End Point of a First-Order Phase Transition in Many-Flavor Lattice QCD at Finite Temperature and Density

Towards the feasibility study of the electroweak baryogenesis in realistic technicolor scenario, we investigate the phase structure of ($2+N_f$)-flavor QCD, where the mass of two flavors is fixed to a small value and the others are heavy. For the baryogenesis, an appearance of a first-order phase transition at finite temperature is a necessary condition. Using a set of configurations of two-flavor lattice QCD and applying the reweighting method, the effective potential defined by the probability distribution function of the plaquette is calculated in the presence of additional many heavy flavors. Through the shape of the effective potential, we determine the critical mass of heavy flavors separating the first-order and crossover regions and find it to become larger with $N_f$. We moreover study the critical line at finite density and the first-order region is found to become wider as increasing the chemical potential. Possible applications to real ($2+1$)-flavor QCD are discussed.

Figure 1

Top: $\ln \overline{R}(P;h,0)$ as functions of the plaquette. Bottom: The curvature of $\ln \overline{R}(P;h,0)$ for $h=0.01–0.07$. The circle and square symbols are $d^2{V}_0/d{P}^2(P)$.

Figure 2

The slope of $V_{\mathrm{eff}}(P;\beta ,h,0)$ normalized at $(\beta ,h)=(3.65,0)$ for $h=0.0–0.1$. The squares are $d{V}_0/dP$.

Figure 3

Left: The curvature of $\ln \overline{R}(P;h,\mu )$ as functions of the plaquette at $\mu /T=1.0$ and ${\mu }_h=0$. Right: The critical line in the ($h$, $\mu$) plane for ${\mu }_h=0$ (circles) and for ${\mu }_h=\mu$ (diamonds). In the region above this line, the transition is of first order. The square at $\mu =0$ is computed using all configurations, and the others are measured with every 10.