Non-Hermitian neutrino oscillations in matter with PT symmetric Hamiltonians

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.

6 pages, 1 figure. Final version (author's post-print version) published in Europhysics Letters

Cited by in corpus (22)

• Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
• Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories
• Spontaneously Breaking Non-Abelian Gauge Symmetry in Non-Hermitian Field Theories
• Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
• PT-Symmetric Non-Hermitian Quantum Field Theories with Supersymmetry
• Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
• Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory
• Relativistic PT-symmetric fermionic theories in 1+1 and 3+1 dimensions
• Light neutrino masses from a non-Hermitian Yukawa theory
• Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians
• Towards perturbative renormalization of ${\varphi }^2(i\varphi {)}^{\epsilon }$ quantum field theory
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Symmetry properties of non-Hermitian PT-symmetric quantum field theories
• Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase
• Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Neutrino mass observables and non-Hermitian version of Type-I seesaw model
• $\mathcal{P}\mathcal{T}-$Symmetric Two-Level Open Quantum Systems: Information Theoretic Facets
• Probing Planck scale effects on absolute mass limit in neutrino flavor evolution