Thermodynamic potential for quark-qluon plasma with finite quark mass and chemical potential

Abstract

We summarize the derivation of the finite temperature, finite chemical potential thermodynamic potential in the bag-model approximation to quantum chromodynamics (QCD) that includes a finite s-quark mass in the Feynman diagram contributions for both zero-order and two-loop corrections to the quark interaction. The thermodynamic potential for quarks in QCD is a desired ingredient for computations of the equation of state in the early universe, supernovae, neutron stars, and heavy-ion collisions. The 2-loop contributions are normally divergent and become even more difficult in the limit of finite quark masses and finite chemical potential. We describe various means to interpolate between the low and high chemical potential limits. Although physically well motivated, we show that the infinite series Padé rational polynomial interpolation scheme introduces spurious poles. Nevertheless, we show that lower order interpolation schemes such as polynomial interpolation reproduce the Padé result without the presence of spurious poles. We propose that in this way one can determine the equation of state for the two-loop corrections for arbitrary chemical potential, temperature and quark mass. This provides a new realistic bag-model treatment of the QCD equation of state. We compute the QCD phase diagram with up to the two-loop corrections. We show that the two-loop corrections decrease the pressure of the quark-gluon plasma and therefore increase the critical temperature and chemical potential of the phase transition. We also show, however, that the correction for finite s-quark mass in the two-loop correction serves to decrease the critical temperature for the quark-hadron phase transition in the early universe.

Cold quark matter with heavy quarks and the stability of charm stars

“…Such conditions can be introduced by choosing appropriate values of the renormalization scaleΛ, depending on the chosen heavy flavor to be introduced in the system. 5 2 Some years ago, numerical interpolation techniques were used to match massless and massive dense pQCD equations of state [34]. 3 One must be careful when defining these quark masses since they only make sense in the UV regime, where asymptotic freedom takes place.…”

Expansion of Free Energy in the Field of Magnetized Quark–Gluon Plasma

“…Among various models, a MIT bag model has been used extensively. An outstanding work with the bag model was done by many authors [21][22][23][24] under the consideration of zero chemical potential μ and it was considered for the relevance of cosmological quark hadron phase transition. Although MIT bag model was very successful in exploring the phase structure of QGP, there were some disagreement pointed out by the Peshier et al [25,26].…”