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

Adolfo Flores-Aguilar, Luis A. Hernández, and J. Carlos Márquez

R. Zamora*

  • Centro de Investigación y Desarrollo en Ciencias Aeroespaciales (CIDCA), Academia Politécnica Aeronáutica, Fuerza Aérea de Chile, Casilla 8020744, Santiago, Chile and Facultad de Ingeniería y Arquitectura, Universidad Central de Chile, Av. Sta. Isabel 1186, Santiago 8330601, Chile

  • *Contact author: rrzamora@uc.cl
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Phys. Rev. D 114, 056029 – Published 30 September, 2026

DOI: https://doi.org/10.1103/n97s-wqft

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.

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Phys. Rev. D 114, 056029– Published 30 September, 2026
  • Received 18 May 2026
  • Accepted 11 August 2026
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