Lattice QCD at finite temperature

In the last years, much effort has been paid to experimentally detect the quark-gluon plasma (QGP) in heavy-ion collisions. In these experiments, precise theoretical inputs about the nature of the transition and the equation of state (EOS) of QGP are indispensable to unambiguously identify the signal of QGP. Here, lattice QCD provides us with the most powerful method to compute thermodynamic properties of QGP from the first principles of QCD. In the quenched approximation of QCD, the study of finite temperature QCD is already well matured: Computations of Tc and EOS have been made on lattices with several temporal lattice sizes Nt, using both the standard plaquette action and various improved actions. Continuum extrapolation to the limit of large Nt has been performed with different actions to confirm good agreement within an accuracy of a few percent[1–3]. For the pressure, precise comparisons of the results from different calculation methods, i.e. the integral method[4] and the derivative method[5], have also been made[6–8]. The expected absence of the pressure gap at the first order deconfinement transition point has also been demonstrated through a new non-perturbative calculation of anisotropy coefficients[7]. The quenched study is now entering a new stage: Thermal effects on the pole mass have been studied by the QCDTARO collaboration using an anisotropic lattice[9]. Several groups are also trying to compute hadron spectral functions at finite-temperature applying the maximum entropy method[10–13]. On the other hand, the study of full QCD at finite temperatures is still at the stage of development. Until recently, EOS with dynamical quarks has been computed only for the staggered fermion. The MILC collaboration calculated EOS in 2 flavor QCD with the standard staggered fermion on Nt = 4 and 6 lattices[14]. The Bielefeld group computed EOS for Nf = 4 using an improved staggered fermion at Nt = 4[15]. This year, the Bielefeld group extended the computation to Nf = 2 and 3 and studied the Nf dependence[16]. A new development of this year is the first calculation of EOS for a Wilson-type fermion[17]. Using a renormalization group (RG) improved gauge action[18] coupled with 2 flavors of cloverimproved Wilson quarks[19], the CP-PACS collaboration performed a systematic study of the pressure and the energy density of QGP. In this report, we concentrate on the development in finite temperature QCD with dynamical quarks, focusing on the topics of EOS, and attempt a comparison of the results from different lattice fermions. In section 2, we discuss about the phase structure, critical properties around the chiral phase transition of 2 flavor QCD, and the transition temperature. we then discuss new calculations of EOS in section 3. A brief summary is given in section 4.