Critical endpoint of finite temperature phase transition for three flavor QCD

Abstract

We investigate the critical endpoint of finite temperature phase transition of $N_f=3$ QCD at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and non-perturbatively $O(a)$-improved Wilson-clover fermion action. The critical endpoint is determined by using the intersection point of kurtosis for the temporal size $N_t$=4, 6, 8. Spatial sizes of $N_l$=6-16 ($N_t$=4), 10-24 ($N_t$=6), and 12-24 ($N_t$=8) are employed. We find that $N_t$=4 is out of the scaling region. Using results for $N_t$=6 and 8, and making linear extrapolations in $1/N_t^2$, we obtain $\sqrt{t_0}{T}_{\mathrm{E}}=0.0975(14)(8)$, $\sqrt{t_0}{m}_{\mathrm{PS},\mathrm{E}}=0.2254(52)(105)$ and $m_{\mathrm{PS},\mathrm{E}}/T_{\mathrm{E}}=2.311(63)(13)$, where the first error is statistical error, the second error is systematic error, and $m_{\mathrm{PS}}$ is the pseudo scalar meson mass. If one uses $1/\sqrt{t_0}=1.347(30)$ GeV reported by Borsanyi et al., one finds $T_{\mathrm{E}}=131(2)(1)(3)$ MeV, $m_{\mathrm{PS},\mathrm{E}}=304(7)(14)(7)$ MeV and $m_{\mathrm{PS},\mathrm{E}}/m_{\mathrm{PS},\mathrm{E}}^{\mathrm{phys},\mathrm{sym}}=0.739(17)(34)(17)$, where the third error comes from error of $\sqrt{t_0}$ and $m_{\mathrm{PS}}^{\mathrm{phys},\mathrm{sym}}=\sqrt{(m_{\pi }^2+2m_K^2)/3}$. Our current estimation of $\sqrt{t_0}{m}_{\mathrm{PS},\mathrm{E}}$ in the continuum limit is about 25% smaller than the SU(3) symmetric point.

Comments: 24 pages, 14 figures