Non-Hermitian neutrino oscillations in matter with PT symmetric Hamiltonians

TL;DR

This paper proposes a novel extension of neutrino oscillation theory using non-Hermitian PT symmetric Hamiltonians, revealing new conditions for real spectra and implications for neutrino flavor transitions.

Contribution

It introduces a PT symmetric non-Hermitian formalism for neutrino oscillations, deriving conditions for real spectra and mapping parameters, expanding the theoretical framework.

Findings

Real spectrum depends on new fundamental parameters

Spectrum is either exactly real with maximal mixing or approximately real with small parameters

Extension can produce effects similar to non-standard neutrino interactions

Abstract

We introduce and develop a novel approach to extend the ordinary two-flavor neutrino oscillation formalism in matter using a non-Hermitian PT symmetric effective Hamiltonian. The condition of PT symmetry is weaker and less mathematical than that of hermicity, but more physical, and such an extension of the formalism can give rise to sub-leading effects in neutrino flavor transitions similar to the effects by so-called non-standard neutrino interactions. We derive the necessary conditions for the spectrum of the effective Hamiltonian to be real as well as the mappings between the fundamental and effective parameters. We find that the real spectrum of the effective Hamiltonian will depend on all new fundamental parameters introduced in the non-Hermitian PT symmetric extension of the usual neutrino oscillation formalism and that either i) the spectrum is exact and the effective leptonic mixing must always be maximal or ii) the spectrum is approximate and all new fundamental parameters must be small.