Rho meson decay in presence of magnetic field

TL;DR

This paper derives a general expression for the neutral rho-meson self-energy in a magnetic field and finds that the decay rate remains nearly unchanged in weak magnetic fields.

Contribution

It provides a novel, general formula for the rho-meson self-energy in magnetic fields, applicable to any field strength, and analyzes decay rate modifications in weak fields.

Findings

Decay rate in weak fields is nearly the same as in vacuum.

Derived a general self-energy expression valid for arbitrary magnetic field strengths.

Used Schwinger propagator to incorporate magnetic field effects.

Abstract

We find a general expression for the one-loop self-energy function of neutral $\rho$-meson due to $\pi^+\pi^-$ intermediate state in a background magnetic field, valid for arbitrary magnitudes of the field. The pion propagator used in this expression is given by Schwinger, which depends on a proper-time parameter. Restricting to weak fields, we calculate the decay rate $\Gamma(\rho^0 \rightarrow \pi^+ +\pi^-)$, which changes negligibly from the vacuum value.