Finite volume effects of the Nambu-Jona-Lasinio model with the running coupling constant

TL;DR

This paper studies how finite volume, magnetic fields, and temperature influence the Nambu-Jona-Lasinio model with a running coupling, revealing their combined effects on quark mass and thermal susceptibility.

Contribution

It introduces a finite volume analysis of the NJL model with a magnetic field-dependent coupling fitted to lattice data, highlighting the interplay of volume, magnetic fields, and temperature.

Findings

Magnetic fields increase the constituent quark mass.

Temperature decreases the quark mass inversely.

Finite volume effects are prominent within a narrow size range.

Abstract

With the Schwinger's proper-time formalism of the Nambu-Jona-Lasinio model, we investigate the finite volume effects in the presence of magnetic fields. Since the coupling constant $G$ can be influenced by strong magnetic fields, the model is solved with a running coupling constant $G(B)$ which is fitted by the lattice average $(\Sigma_u+\Sigma_d)/2$ and difference $\Sigma_u-\Sigma_d$. The investigation mainly focuses on the constituent quark mass and the thermal susceptibility depending on the magnetic fields, the temperatures and the finite sizes. For the model in finite or infinite volume, the magnetic fields can increase the constituent quark mass while the temperatures can decrease it inversely. There is a narrow range of the box length that makes the effects of finite volume perform prominently. The model will behave close to infinite volume limit for larger box length. It is shown that the influence of finite volume can be changed by magnetic fields and temperatures. Finally, we discuss the thermal susceptibility depending on the temperature in finite volume in the presence of magnetic fields.