First order transition regions in the quark masses and chemical potential parameter space of QCD

We investigate the phase transitions of (2+Nf)-flavor QCD, where two light flavors and Nf massive flavors exist, aiming to understand the phase structure of (2+1)-flavor QCD. Performing simulations of 2-flavor QCD with improved staggered and Wilson fermions and using the reweighting method, we calculate probability distribution functions in the many-flavor QCD. Through the shape of distribution functions, we determine the critical surface terminating first order phase transitions in the parameter space of the light quark mass, heavy quark mass and the chemical potential, and find that the first order region becomes larger with Nf. We then study the critical surface at finite density for large Nf and the first order region is found to become wider with the increasing chemical potential. On the other hand, the light quark mass dependence of the critical mass of heavy quarks seems weak in the region we investigated. The result of this weak dependence suggests that the critical mass of heavy quark remains finite in the chiral limit of 2-flavors and there exists a second order transition region on the line of the 2-flavor massless limit above the tri-critical point. Moreover, we extend the study of 2-flavor QCD at finite density to the case of a complex chemical potential and investigate the singularities where the partition function vanishes, so-called Lee-Yang zeros. The plaquette effective potential is computed in the complex plane. We find that the shape of the effective potential changes from single-well on the real axis to double-well at large imaginary chemical potential and the double-well potential causes the singularities.

Nature of finite temperature and density phase transitions in many-flavor QCD

We investigate the phase structure of (2+Nf)-flavor QCD, where two light flavors and Nf massive flavors exist, to discuss the feasibility of the electroweak baryogenesis in realistic technicolor scenario and to understand properties of finite density QCD. Because an appearance of a first order phase transition at finite temperature is a necessary condition for the baryogenesis, it is important to study the nature of finite temperature phase transition. Applying the reweighting method, the probability distribution function of the plaquette is calculated in the many-flavor QCD. Through the shape of the distribution function, we determine the critical mass of heavy flavors terminating the first order region, and find it to become larger with Nf. We moreover study the critical line at finite density and the first order region is found to become wider as increasing the chemical potential. We discuss how the properties of real (2+1)-flavor QCD at finite temperature and density can be extracted from simulations of many-flavor QCD.

Histograms in heavy-quark QCD at finite temperature and density

We study the phase structure of lattice QCD with heavy quarks at finite temperature and density by a histogram method. We determine the location of the critical point at which the first-order deconfining transition in the heavy-quark limit turns into a crossover at intermediate quark masses through a change of the shape of the histogram under variation of coupling parameters. We estimate the effect of the complex phase factor which causes the sign problem at finite density, and show that, in heavy-quark QCD, the effect is small around the critical point. We determine the critical surface in 2+1 flavor QCD in the heavy-quark region at all values of the chemical potential mu including mu=infty.

Equation of State and Heavy-Quark Free Energy at Finite Temperature and Density in Two Flavor Lattice QCD with Wilson Quark Action

We study the equation of state at finite temperature and density in two-flavor QCD with the RG-improved gluon action and the clover-improved Wilson quark action on a $ 16^3 times 4$ lattice. Along the lines of constant physics at $m_{rm PS}/m_{rm V} = 0.65$ and 0.80, we compute the second and forth derivatives of the grand canonical partition function with respect to the quark chemical potential $mu_q = (mu_u+mu_d)/2$ and the isospin chemical potential $mu_I = (mu_u-mu_d)/2$ at vanishing chemical potentials, and study the behaviors of thermodynamic quantities at finite $mu_q$ using these derivatives for the case $mu_I=0$. In particular, we study density fluctuations at none-zero temperature and density by calculating the quark number and isospin susceptibilities and their derivatives with respect to $mu_q$. To suppress statistical fluctuations, we also examine new techniques applicable at low densities. We find a large enhancement in the fluctuation of quark number when the density increased near the pseudo-critical temperature, suggesting a critical point at finite $mu_q$ terminating the first order transition line between hadronic and quark gluon plasma phases. This result agrees with the previous results using staggered-type quark actions qualitatively. Furthermore, we study heavy-quark free energies and Debye screening masses at finite density by measuring the first and second derivatives of these quantities for various color channels of heavy quark-quark and quark-anti-quark pairs. The results suggest that, to the leading order of $mu_q$, the interaction between two quarks becomes stronger at finite densities, while that between quark and anti-quark becomes weaker.