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 {βi}-terms, and determines the optimal renormalization scale at each order. Our analysis shows that a more accurate free energy density up to gs5-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 shall be consistent with the Lattice QCD prediction derived at the low temperature.
@article{arxiv.1804.02636,
title = {Properties of the Free Energy Density Using the Principle of Maximum Conformality},
author = {Shi Bu and Xing-Gang Wu and Jian-Ming Shen and Jun Zeng},
journal= {arXiv preprint arXiv:1804.02636},
year = {2018}
}