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.
Highlights
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
A description of the equation of state (EoS) of matter formed in the early universe, heavyion nuclear collisions, supernovae, or neutron stars should include the consequences of a possible phase transition between hadronic matter and quark gluon plasma (QGP)
There are three aspects of the present work of physical relevance: 1) On the one hand, we have made a study of the importance of two-loop corrections to the QGP EoS. These are shown to be significant even in the massless limit; 2) On the other hand, we have discussed the fact that including the mass of the s-quark in the two-loop correction is divergent, but possible for low to moderate chemical potential by introducing periodic regularization of the relevant Feynman diagrams; and 3) We have shown, that there is a natural way to extrapolate from the low to high chemical potential regime that allows for the inclusion of the finite s-quark mass
Summary
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. 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. Considerable recent progress has been made in this later approach, here we consider the former bag model approach because it is often employed in astrophysical simulations for its simplicity In this approach, it is convenient to compute the EoS for the QGP in terms of the grand thermodynamic potential, Ω(T, V, μ) [10]. In quantum chromodynamics the fields φ are the fermion, gluon, and ghost fields [7]
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