Crossover-model approach to QCD phase diagram, equation of state and susceptibilities in the 2+1 and 2+1+1 flavor systems

We construct a simple model for describing the hadron quark crossover transition by using lattice QCD (LQCD) data in the 2 +1 flavor system, and draw the phase diagram in the 2 + 1 and 2 + 1 + 1 flavor systems through analyses of the equation of state (EoS) and the susceptibilities. In the present hadron quark crossover (HQC) model, the entropy density s is defined by s = fH(S)H + (1-f(H))sQ with the hadron-production probability fH, where sH is calculated by the hadron resonance gas model that is valid in low temperature (T) and s(Q) is evaluated by the independent quark model that explains LQCD data on the EoS in the region 400 less than or similar to T <= 500 MeV for the 2 + 1 flavor system and 400 less than or similar to T <= 1000 MeV for the 2 + 1 + 1 flavor system. The f(H) is determined from LQCD data on s and susceptibilities for the baryon-number (B), the isospin (I) and the hypercharge (Y) in the 2 + 1 flavor system. The HQC model is successful in reproducing LQCD data on the EoS and the flavor susceptibilities for X-f, f'((2)) ,for f,f'= u, d, s in the 2+1+1 flavor system, without changing the fH. We define the hadron quark transition temperature with f(H) = 1/2. For the 2+1 flavor system, the transition line thus obtained is almost identical in mu B-T, mu I-T,mu Y-T planes, when the chemical potentials it, (alpha = B, I, Y) are smaller than 250 MeV. This BIY approximate equivalence is also seen in the 2 + 1 + 1 flavor system. We plot the phase diagram also in mu u-T, mu d-T, mu(s)-T, mu(C)-T planes in order to investigate flavor dependence of transition lines. In the 2+1+1 flavor system, c quark does not affect the 2+1 flavor subsystem composed of u, d, s. Temperature dependence of the off-diagonal susceptibilities and the f(H) show that the transition region at it,mu alpha = 0 is 170 less than or similar to T less than or similar to 400 MeV for both the 2 + 1 and 2 + 1 + 1 flavor systems.