Analytic treatment of 3-flavor neutrino oscillation and decay in matter

Abstract

We present compact analytic expressions for 3-flavor neutrino oscillation probabilities with invisible neutrino decay, where matter effects have been explicitly included. We take into account the possibility that the oscillation and decay components of the effective Hamiltonian do not commute. This is achieved by employing the techniques of inverse Baker-Campbell-Hausdorff (BCH) expansion and the Cayley-Hamilton theorem applied in the 3-flavor framework. If only the vacuum mass eigenstate ν3 decays, we show that the treatment of neutrino propagation may be reduced to an effective 2-flavor analysis in the One Mass Scale Dominance (OMSD) approximation. The oscillation probabilities for Pμμ, Pee, Peμ and Pμe — relevant for reactor, long baseline and atmospheric neutrino experiments — are obtained as perturbative expansions for the case of only ν3 decay, as well as for the more general scenario where all components of the decay matrix are non-zero. The analytic results thus obtained match the exact numerical results for constant density matter to a high precision and provide physical insights into possible effects of the decay of neutrinos as they propagate through Earth matter. We find that the effects of neutrino decay are most likely to be observable in Pμμ. We also point out that at any long baseline, the oscillation dips in Pμμ can show higher survival probabilities in the case with decay than without decay, and explain this feature using our analytic approximations.

Determining the neutrino mass ordering and oscillation parameters with KM3NeT/ORCA

“…OscProb numerical computations are compatible with analytical expressions for neutrino decay in matter derived in refs [24,25]…”

Oscillation and Decay of Neutrinos in Matter: An Analytic Treatment

“…We have also obtained the probability expressions with exact dependence on γ 3 [4]. In addition to the naively expected e −γ 3 ∆ behavior, analytic expressions also involve additional terms with non-trivial dependence on γ 3 .…”

“…From the probability expression with exact dependence on γ 3 in [4], we obtain the leading contribution to the survival probability P µµ due to ν 3 decay as…”

“…We employ the Cayley-Hamilton theorem to calculate the neutrino oscillation probabilities for long-baseline neutrino experiments like DUNE. The analytic expressions [4] help in understanding the nature of modifications to oscillation probabilities in the presence of neutrino decay and will aid in the interpretation of future data.…”

“…Figure 1.The top panels show the probabilities P µe and P µµ with γ 3 = 0.1, for L = 1300 km, for the analytic expressions mentioned in these Proceedings, as well as for the One Mass Scale Dominance (OMSD) approximation[4]. The bottom panels show the absolute accuracy |∆P αβ | of these approximations.…”