Quark Mass and Flavour Dependence of the QCD Phase Transition

TL;DR

This study investigates how the QCD transition temperature Tc depends on quark mass and flavor using improved gauge and staggered fermion actions on lattices with finite temporal extent. By analyzing pseudo-critical couplings and zero-temperature observables to set the scale, the authors show Tc decreases as the light quark mass decreases and that Tc for nf=2 is about 10% larger than for nf=3 across a broad range of pseudoscalar-to-vector meson masses; extrapolations to the chiral limit yield Tc ≈ 173 MeV for nf=2 and 154 MeV for nf=3. They also explore the heavy quark free energy and find strong screening near Tc, with screening effects largely mass-independent for lighter quark masses and setting in at short distances, ~0.3 fm. Overall, the results clarify the interplay between quark masses, flavor content, and the QCD phase transition, while highlighting the need for continuum extrapolations and cross-checks with alternative discretizations.

Abstract

We analyze the quark mass and flavour dependence of the QCD phase transition temperature. When the lightest pseudo-scalar meson mass (m_PS) is larger than 2 GeV the critical temperature is controlled by the gluonic sector of QCD alone. For smaller values of the lightest meson mass the pseudo-critical temperature decreases slowly with m_PS. For a large regime of meson masses the pseudo-critical temperature of 2-flavour QCD is about 10% larger than in the 3-flavour case. On lattices with temporal extent N_t=4 an extrapolation to the chiral limit yields T_c = 173(8) MeV and 154(8) MeV for 2 and 3-flavour QCD, respectively. We also analyze dynamical quark mass effects on the screening of the heavy quark potential. A detailed analysis of the heavy quark free energy in 3-flavour QCD shows that close to T_c screening effects are approximately quark mass independent already for pseudo-scalar meson masses m_PS = 800 MeV and screening sets in at distances r = 0.3 fm.

Figures (7)

• Figure 1: Pseudo-critical couplings of 2 and 3 flavour QCD versus bare quark mass calculated on lattices of size $16^3\times 4$ with the standard Wilson plaquette and standard staggered fermion action (std) and the improved gauge and fermion action (p4) described in section 2. The data for the standard action have been shifted by $\Delta\beta= -1.5$. Lines show linear fits to the 3-flavour data for $m_q \le 0.05$ and "O(4)+linear" fits for the 2-flavour data with $m_q \le 0.2$.
• Figure 2: Square root of the string tension in units of the vector meson mass as a function of the ratio of pseudo-scalar and vector meson masses. Shown are results for 2, 2+1 and 3 flavour QCD obtained with the improved gauge and staggered fermion action given in Eqs. \ref{['sg']} and \ref{['sf']} . Also shown are results from calculations with unimproved staggered fermions Luetgemeier1998. The black squares show results from quenched calculations and partially quenched calculations with a sea quark mass of $m_q=0.1$.
• Figure 3: The transition temperature versus $(m_{\rm PS}/m_{\rm V})^2$ for 2 and 3-flavour QCD obtained from calculations with the p4 action on lattices with temporal extent $N_\tau=4$. Also shown are results from calculations using unimproved gauge and staggered fermion actions Luetgemeier1998.
• Figure 4: The transition temperature for 2 and 3 flavour QCD in units of the string tension versus $m_{\rm PS}/\sqrt{\sigma}$ obtained with standard (std) Luetgemeier1998 and improved (p4) staggered fermions on lattices with temporal extent $N_\tau= 4$. The hatched band to the right of the figure denotes the quenched result, the vertical line to the left is the physical $m_{PS}/\sqrt{\sigma}$ value.
• Figure 5: Quark mass dependence of the heavy quark potential for three flavour QCD below the transition temperature at a temperature $T\simeq 0.97~T_c$. The band of lines gives the Cornell-potential in units of the square root of the string tension, $V(r)/\sqrt{\sigma} = -\alpha / r\sqrt{\sigma} + r\sqrt{\sigma}$ with $\alpha = 0.25\pm 0.05$.The gauge couplings corresponding to the different quark mass values are $\beta =$ 4.06, 3.97, 3.86, 3.76, 3.59, 3.46, 3.38, 3.32 (from top to bottom).