Spectral properties of $\rho$ meson in a magnetic field

TL;DR

This paper investigates how a weak magnetic field affects the mass, dispersion relation, decay width, and spectral functions of rho mesons, revealing decreases in mass and width, and differences between neutral and charged states.

Contribution

It provides the first detailed calculation of rho meson properties in a magnetic field using effective interaction models, highlighting differences between neutral and charged rho mesons.

Findings

Both rho^0 and rho^± masses decrease with magnetic field.

Decay width of rho mesons decreases as magnetic field increases.

Spectral functions become narrower under magnetic field.

Abstract

We calculate the rho meson mass in a weak magnetic field using effective $\rho\pi\pi$ interaction. It is seen that both $\rho^0$ and $\rho^\pm$ masses decrease with the magnetic field in vacuum. $\rho$ meson dispersion relation has been calculated and shown to be different for $\rho^0$ and $\rho^\pm$. We also calculate the $\rho\pi\pi$ decay width and spectral functions of $\rho^0$ and $\rho^\pm$. The width is seen to decrease with $eB$ and the spectral functions become narrower.