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

Non-Hermitian neutrino oscillations in matter with PT symmetric Hamiltonians