Non-perturbative determination of the QCD Equation of State up to the electroweak scale

Abstract

The QCD Equation of State with $N_f=3$ massless quark flavours is determined non-perturbatively over a broad range of temperatures, extending from the electroweak scale down to 3 GeV, and smoothly connecting to the low-temperature regime. The comparison with perturbative predictions shows that, even at temperatures approaching the electroweak scale, the Equation of State can be accurately described only by adding terms beyond the known perturbative series, including non-perturbative contributions. The strategy that allows this investigation in the previously unexplored high-temperature regime combines shifted boundary conditions with a determination of the lines of constant physics based on the running of a non-perturbatively defined renormalized coupling. This methodology is general and can be applied to QCD with four or five massive quark flavours.

Figures (7)

• Figure 1: Non-perturbative running of renormalized gauge couplings for QCD with $N_f=3$ over a wide range of momentum scales. Plot taken from Ref. Bruno:2017gxd.
• Figure 2: Plot of the integrand function in Eq. \ref{['eq:Df_gauge']} as a function of the bare coupling $g_0^2$. Points have been shifted horizontally by $0.03\times(L_0/a-4)$ for better readability.
• Figure 3: Left: plot of the integrand function in Eq. \ref{['eq:Df_quark']} computed at the bare parameters of temperature $T_1$ and at the resolutions $L_0/a=4,6,8,10$, as a function of $m_q/T$. Points have been interpolated with a cubic spline to guide the eye. In most cases, errors are smaller than the markers. Right: the same integrand function is shown at the resolution $L_0/a=6$ and at three temperatures.
• Figure 4: Black dots are the values of the one-loop improved entropy density as a function of $(a/L_0)^2$ at the temperatures $T_0, T_1, ..., T_8$. The red band is our best extrapolation to the continuum limit and red crosses are the continuum extrapolated values for $s/T^3$. The horizontal axis is common to all the subplots.
• Figure 5: Temperature dependence of the entropy density in terms of $\hat{g}^2$. The data are fitted by enforcing the Stefan--Boltzmann limit (SB) at infinite temperature and including quadratic and cubic corrections. The shaded area indicates the uncertainty of the fit.