Volume 421 - Neutrino Oscillation Workshop (NOW2022) - Session III. Multimessenger astrophysics
Analytical treatment of neutrino oscillation and decay in matter
S. Goswami*, D.S. Chattopadhyay, K. Chakraborty and A. Dighe
Full text: pdf
Pre-published on: January 25, 2023
Published on:
Abstract
We discuss the propagation of decaying neutrinos in matter and outline a procedure to obtain the analytic
oscillation probabilities in two and three generation framework. For unstable neutrinos,
the Hermitian and anti-Hermitian components of the effective Hamiltonian
do not commute and cannot be simultaneously diagonalised by unitary transformations for all
matter densities. We present the compact analytic expressions for neutrino probabilities in matter for the two flavour case,
obtained using a re-summation of the inverse Baker-Campbell-Hausdorff (BCH) or Zassenhaus
expansion,
We also outline briefly how the approximate probabilities for the three flavour case can be obtained assuming
only the vacuum mass eigenstate $\nu_3$ decays. We show the baselines and energies where
the different approximations give good matching with the numerical probabilities
DOI: https://doi.org/10.22323/1.421.0059
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