Finite temperature transitions in lattice QCD with Wilson quarks: Chiral transitions and the influence of the strange quark

The nature of finite temperature transitions in lattice QCD with Wilson quarks is studied near the chiral limit for the cases of two, three, and six flavors of degenerate quarks ($N_F=2, 3, \mathrm{and} 6$) and also for the case of massless up and down quarks and a light strange quark ($N_F=2+1\mathrm{}$). Our simulations mainly performed on lattices with the temporal direction extension $N_t=4\mathrm{}$ indicate that the finite temperature transition in the chiral limit (chiral transition) is continuous (or at most very weakly first order) for $N_F=2\mathrm{}$, while it is of first order for $N_F=3\mathrm{} \mathrm{and} 6$. We find that the transition is of first order for the case of massless up and down quarks and the physical strange quark where we obtain a value of $\frac{m_{\phi }}{m_{\rho }}$ consistent with the physical value. This result is different from the previous result with staggered quarks at $N_t=4\mathrm{}$ which suggests that the transition in the real world is a crossover. Since the deviation from the continuum limit is large in both studies at $N_t=4\mathrm{}$, a calculation with larger $N_t$ or with an improved action would be needed in order to obtain a definite conclusion about the nature of the QCD transition. We also discuss the phase structure at zero temperature as well as that at finite temperatures.