Mesons, baryons and the confinement/deconfinement transition

Abstract

We identify an observable that could operate as a probe of the quark versus hadron content of a bath of quarks and gluons at finite temperature and chemical potential. To this purpose, we relate the Polyakov and anti-Polyakov loops, which determine how energetically costly it is to bring an external static quark or antiquark probe into the thermal bath, to the ability of that medium to provide favorable conditions for the formation of meson-like or baryon-like configurations that would screen the probes.

Figures (6)

• Figure 1: The system's net quark number gains ${\Delta Q_q+1}$ and $\Delta Q_{\bar{q}}-1$ in the presence of a quark or antiquark probe, as functions of the chemical potential $\mu$ (bottom part), compared to the Polyakov and anti-Polyakov loops $\ell$ and $\bar{\ell}$ (top part). We considered ${N_f=3}$ degenerate heavy flavors and various temperatures below and above the confinement-deconfinement transition temperature $T_c^0$ at ${\mu=0}$. The corresponding plots for negative $\mu$ can be obtained using the formulas ${\ell(-\mu)=\bar{\ell}(\mu)}$ and $\Delta Q_q(-\mu)+1=-(\Delta Q_{\bar{q}}(\mu)-1)$ which are consequences of charge conjugation.
• Figure 2: Phase diagram of heavy-quark QCD, as resulting from Eqs. (\ref{['eq:V']}) and (\ref{['eq: quark']}), with $V_{\rm glue}(\ell,\bar{\ell})$ modeled as in Ref. MariavanEgmond2022ATemperature. The outer line shows the confinement-deconfinement transition. The line within the confined phase separates the regions where the medium screens the quark probe $q$ via a meson-like ($\to0$) or a baryon-like ($\to3$) configuration. It was cut around where the plateaux disappear. The dashed line is the qualitative estimate derived from Eq. \ref{['eq:nice']}, the quantitative estimate from Eq. \ref{['eq:corr']} is indistinguishable from the full result.
• Figure A.1: For a grid of values of $r_3$ between $0$ (dark) and $2\pi$ (light), we show $({\rm Re}\,\ell_0,{\rm Im}\,\ell_0)$ as $r_8$ is varied such that $(r_3,r_8)$ remains in the same Weyl chamber. The corresponding curves do not cross each other and cover a certain region in the plane $({\rm Re}\,\ell_0,{\rm Im}\,\ell_0)$.
• Figure A.2: For a grid of values of $\hat{r}_3$ between $0$ and $2\pi$, we show $(\ell_0,\bar{\ell}_0)$ as $\hat{r}_8$ is varied. The corresponding curves do not cross each other and cover a certain region in the plane $(\ell_0,\bar{\ell}_0)$.
• Figure A.3: Blue: boundary of the region where ${\ell=\bar{\ell}=1}$ for the model of Ref. Reinosa:2014ooa where the quark contribution dominates over the glue contribution at low temperatures. Red: confinement/deconfinement transition (with some definition of the crossover transition)