1. Probing neutrino flavor transition mechanism with ultrahigh energy astrophysical neutrinos 賴光昶長庚大學通識中心賴光昶長庚大學通識中心 2014 海峡两岸粒子物理与宇宙学研讨会 黃山，安徽， May 9th, 2014 KCL, T.-C. Liu and G.-L. Lin, PRD 82, 103003 KCL, T.-C. Liu and G.-L. Lin, PRD 89, 033002

2. Astrophysical neutrino Neutrino flavor transition Neutrino signals in neutrino telescopes Test of transition models

3. ErnieErnie

4. Bert, 1.04PeV Ernie, 1.14PeV

5. Astrophysical neutrino “Astrophysical” means

6. Q-representation Standard oscillation Neutrino decay Quantum decoherence Pseudo-Dirac neutrino Flavor transition

7. Q-representationQ-representation neutrino on Earth →φ=Pφ 0 ← neutrino at the source φ 0 =(φ 0 (), φ 0 (), φ 0 ())=1/3V 1 +aV 2 +bV 3 φ 0 =(φ 0 (ν e ), φ 0 (ν μ ), φ 0 (ν τ ))=1/3V 1 +aV 2 +bV 3 φ= ϰ V 1 + ϱ V 2 +λV 3 ( ϰ, ϱ, λ ) T = Q ( 1 / 3, a, b ) T ⇒ Q≡A -1 PA Tri-bimaximal matrix, eigenvectors of TBM:

8. Q-representationQ-representation

9. Standard oscillation

10. Neutrino decay Normalhierarchy Invertedhierarchy

11. The heaviest and middle states decay into the lightest one(j=1 or 3).-dec1 The heaviest state decays into the middle and lightest ones.- dec2 { ε 1 = cos 2 ϑ 23 -(√2/3)sin ϑ 13, ε 2 =(1/2) cos 2 ϑ 23 - ε 1

12. Quantum decoherence distance dependent γ →0 or d→∞, Q dc =Q osc

13. ∆m i 2 : the mass-squared difference between active and sterile states. Pseudo-Dirac neutrino ∆m i 2 =∆m 2 In the limit of L(z)/4E ν ≫ 1/∆m i 2, Q pd =1/2 Q osc

15. Neutrino events 125m corresponds to the decay length of a 2.5 PeV tau lepton.-dist. between strings ≈1km corresponds to the decay length of a 25 PeV tau lepton.-size of IceCube ≈1km corresponds to the decay length of a 25 PeV tau lepton.-size of IceCube1054.5154

16. ObservablesObservables Case I: E ν <33PeV Case II: E ν >33PeV R I = ϕ (ν μ )/( ϕ (ν e )+ ϕ (ν τ )) S I = ϕ (ν e )/ ϕ (ν τ ) R II = ϕ (ν e )/( ϕ (ν μ )+ ϕ (ν τ )) S II = ϕ (ν μ )/ ϕ (ν τ ) R I : track-to-shower ratio; R II :shower-to-track ratio

17. ObservablesObservables ϕ 0 =( ϕ (ν e ), ϕ (ν μ ), ϕ (ν τ ))=1/3 V 1 +aV 2 +bV 3. for non-ν τ sources, a=-1/3+b and let R II ≡R. flux conservation assumed For pion and damped-muon sources

18. Statistical analysis We consider: i=π, only pion source i=π, only pion source i=π and µ, both pion and damped-muon source i=π and µ, both pion and damped-muon source σ =10% assumed σ =10% assumed G. Fogli, et al., PRD 86, 013012

19. Statistical analysis Legend: ✕ : oscillation ✕ : oscillation ▵ : dec1-n, ▴ :dec1-i ▵ : dec1-n, ▴ :dec1-i ￮, ◇, ⃞ : dec2-n￮, ◇, ⃞ : dec2-n, ◆, ▪ : dec2-i, ◆, ▪ : dec2-i

20. Pion source 1 σ region 3 σ region

21. Pion source 1 σ region 3 σ region

22. Pion source 1 σ region 3 σ region

23. Pion and Muon sources 1 σ region 3 σ region

24. Pion and Muon sources 1 σ region 3 σ region

25. Pion and Muon sources 1 σ region 3 σ region

26. SummarySummary Neutrino astronomy has begun. ✦ 28 astrophysical events observed Flavor transitions can be probed: ✦ Q-representation ✦ Observable defined ✦ 2 -analysis performed