PDF《BNL-NT-07/38, BI-TP 2007/20, CU-TP-》

arXiv:0710.

0354v2 [hep-lat]

15 Jan

2008 BNL-NT-07/38, BI-TP 2007/20, CU-TP-1181 The QCD Equation of State with almost Physical Quark Masses M. Chenga , N. H. Christa , S. Dattab , J. van der Heidec , C. Jungd , F. Karschc,d , O. Kaczmarekc , E. Laermannc , R. D. Mawhinneya , C. Miaoc , P. Petreczkyd,e , K. Petrovf , C. Schmidtd , W. Soeldnerd and T. Umedag a Physics Department,Columbia University, New York, NY 10027, USA b Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India c Fakult¨ at f¨ ur Physik, Universit¨ at Bielefeld, D-33615 Bielefeld, Germany d Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA e RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA f Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark g Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan (Dated: October 29, 2018) We present results on the equation of state in QCD with two light quark ?avors and a heavier strange quark. Calculations with improved staggered fermions have been performed on lattices with temporal extent Nτ =

4 and

6 on a line of constant physics with almost physical quark mass values;

the pion mass is about

220 MeV, and the strange quark mass is adjusted to its physical value. High statistics results on large lattices are obtained for bulk thermodynamic observables, i.e. pressure, energy and entropy density, at vanishing quark chemical potential for a wide range of temperatures,

140 MeV ≤ T ≤

800 MeV. We present a detailed discussion of ?nite cut-o? e?ects which become particularly signi?cant for temperatures larger than about twice the transition temperature. At these high temperatures we also performed calculations of the trace anomaly on lattices with temporal extent Nτ = 8. Furthermore, we have performed an extensive analysis of zero temperature observables including the light and strange quark condensates and the static quark potential at zero temperature. These are used to set the temperature scale for thermodynamic observables and to calculate renormalized observables that are sensitive to decon?nement and chiral symmetry restoration and become order parameters in the in?nite and zero quark mass limits, respectively. PACS numbers: 11.15.Ha, 11.10.Wx, 12.38Gc, 12.38.Mh I. INTRODUCTION Reaching a detailed understanding of bulk thermodynamics of QCD, e.g. the temperature dependence of pressure and energy density as well as the equation of state, p(?) vs. ?, is one of the central goals of non-perturbative studies of QCD on the lattice. The equation of state clearly is of central importance for the understanding of thermal properties of any thermodynamic system. It provides direct insight into the relevant degrees of freedom and their correlation in di?erent phases of strongly interacting matter. We have some understanding of the equation of state in limiting cases of high and low temperatures from perturbation theory [1, 2, 3, 4, 5] and hadron gas phenomenology [6], respectively. In the transition region from the low temperature hadronic regime to the high temperature quark gluon plasma, however, one has to rely on a genuine non-perturbative approach, lattice regularized QCD, to study the non-perturbative properties of strongly interacting matter. Lattice studies of bulk thermodynamics are particularly demanding as the most interesting observables, pressure and energy density, are given in terms of di?erences of dimension