Nature of the phase transition for finite temperature $N_{\mathrm{f}}=3$ QCD with nonperturbatively O($a$) improved Wilson fermions at $N_{\mathrm{t}}=12$

We study the nature of the finite temperature phase transition for three-flavor QCD. In particular we investigate the location of the critical endpoint along the three flavor symmetric line in the light quark mass region of the Columbia plot. In the study, the Iwasaki gauge action and the nonperturvatively O($a$) improved Wilson-Clover fermion action are employed. We newly generate data at $N_{\mathrm{t}}=12$ and set an upper bound of the critical pseudoscalar meson mass in the continuum limit $m_{\mathrm{P}\mathrm{S},\mathrm{E}}\lesssim 110$MeV.