Critical endpoint of finite temperature phase transition for three flavor QCD

TL;DR

This study determines the critical endpoint of the finite temperature phase transition in three-flavor QCD using lattice simulations with improved actions, finding results consistent with theoretical expectations and previous estimates.

Contribution

The paper provides a new lattice QCD determination of the critical endpoint parameters using improved actions and multiple lattice sizes, with extrapolation to the continuum limit.

Findings

Critical endpoint temperature is approximately 131 MeV.

Pseudo scalar meson mass at the critical point is about 304 MeV.

The continuum estimate of the meson mass is about 25% smaller than the SU(3) symmetric point.

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 $\sqrt{t_0}T_{\rm E}=0.0975(14)(8)$, $\sqrt{t_0}m_{\rm PS,E}=0.2254(52)(105)$ and $m_{\rm PS,E}/T_{\rm E}=2.311(63)(13)$, where the first error is statistical error, the second error is systematic error, and $m_{\rm PS}$ is the pseudo scalar meson mass. If one uses $1/\sqrt{t_0}=1.347(30)$ GeV reported by Borsanyi et al., one finds $T_{\rm E}=131(2)(1)(3)$ MeV, $m_{\rm PS,E}=304(7)(14)(7)$ MeV and $m_{\rm PS,E}/m_{\rm PS,E}^{\rm phys, sym}=0.739(17)(34)(17)$, where the third error comes from error of $\sqrt{t_0}$ and $m_{\rm PS}^{\rm phys, sym}=\sqrt{(m_\pi^2+2m_K^2)/3}$. Our current estimation of $\sqrt{t_0}m_{\rm PS,E}$ in the continuum limit is about 25% smaller than the SU(3) symmetric point.