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

Mar 2023

We present a lattice calculation of the entropy density of gluedynamics inthe region near the critical temperature, $T_{c}$, in the deconfined phase. Byexploring the temperature dependence of entropy density in this temperatureregime, we aim to analyse the significant discrepancies between the previouscomputations. The calculation of entropy density is carried out by numericalsimulation of $O(a^{4})$ mean-field improved energy-momentum tensor (EMT) ofSU(3) lattice gauge theory. We expand on reaching $O(a^{4})$ improvement usingtadpole-improved Symanzik action. The entropy density is calculated directlyfrom the expectation value of the space-time component of the improved EMT inthe presence of shifted boundary conditions at several lattice spacings ($a\approx 0.043 - 0.012$ fm). The absence of ultraviolet divergences and theminimal discretisation effects allow for the precision determination of theentropy density. It is demonstrated that the entropy density can beextrapolated to the continuum limit with precision and control. Furthermore,the continuum results are well represented by Pade approximation and in goodagreement with the results of previous high-precision data obtained using thegradient flow method. We find that at temperatures of about $3T_{c}$,deviations of entropy density from the Stefan-Boltzmann limit for a free theoryare about 10$\%$. The speed of sound in SU(3) gluedynamics is found to be$c_{s}^{2}\leq 0.333$ in the temperature region $1.06T_{c}\leq T\leq 3.05T_{c}$explored in this study.

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