Budget Amount *help 
¥2,700,000 (Direct Cost : ¥2,700,000)
Fiscal Year 2000 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Research Abstract 
This work aimed to elucidate the nature of the phase transition from hadron phase to quark gluon plasma phase, and physical properties of the consequent high temperature phase, using largescale numerical simulations of quantum chromodynamics on the lattice. In the first year of the project, we investigated the properties of the phase transition itself. In the second and third years of the project, we calculated the equation of state which represent the fundamental information concerning the plasma phase. The main results we have obtained are as follows. 1. For understanding the finitetemperature phase transition of the real world, it is very important to learn how the difference of masses of the up and down quark m_<ud> and that of the strange quark m_s affects the nature of the phase transition. We have carried out a systematic determination of the line of phase transition on the (m_<ud>, m_s) plane using the KogutSusskind quark action, and identified the critical quark mass beyond
… More
which the firstorder phase transition becomes absent. Further investigation of the SU (3) symmetric case has shown that the endpoint of the firstorder transition is a secondorder transition point, and that the sigma particle becomes massless at that point. 2. Past calculations of the equation of state of the quark gluon plasma phase has exclusively used the KogutSusskind quark action. In our work we employed the Wilsontype quark action which is far more natural than the KogutSusskind quark action in the spinflavor content. Since this calculation is CPU time intensive, being a full QCD calculation, we have exploited the use of improved actions both for the gluon and quark sectors. We adopted the integral method for calcuation of equation of state. For a methodological preparation, we first calculated the equation of state for pure gauge theory, and determined the temperature dependence of energy density and pressure. Taking the continuum limit, we obtained results for the equation of state which are in agreement with those of the standard plqquette action within 3%. For full QCD, we first determined the phase diagram on the (K,β) plane, identifying the region of parity broken phase and the critical line. We then carried out simulations on lattices with the temporal lattice size N_1=4 and 6 and the spatical size mostly 16^3. The region of quark masses corresponding to m_π/m_ρ=O.60.95 were explored, and the energy density and pressure were determined as a function of temperature and quark mass. The main features found in these results are (i) only weak dependence is seen once quark mass falls below m_π/m_ρ=0.9, and (ii) N_1=6 results show an approximate agreement with the continuum StefanBoltzmann values above T/ T_1=2. Further studies are needed to confirm and extend these results, in particulr to carry out scaling study using lattices with larger temporal sizes. Less
