Magnetized pole-mass of neutral $\rho$ meson within full RPA evaluation

TL;DR

This paper calculates the magnetic field dependence of the neutral rho meson mass using a full RPA approach within the NJL model, revealing spin-dependent behaviors consistent with lattice QCD for some projections.

Contribution

It introduces a comprehensive RPA evaluation of the rho meson pole-mass in a magnetized NJL model, including spin projection effects and advanced regularization techniques.

Findings

Mass with s_z=±1 increases with magnetic field, matching lattice QCD.

Mass with s_z=0 shows non-monotonic behavior, decreasing then increasing.

Results highlight spin-dependent magnetic catalysis effects.

Abstract

In this work we calculate the pole-mass of the $\rho^0$ meson with different spin projections $s_z=0,\pm 1$ in the context of the magnetized two-flavor Nambu--Jona--Lasinio model. Making use of the mean field approximation to obtain the effective quark mass as a function of the magnetic field, we apply the random phase approximation (RPA) to the vector channel in order to calculate the polarization function for each spin component. We adopt the magnetic field independent regularization (MFIR) in our evaluations as a method of separating divergences and the Pauli-Villars regularization for the vacuum contributions. The $\rho^0$ meson mass with spin projection $s_z=\pm 1$ is always catalysed with the magnitude of the magnetic field, showing good agreement with Lattice QCD results. The mass projection $s_z=0$ has a non-monotonic behavior, decreasing until the minimum at $eB\lesssim 0.15$ GeV$^2$, which is in contrast with available LQCD data.