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We investigate the phase structure of three-flavor QCD in the presence offinite quark chemical potential $\mu/T\lesssim1.2$ by using thenon-perturbatively $O(a)$ improved Wilson fermion action on lattices with afixed temporal extent $N_{\rm t}=6$ and varied spatial linear extents $N_{\rms}=8,10,12$. Especially, we focus on locating the critical end point thatcharacterizes the phase structure, and extracting the curvature of the criticalline on the $\mu$-$m_{\pi}$ plane. For Wilson-type fermions, the correspondencebetween bare parameters and physical parameters is indirect. Hence we present astrategy to transfer the bare parameter phase structure to the physical one, inorder to obtain the curvature. Our conclusion is that the curvature ispositive. This implies that, if one starts from a quark mass in the region ofcrossover at zero chemical potential, one would encounter a first-order phasetransition when one raises the chemical potential.

Curvature of the critical line on the plane of quark chemical potential and pseudo scalar meson mass for three-flavor QCD