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, KCL, T.-C. Liu and G.-L. Lin, PRD 89,

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

ErnieErnie

Bert, 1.04PeV Ernie, 1.14PeV

Astrophysical neutrino “Astrophysical” means

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

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:

Q-representationQ-representation

Standard oscillation

Neutrino decay Normalhierarchy Invertedhierarchy

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

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

∆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

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 IceCube

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

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

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,

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

Pion source 1 σ region 3 σ region

Pion source 1 σ region 3 σ region

Pion source 1 σ region 3 σ region

Pion and Muon sources 1 σ region 3 σ region

Pion and Muon sources 1 σ region 3 σ region

Pion and Muon sources 1 σ region 3 σ region

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