1. Neutrino Flavor ratio on Earth and at Astrophysical sources K.-C. Lai, G.-L. Lin, and T. C. Liu, National Chiao Tung university Taiwan INTERNATIONAL SCHOOL OF NUCLEAR PHYSICS 31st Course Neutrinos in Cosmology, in Astro-, Particle- and Nuclear Physics Erice-Sicily: 16 - 24 September 2009

2. Neutrino flavor ratio at sources (0, 0, 1)  Source (1, 0, 0) Muon damped source (0, 1, 0) ● (1/3,2/3,0) Pion source ●

3. Basic measured parameter definition – R : The ratio of track to shower events. – S: The ratio of two flavor shower. Experimental results are limited by number of detected events,  fluctuation  R and  S Assumed K. Blum, Y. Nir and E. Waxman, arXiv:0706.2070 [hep-ph].

4. Basic idea I: What is the real source we observed. From measured data to original source: P True flavor ratio at source Measured flavor ratio at Earth  R i,th and S i,th R i,exp and S i,exp  22 1  region  2 < 2.3  2 < 11.8 3  region. 00  ’0’0 ’0’0 + Choubey et al., PHYSICAL REVIEW D 77, 113006 (2008)

5. # 1: Only 10% R For E < 0.3PeV, difficult to distinguish e from .  Only R Even at  R/R ~ 10%, could not resolve muon damp source from pion source. muon damp source Pion source R only is unable to determine the original source. Measuring S is necessary. M. C. Gonzalez-Garcia and M. Maltoni, Phys. Rep. 460, 1 (2008); M. Maltoni, T. Schwetz, M. A. Tortola, and J. W. F. Valle, New J. Phys. 6, 122 (2004); S. Choubey, Phys. At. Nucl. 69, 1930 (2006); S. Goswami, Int. J. Mod. Phys. A 21, 1901 (2006); A. Bandyopadhyay, S. Choubey, S. Goswami, S. T. Petcov, and D. P. Roy, Phys. Lett. B 608, 115 (2005); G. L. Fogli et al., Prog. Part. Nucl. Phys. 57, 742 (2006).

6. # 2-1: sin 2  13 =0 for   Can rule-out pion source from muon-damped source under  R/R ~ 10%,  S  /S  ~ (11~14)% Astrophysical hidden source (1/2, a, (2/3 –a)) can be rule-out too. 2015/5/126 sin 2  23 =0.45 sin 2  23 =0.55 muon damp source Pion source Astrophysical Hidden source O. Mena, et al., PRD, 2007

7. # 2-2: sin 2  13 = 0 for   Can't rule-out muon-damped source from pion source under  R/R ~ 10%,  S  /S  ~ (11~12)%, sin 2  23 =0.45sin 2  23 =0.55 muon damp source Pion source

8. # 3-1: CP phase ,   Under  R/R ~ 10%,  S  /S  ~ 13% 2015/5/128 muon damp source sin 2  13 = 0 sin 2  13 = 0.016  0.01 (non zero) Gray:  =0 Blue:  =  /2 Red:  =  Pion source No dependence on CP phase  when (sin 2  13 ) best-fit = 0

9. # 3-2: CP phase  for   muon damp source sin 2  13 = 0 sin 2  13 = 0.016  0.01 Gray:  =0 Blue:  =  /2 Red:  =  Pion source Under  R/R ~ 10%,  S  /S  ~ 13%

10. # 4-1: Critical uncertainty  R  /R  = 13%  S  /S  = 16%  R  /R  = 5%  S  /S  = 6% Need several hundreds of neutrino events to confirm the source.

11. Basic idea II: From Oscillation mechanism to new physics flavor ratio measured on Earth oscillation Possible source flavor ratio oo  ij,  Decay  ij,  Other mechanism

12. Normal hierarchy: sin 2 θ 13 < 0.14 and 0.37 < sin 2 θ 23 <0.65 Inverted hierarchy: sin 2 θ 13 < 0.27 and 0.37 < sin 2 θ 23 <0.69 Possible measured region with different strategy Pion source with normal hierarchy Muon source with normal hierarchy Pion source with inverted hierarchy Muon source with inverted hierarchy * * Inverted hierarchy is only possible # # Allow both hierarchy Super-Kamiokande Collaboration Phys. Rev. D 74, 032002 (2006)

13. All possible measured ratio for neutrino oscillation mechanism Neutrino oscillation # # New physics Beyond osciallation normal hierarchy inverted hierarchy measured ratio All possible source

14. One example: Decay with normal mixing angle # # #: Only decay in this region is available. Michele Maltoni et al JHEP07(2008)064

15. Another example: Decay with inverted hierarchy mixing angle # # # #: Only decay in this region is available.

16. Conclusion Part I Measuring the R ratio only is not sufficient to determine the source type. The Critical uncertainties required to distinguish between pion and muon damped source: for pion source:  R  /R  = 5%  S  /S  = 6% for muon source:  R  /R  = 13%  S  /S  = 16% Part II New method to probe new physics.

17. Reference:

18. The exact form of oscillation probability matrix K.-C. Lai, G.-L. Lin, and T. C. Liu, arXiv:0905.4003 [hep-ph] ω ≡ sin 2 2θ 12, Δ ≡ cos 2 θ 23, D ≡ sinθ 13, δ the CP phase.