Abstract
We present a detailed study on the properties of the free energy density at high temperature by applying the principle of maximum conformality (PMC) scale-setting method within effective field theory. The PMC utilizes the renormalization group equation recursively to identify the occurrence and pattern of the non-conformal {βi}-terms, and determines the optimal renormalization scale at each order. Our analysis shows that a more accurate free energy density up to -order level without renormalization scale dependence can be achieved by applying the PMC. We also observe that by using a smaller factorization scale around the effective parameter mE, the PMC prediction is consistent with the lattice QCD prediction derived at low temperature.
Highlights
At extremely high temperature, the hadronic matter are assumed to occur a phase transition to the quarkgluon plasma (QGP)
The QGP might come from the early universe up to a few milliseconds after the Big Bang or from the heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadronic Collider (LHC), and etc
We shall focus on the circumstance that the QGP has a high temperature T (T is considered as a measure of the average energy of the constituents), indicating the quarks and gluons are of high energy and the strong couplings among them are small due to asymptotic freedom
Summary
The hadronic matter are assumed to occur a phase transition to the quarkgluon plasma (QGP). We shall focus on the circumstance that the QGP has a high temperature T (T is considered as a measure of the average energy of the constituents), indicating the quarks and gluons are of high energy and the strong couplings among them are small due to asymptotic freedom Within this temperature region, the pQCD theory is a feasible tool to study the free energy density. One usually sets μr = 2πT , which corresponds to the energy of the first non-vanishing Matsubara mode [35] Such a simple choice of “guessed” scale leads to the miss-matching of the perturbative coefficients to the strong coupling constant, resulting in the well-known scheme-and-scale ambiguities persist at any fixed order [36,37,38,39,40,41].
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