One-loop constituent quark contributions to the vector and axial-vector meson curvature mass

TL;DR

This paper calculates the fermionic one-loop contributions to the curvature masses of vector and axial-vector mesons within a (2+1)-flavor constituent quark-meson model, analyzing temperature effects and mixing phenomena.

Contribution

It provides a transparent derivation of fermionic contributions to vector and axial-vector meson masses and clarifies the renormalization process within the extended linear sigma model.

Findings

Fermionic corrections are expressed as simple integrals involving Fermi-Dirac distributions and Polyakov-loop effects.

Temperature dependence of vector and axial-vector meson masses is characterized.

Renormalization lifts redundancies in the extended linear sigma model.

Abstract

The renormalized contribution of fermions to the curvature masses of vector and axial-vector mesons is derived with two different methods at leading order in the loop expansion applied to the (2+1)-flavor constituent quark-meson model. The corresponding contribution to the curvature masses of the scalar and pseudoscalar mesons, already known in the literature, is rederived in a transparent way. The temperature dependence of the curvature mass of various (axial-)vector modes obtained by decomposing the curvature mass tensor is investigated along with the (axial-)vector--(pseudo)scalar mixing. All fermionic corrections are expressed as simple integrals that involve at finite temperature only the Fermi-Dirac distribution function modified by the Polyakov-loop degrees of freedom. The renormalization of the (axial-)vector curvature mass allows us to lift a redundancy in the original Lagrangian of the globally symmetric extended linear sigma model, in which terms already generated by the covariant derivative were reincluded with different coupling constants.