QCD Thermodynamics with Three Flavors of Improved Staggered Quarks

TL;DR

The study investigates QCD thermodynamics with $ ext{N}_f={3}$ and $ ext{N}_f={2+1}$ using the Symanzik-improved gauge action and the Asqtad staggered quark action to map the finite-temperature phase structure and quark-number fluctuations. By simulating at multiple lattice spacings ($a=1/(4T)$, $1/(6T)$, $1/(8T)$) and varying quark masses, the authors find rapid crossovers rather than true phase transitions, with the crossover sharpening as the light-quark masses decrease; they also compute quark number susceptibilities, showing these observables approach continuum values and exhibit characteristic changes near the crossover. The analysis yields a rough estimate of the critical temperature in the $ ext{N}_f={2+1}$ limit in the chiral regime, $T_c o ext{(169–174) MeV}$ depending on the assumed universality class, reinforcing the absence of a transition at physical quark masses. Overall, the work demonstrates the reliability and scaling of the Asqtad action for finite-temperature QCD and sets the stage for future studies at smaller quark masses and finer lattices to pinpoint the phase structure more precisely.

Abstract

We report on a study of QCD thermodynamics with three flavors of quarks, using a Symanzik improved gauge action and the Asqtad O(a^2) improved staggered quark action. Simulations were carried out with lattice spacings 1/4T, 1/6T and 1/8T both for three degenerate quarks with masses less than or equal to the strange quark mass, m_s, and for degenerate up and down quarks with masses in the range 0.1 m_s \leq m_{u,d} \leq 0.6 m_s, and the strange quark mass fixed near its physical value. We present results for standard thermodynamics quantities, such as the Polyakov loop, the chiral order parameter and its susceptibility. For the quark masses studied to date we find a rapid crossover rather than a bona fide phase transition. We have carried out the first calculations of quark number susceptibilities with three flavors of sea quarks. These quantities are of physical interest because they are related to event-by-event fluctuations in heavy ion collision experiments. Comparison of susceptibilities at different lattice spacings show that our results are close to the continuum values.

Figures (18)

• Figure 1: The energy density, pressure and quark number susceptibility for free, massless quarks as a function of the temporal lattice size, $N_t$, for conventional and improved actions. For free fermions the Asqtad action reduces to the Naik action. The $P4$ action is the improved staggered fermion action studied by the Bielefeld group BIELEFELD.
• Figure 2: The real part of the Polyakov loop as a function of temperature on $16^3\times 8$ lattices for three degenerate flavors of quarks with masses $m_q/m_s=1.0$, 0.6, 0.4 and 0.2.
• Figure 3: The number of conjugate gradient iterations required for convergence of the inversion of the Dirac operator for three degenerate flavors of quarks with masses $m_q/m_s=1.0$, 0.6, 0.4 and 0.2 on $16^3\times 8$ lattices.
• Figure 4: The $\bar{\psi}\psi$ susceptibility as a function of temperature for three equal mass quarks on $12^3\times 6$ lattices. Results are shown for quark masses $m_q/m_s=1.0$, 0.6, 0.4, and 0.2. Note the increase in the height of the peak as the quark mass is decreased.
• Figure 5: The chiral order parameter, $\langle\bar{\psi}\psi\rangle$, as a function of temperature on $12^3\times 6$ lattices for $N_f=3$. The bursts are linear extrapolations of $\langle\bar{\psi}\psi\rangle$ for the two lowest quark masses to $m_q=0$ at fixed temperature.