Models with non-Hermitian Hamiltonian and optical theorem

TL;DR

This paper examines the limitations of the optical theorem when applied to models with non-Hermitian Hamiltonians, especially in the context of $nar{n}$ transitions, highlighting potential errors and providing bounds on oscillation time.

Contribution

It demonstrates that applying the optical theorem to non-unitary $S$-matrix models causes qualitative errors and offers bounds on $nar{n}$ oscillation time using Hermitian Hamiltonian models.

Findings

Optical theorem application leads to qualitative errors in non-Hermitian models.

Lower limit on $nar{n}$ oscillation time is between $10^{16}$ years and $1.2 imes 10^{9}$ seconds.

Non-Hermitian Hamiltonian models may produce inaccurate results for $nar{n}$ transition studies.

Abstract

The applicability of the optical theorem in the models with the non-Hermitian Hamiltonian is studied. By way of example we consider the $n\bar{n}$ transition in a medium followed by annihilation. It is shown that an application of optical theorem for the non-unitary $S$-matrix leads to the qualitative error in the result. The lower limit on the free-space $n\bar{n}$ oscillation time $\tau $ calculated by means of the model with Hermitian Hamiltonian lies in the range $10^{16}\; {\rm yr}>\tau >1.2\cdot 10^{9}\; {\rm s}$.