Using net quark number gain to probe the phases of QCD

TL;DR

This work introduces the net quark number gain as a gauge- and RG-invariant observable that probes the content of a QCD medium at finite temperature and chemical potential. By relating the Polyakov loop and its μ-derivative to the medium’s response to a static color source, the authors derive how the addition of a single quark or antiquark can induce meson-like or baryon-like screening in the confined phase, while the deconfined phase yields minimal net screening. In the heavy-quark, low-$T$ limit, explicit expressions tie the net quark number gain to the μ-dependent behavior of the Polyakov-loop potential $V_{ m glue}$ and associated functions $f_y$, unveiling a clear $T\to0$ phase structure with thresholds at $\mu=\pm M/3$. The approach provides a new lens to study the QCD phase diagram, with potential extensions to color superconductivity, critical-point physics, and correlations with other conserved charges via Polyakov-loop operators, as supported by planned NJL-Polyakov modeling and further work.

Abstract

We discuss an observable that probes the content of a QCD medium at finite temperature and chemical potential, the net quark number gain. It is the response of the thermal bath to a static quark or antiquark probe. While insignificant at high temperatures, it reveals the bath's tendency to form meson-like or baryon-like configurations (depending on the probe and chemical potential) at low temperatures, which would screen the probe's color charge. The net quark number gain also helps explain how a single quark/antiquark can be added to a supposedly confining medium in the first place: the latter provides the missing quarks/antiquarks to form hadron-like states. We sketch the derivation of this general result for temperatures much smaller than the constituent quark masses and discuss possible further applications to study the various features of the QCD phase diagram.

Figures (2)

• Figure 1: Polyakov loop $\ell$ (solid) and anti-Polyakov loop $\bar{\ell}$ (dashed) at a low temperature $T\ll M$ as a function of chemical potential $\mu$ normalized to the quark mass $M$, in (left) a linear scale and (right) a logarithmic scale. The logarithmic scale reveals a striking behavior of differing but constant slopes in the confined region, invisible in the linear scale plot due to the Polaykov loops' exponential suppression.
• Figure 2: Left: Net quark number gain upon addition of a quark (solid) or an antiquark (dashed) as a function of $\mu$ in units of the quark mass $M$, for a temperature below and above the transition temperature as well as in the zero temperature limit, where it becomes a step function. Right: Phase diagram of heavy quark QCD characterized by the net quark number gain. In addition to the separation of the deconfined (upper) and confined (both lower) phases, we distinguish where quarks are screened into meson-like (0, lower left) and baryon-like (3, lower-right) configurations.