Properties of the Free Energy Density Using the Principle of Maximum Conformality

TL;DR

This paper applies the principle of maximum conformality (PMC) to study the free energy density at high temperature, achieving scale independence and consistency with lattice QCD results.

Contribution

It introduces a PMC-based method for calculating free energy density, improving accuracy and eliminating renormalization scale dependence in high-temperature QCD.

Findings

Achieves scale-independent free energy density up to order g_s^5.

Finds consistency between PMC predictions and lattice QCD at low temperature.

Demonstrates improved precision over traditional scale-setting methods.

Abstract

We present a detailed study on the properties of the free energy density at the high temperature by applying the principle of maximum conformality (PMC) scale-setting method within the effective field theory. The PMC utilizes the renormalization group equation recursively to identify the occurrence and pattern of the non-conformal $\{\beta_i\}$-terms, and determines the optimal renormalization scale at each order. Our analysis shows that a more accurate free energy density up to $g_s^5$-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 $m_E$, the PMC prediction shall be consistent with the Lattice QCD prediction derived at the low temperature.