A new approach to determine the thermodynamics of deconfined matter to high accuracy

TL;DR

The paper proposes a precision route to QCD thermodynamics at finite density and high temperatures by combining phase-quenched (PQ) lattice simulations with perturbation theory. It shows that, in a regime where the strong coupling is small, the PQ pressure $p_{PQ}$ approximates the full QCD pressure $p$ with a small perturbative correction, $\Delta p = p_{PQ}-p = O(\alpha_s^3)$, augmented by higher-order terms computed using electrostatic QCD (EQCD) and a novel numerical method for four-loop sum-integrals. The authors evaluate $\Delta p$ up to $O(\alpha_s^{7/2})$ and provide explicit expressions for the coefficients $c_1$, $c_2$, and $c_3$, leveraging a Loop-Tree Duality (LTD) approach to perform the required four-loop integrals. This framework enables determining the perturbative QCD pressure with unprecedented accuracy across a large region of the phase diagram while incorporating nonperturbative pure-gluonic contributions from lattice QCD, potentially guiding future lattice computations and phenomenological applications in heavy-ion physics and neutron-star contexts.

Abstract

We demonstrate that at finite density and sufficiently high temperatures, phase-quenched (PQ) lattice simulations combined with perturbation theory provide a new precision approach to determining the thermodynamics of QCD across a wide arc of the phase diagram where the strong coupling constant $α_s$ remains small. In this regime, nonperturbative pairing effects in the PQ theory are parametrically suppressed, so that the difference between the PQ and full QCD pressures becomes a small perturbative correction. We compute this correction up to and including $O(α_s^{7/2})$ using electrostatic QCD together with a novel numerical method to compute four-loop sum-integrals. This enables the determination of the perturbative QCD pressure with precision beyond the current state of the art while including nonperturbative pure-gluonic contributions from the lattice.

Figures (2)

• Figure 1: The QCD phase diagram with its phases (in italic text) and the regions accessible using various computational techniques (shaded regions and colored text). The PQ critical temperature of the paired phase restricts the applicability of PQ simulations to determine the QCD pressure indicated by the blue to orange fade in the bottom right. Note the region of overlap in applicability between lattice simulations in QCD and the PQ theory in the upper left corner.
• Figure 2: Pressure difference $\Delta p$ from Eq. \ref{['eq:resummedpresult']} throughout the phase-diagram arc $(4.338\pi T)^2+(3\mu_\mathrm{q})^2=(3\text{ GeV})^2$ for $T\in [0,220]$ MeV. The renormalization scale is chosen as $\bar{\Lambda} = X \sqrt{(2 \mu_\mathrm{q})^2 + (0.723 \times 4 \pi T)^2}$, where $X$ is varied in the range $[1/2,2]$ for the full $\Delta p$ and fixed to $X=1$ for the partial result with $c_3=0$. The numerical errors from the MC integration for $c_1$ are very small and hence not shown here.