SU(3) Polyakov linear-sigma model in magnetic fields: Thermodynamics, higher-order moments, chiral phase structure, and meson masses

Abstract

Effects of an external magnetic field on various properties of quantum chromodynamics (QCD) matter under extreme conditions of temperature and density (chemical potential) have been analyzed. To this end, we use SU(3) Polyakov linear-sigma model and assume that the external magnetic field (eB) adds some restrictions to the quarks' energy due to the existence of free charges in the plasma phase. In doing this, we apply the Landau theory of quantization, which assumes that the cyclotron orbits of charged particles in a magnetic field should be quantized. This requires an additional temperature to drive the system through the chiral phase transition. Accordingly, the dependence of the critical temperature of chiral and confinement phase transitions on the magnetic field is characterized. Based on this, we have studied the thermal evolution of thermodynamic quantities (energy density and trace anomaly) and the first four higher-order moment of particle multiplicity. Having all these calculations, we have studied the effects of the magnetic field on the chiral phase transition. We found that both critical temperature T-c and critical chemical potential increase with increasing magnetic field, eB. Last but not least, the magnetic effects of the thermal evolution of four scalar and four pseudoscalar meson states are studied. We concluded that the meson masses decrease as the temperature increases up to T-c. Then, the vacuum effect becomes dominant and rapidly increases with the temperature T. At low T, the scalar meson masses normalized to the lowest Matsubara frequency rapidly decrease as T increases. Then, starting from T-c, we find that the thermal dependence almost vanishes. Furthermore, the meson masses increase with increasing magnetic field. This gives a characteristic phase diagram of T vs external magnetic field eB. At high T, we find that the masses of almost all meson states become temperature independent. It is worthwhile to highlight that the various meson states likely have different critical temperatures.