BEC-BCS crossover in a cold and magnetized two color NJL model

TL;DR

This paper investigates the BEC-BCS crossover in a two-color NJL model under magnetic fields, revealing how magnetic catalysis and inverse magnetic catalysis influence the critical chemical potential for phase transitions.

Contribution

It provides a comparative analysis of regularization schemes and details the magnetic field effects on the BEC-BCS crossover in a cold, magnetized two-color NJL model.

Findings

Critical chemical potential for BEC transition shows inverse magnetic catalysis.

Critical chemical potential for BEC-BCS crossover is weakly affected by magnetic fields up to a certain strength.

Strong magnetic catalysis occurs at higher magnetic field strengths.

Abstract

The BEC-BCS crossover for a NJL model with diquark interactions is studied in the presence of an external magnetic field. Particular attention is paid to different regularization schemes used in the literature. A thorough comparison of results is performed for the case of a cold and magnetized two-color NJL model. According to our results, the critical chemical potential for the BEC transition exhibits a clear inverse magnetic catalysis effect for magnetic fields in the range $ 1 \lesssim eB/m_\pi^2 \lesssim 20 $. As for the BEC-BCS crossover, the corresponding critical chemical potential is very weakly sensitive to magnetic fields up to $eB \sim 9\ m_\pi^2$, showing a much smaller inverse magnetic catalysis as compared to the BEC transition, and displays a strong magnetic catalysis from this point on.