Entropy Density and Speed of Sound from Improved Energy-Momentum Tensor in Lattice QCD

Abstract

We present a lattice calculation of the entropy density of gluedynamics in the region near the critical temperature, Tc, in the deconfined phase. By exploring the temperature dependence of entropy density in this temperature regime, we aim to analyse the significant discrepancies between the previous computations. The calculation of entropy density is carried out by numerical simulation of O(a4) mean-field improved energy-momentum tensor (EMT) of SU(3) lattice gauge theory. We expand on reaching O(a4) improvement using tadpole-improved Symanzik action. The entropy density is calculated directly from the expectation value of the space-time component of the improved EMT in the presence of shifted boundary conditions at several lattice spacings (a≈0.043−0.012 fm). The absence of ultraviolet divergences and the minimal discretisation effects allow for the precision determination of the entropy density. It is demonstrated that the entropy density can be extrapolated to the continuum limit with precision and control. Furthermore, the continuum results are well represented by Pade approximation and in good agreement with the results of previous high-precision data obtained using the gradient flow method. We find that at temperatures of about 3Tc, deviations of entropy density from the Stefan-Boltzmann limit for a free theory are about 10%. The speed of sound in SU(3) gluedynamics is found to be c2s≤0.333 in the temperature region 1.06Tc≤T≤3.05Tc explored in this study.