Complete one-loop self-energies of the linear sigma model coupled to quarks at finite temperature and in a magnetic field

TL;DR

This paper provides a comprehensive calculation of one-loop self-energies in the linear sigma model coupled to quarks, incorporating finite temperature and magnetic field effects using advanced formalisms.

Contribution

It introduces a unified framework for calculating thermomagnetic corrections in effective QCD models, including charged and neutral particles with detailed treatment of Schwinger phases.

Findings

Explicit expressions for self-energies with thermal and magnetic effects

Systematic evaluation of charged particle contributions using Ritus formalism

Clear separation of vacuum and matter contributions in the self-energy calculations

Abstract

We present a complete calculation of the one-loop self-energies for all fields in the linear sigma model coupled to quarks at finite temperature and in the presence of a uniform magnetic field. The analysis consistently incorporates thermal and magnetic effects for both neutral and charged degrees of freedom, providing a unified framework valid for arbitrary values of the temperature and the field strength. The computation is performed using the Matsubara formalism to account for finite temperature effects and the Schwinger proper-time representation for charged propagators in a magnetic background. Special attention is given to loop contributions involving particles with different electric charges, for which the associated Schwinger phases do not cancel. We show that these terms can be systematically evaluated in coordinate space using the Ritus formalism, which provides the appropriate framework for treating external charged states in the presence of a magnetic background, and consistently expressed in momentum space. The resulting expressions exhibit a nontrivial interplay between thermal fluctuations and magnetic effects and allow for a clear separation between vacuum and matter contributions, providing a well-defined structure for the identification of ultraviolet divergences. Our results establish a consistent and systematic framework for the computation of thermomagnetic one-loop corrections in effective models of QCD, capturing the full interplay between thermal and magnetic effects for all dynamical degrees of freedom.