Lifetime and mass of rho meson in correlation with magnetic-dimensional reduction

TL;DR

This paper investigates how strong magnetic fields influence the lifetime and mass of the neutral rho meson, revealing complex polarization-dependent behavior due to magnetic dimensional reduction effects.

Contribution

It provides a detailed calculation of rho meson properties in magnetic fields, highlighting the polarization-dependent mass and width modifications caused by Landau quantization and dimensional reduction.

Findings

Rho meson width for s_z=0 peaks and vanishes at a critical magnetic field.

Decay rates for s_z=-1,+1 increase monotonically with magnetic field.

Polarization dependence is linked to Landau-level truncation effects.

Abstract

It is simply anticipated that in a strong magnetic configuration, the Landau quantization ceases the neutral rho meson to decay to the charged pion pair, so the neutral rho meson will be long-lived. To closely access this naive observation, we explicitly compute the charged pion-loop in the magnetic field at the one-loop level, to evaluate the magnetic dependence of the lifetime for the neutral rho meson as well as its mass.Due to the dimensional reduction induced by the magnetic field (violation of the Lorentz invariance), the polarization (spin $s_z=-1,0,+1$) modes of the rho meson, as well as the corresponding pole mass and width, are decomposed in a nontrivial manner compared to the vacuum case. To see the significance of the reduction effect, we simply take the lowest-Landau level approximation to analyze the spin-dependent rho masses and widths. We find that the "fate" of the rho meson may be more complicated because of the magnetic-dimensional reduction: as the magnetic field increases, the rho width for the spin $s_z=0$ starts to develop, reach a peak, to be vanishing at the critical magnetic field to which the folklore refers. On the other side, the decay rates of the other rhos for $s_z=-1,+1$ monotonically increase as the magnetic field develops. The correlation between the polarization dependence and the Landau-level truncation is also addressed.