program LBL

  25. Varying E at long enough baseline atmospheric • 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 solar a=sqrt{2}GFNe the best way for everything if perfect event reconstruction with 2-3 oscillation periods spanned INT Program LBL

  26. Project X: Off-axis NOVA --> VLBL multi-OM type approach INT Program LBL

  27. 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? INT Program LBL

  28. Background at low E for HE  beam Fanny Dufour@3rd T2KK WS INT Program LBL

  29. Varying L If a=sqrt{2}GFNe is small • 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) INT Program LBL

  30. Two detector method is powerful INT Program LBL

  31. Kamioka-Korea 2 detector setting Why don’t you bring one of the 2 tanks to Korea? (@EPP2010) INT Program LBL

  32. Original idea: sensitive because dynamism in 2nd oscillation maximum INT Program LBL

  33. from 1000 page Ishitsuka file Spectral information solvesintrinsic degeneracy T2K T2KK 2 detector method powerful! SK momentum resolution ~30 MeV at 1 GeV Ishitsuka-Kajita-HM-Nunokawa 05 INT Program LBL

  34. Two-detector setting is powerful T2KK Korea only • With the same input parameter and Korean detector of 0.54 Mt the sign-m2 degeneracy is NOT completely resolved INT Program LBL

  35. T2KK vs. T2K II Comparison hep-ph/0504026 Total mass of the detectors = 0.54 Mton fid. mass 4 years neutrino beam + 4 years anti-neutrino beam T2KK Mass hierarchy CP violation (sind≠0) T2K 3 s (thick) 2 s (thin) INT Program LBL

  36. Relative cross section error does matter T2KK • 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 T2K II INT Program LBL

  37. T2KK can solve q23 degeneracy in situ d=0 assumed T2K-II + phase II reactor T2KK sin2 2q13 T2KK 2s (rough) > 3s 2~3s sin2 2q13 hep-ph/0601258 T2KK has better sensitivity at sin2 2q13 < 0.06~0.07 . INT Program LBL sin2 q23

  38. 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-Dm2 and q23 octant degeneracies are robust against spectrum analysis • Some ideas are discussed on how to solve P degeneracy INT Program LBL

  39. Another example; sign-Dm2 degeneracy INT Program LBL

  40. Another example; sign-Dm2 degeneracy2 INT Program LBL

  41. Another example; sign-Dm2 degeneracy3 INT Program LBL

  42. Neutrino factory INT Program LBL

  43. Nufact INT Program LBL

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