Dynamical quark mass and finite volume effects in the Dyson-Schwinger Equations

Abstract

Within the framework of Dyson-Schwinger equations(DSEs) and by means of the Multiple Reflection Expansion approximation, we study the finite volume effects of the constituent quark mass in a strong external magnetic field. Since the magnetic field has influence on the coupling constant, the coupling constant controls the strength of strongly interaction in QCD, so we adopt the magnetic-field-dependent running coupling constant in simulation. The results show that in addition to the magnetic field, the masses of constituent quarks also have a significant dependence on the volume and the running coupling constant. The model behaves close to the infinite volume limit for large size, but the effect of the finite volume is significant when the system size $R$ is about $2-6$ fm.The finite volume effects and the magnetic-field-dependent running coupling constant have considerable influence on the phase transition.