A magnetic field independent regularization scheme (zMFIR) based on the Hurwitz-Riemann zeta function is introduced. The new technique is applied to the regularization of the mean-field thermodynamic potential and mass gap equation within the SU(2) Nambu-Jona-Lasinio model in a hot and magnetized medium. The equivalence of the new and the standard MFIR scheme is demonstrated. The neutral meson pole mass is calculated in a hot and magnetized medium and the advantages of using the new regularization scheme are shown.

We study the regularization dependence of the Nambu-Jona–Lasinio model (NJL) predictions for some properties of magnetized quark matter at zero temperature (and baryonic density) in the mean field approximation. The model parameter dependence for each regularization procedure is also analyzed in detail. We calculate the average and difference of the quark condensates using different regularization methods and compare with recent lattice results. In this context, the reliability of the different regularization procedures is discussed.

We studied the effect of a strong magnetic field ($B$) on the electrical conductivity of hot quark matter. The electrical conductivity is a key transport coefficient determining the time dependence and strength of magnetic fields generated in a relativistic heavy-ion collision. A magnetic field induces Hall anisotropic conduction, phase-space Landau-level quantization and, if sufficiently strong, interferes with prominent QCD phenomena such as dynamical quark mass generation, likely affecting the quark matter electrical conductivity, which depends strongly on the quark masses. To address these issues, we used a quasiparticle description of quark matter in which the electric charge carriers are constituent quarks with temperature- and magnetic-field-dependent masses predicted by a Nambu–Jona-Lasinio model. The model accurately describes recent lattice QCD results showing magnetic catalysis at low temperatures and inverse magnetic catalysis at temperatures close to the pseudocritical temperature ($T_{\mathrm{pc}}$) of the QCD phase transition. We found that the magnetic field increases the conductivity component parallel to it and decreases the transverse component, in qualitative agreement with recent lattice QCD results. In addition, we found that (1) the space anisotropy of the conductivity increases with $B$, (2) the longitudinal conductivity increases due to phase-space Landau-level quantization, (3) a lowest Landau level approximation behaves poorly for temperatures close to $T_{\mathrm{pc}}$, and (5) inverse magnetic catalysis leaves a distinctive signal in all components of the conductivity, a prominent peak at $T_{\mathrm{pc}}$. Our study adds to the existing body of work on the hot quark matter electrical conductivity by incorporating nontrivial temperature and magnetic field effects on dynamical mass generation. Our results are useful both for studies employing magnetohydrodynamics simulations of heavy-ion collisions and for getting insight on lattice QCD results.

We compute the QCD equation of state for zero temperature and finite isospin density within the Nambu–Jona-Lasinio model in the mean field approximation, motivated by the recently obtained lattice QCD results for a new class of compact stars: pion stars. We have considered both the commonly used traditional cutoff regularization scheme and the medium separation scheme, where in the latter purely vacuum contributions are separated in such a way that one is left with ultraviolet divergent momentum integrals depending only on vacuum quantities. We have also compared our results with the recent results from lattice QCD and chiral perturbation theory.