Critical endpoint of the finite temperature phase transition for three flavor QCD

We investigate the critical endpoint of finite temperature phase transition of Nf=3 QCD at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson-clover fermion action. The critical endpoint is determined by using the intersection point of kurtosis for the temporal size Nₜ=4, 6, 8. Spatial sizes of Nₗ=6--16 (Nₜ=4), 10--24 (Nₜ=6), and 12--24 (Nₜ=8) are employed. We find that Nₜ=4 is out of the scaling region. Using results for Nₜ=6 and 8 and making linear extrapolations in 1/Nₜ², we obtain √t₀TE=0.0988(14)(9), √t₀mPS,E=0.2274(52)(108), and mPS,E/TE=2.302(62)(13), where the first error is statistical error, the second error is systematic error, and mPS is the pseudoscalar meson mass. If one uses 1/√t₀=1.347(30) GeV, as reported by Borsanyi et al., one finds TE=133(2)(1)(3) MeV, mPS,E=306(7)(14)(7) MeV, and mPS,E/mPSphys,sym=0.745(17)(35)(17), where the third error comes from the error of √t₀ and mPSphys,sym=√(m_π²+2mK²)/3. Our current estimation of √t₀mPS,E in the continuum limit is about 25% smaller than the SU(3) symmetric point.