Thermal quarks and Polyakov loops in two-color dense QCD

TL;DR

This work investigates confinement and deconfinement in dense QC$_2$D by analyzing thermal quarks, gluons, and Polyakov-loop dynamics. It combines lattice-informed Polyakov-loop potentials (BFH and inverse Weiss) with a massive Yang–Mills description and PNJL-type quark physics to study in-medium modifications at finite temperature and density, calibrating at $\mu_q=0$ against lattice data. By computing one-loop gluon propagators in a Polyakov background and comparing screening masses and propagators to lattice results, the study finds that thermal excitations are strongly suppressed by the Polyakov loop and by a sizable diquark gap, yielding hadron-dominated behavior at low $T$ and density, with partial quark screening emerging only when quark excitations overcome the confining background. The results highlight a separation between confinement-related gluonic dynamics and quasi-particle excitations, and point to the need for higher-order and nonperturbative effects to fully capture magnetic sectors and finite-momentum behavior, with implications for extending these insights toward three-color QCD and dense hadronic/quarkyonic matter.

Abstract

We study confinement and deconfinement in dense two color QCD by analyzing the dynamics of thermal quarks and gluons. The Polyakov loop is used as a probe of the relevant thermal excitations, distinguishing quark and hadron dominated regimes in dense matter. To describe the Polyakov loop, we adopt both lattice informed phenomenological models and the massive Yang Mills framework. After calibrating these models at zero density, we investigate in medium modifications of the Polyakov loops and gluon propagators at finite temperature and density. Diquark gaps control the screening at zero temperature, whereas the screening due to thermal quarks is sensitive to the Polyakov loop. Inclusion of the Polyakov loop helps to reproduce lattice data at low temperature, suggesting that thermal excitations are predominantly hadronic rather than uncorrelated quarks.

Figures (15)

• Figure S1: The Polyakov loop potential before (left) and just after (right) the deconfinement transition. The results at $T=$ 20 and 260 MeV are shown for illustrative purposes. The potential is normalized by $T^4$. The normalized potential for ghosts does not depend on $T$. The absolute value of the gluonic part grows with $T$, shifting the minimum from $\Phi=0$ to $1$.
• Figure S2: (Left) Comparisons of the Polyakov loop potential for the mYM for $m_g^{\rm vac} =800$ MeV with and without the $\Phi$-dependence of $m_g$, and the pYM part used in the PNJL model (BFH). For $\Phi$-dependent $m_g^T$, we chose $c_g =4$ and $n_g =2$ in Equation \ref{['eq:phi_dep_mg']}. All these models lead to the transition temperature being somewhere between $T=$ 240 and 280 MeV. The potential used in the PNJL model has an energy cost around $\Phi \sim1$, much bigger than in the mYM. (Right) The temperature dependence of the Polyakov loop $\Phi$ for mYM models with $c_g=0,2,$ and 4, and for the BFH model.
• Figure S3: The Polyakov loop dependence of the quark pressure in Equation \ref{['eq:F_q^T']} at $\mu_q=0$. Here, we fix $M_q=$ 400 (500) MeV for solid (dotted) curves. The Polyakov loop values $\Phi_*$ are dynamically determined for the mYM and BFH with quarks. The results for fixed $\Phi=0$ and $\Phi=1$ (common for the mYM and BFH models) are also shown.
• Figure S4: (Left) The Polyakov loop potential at $\mu_q=0$ in the same setup as in Figure \ref{['fig:graph_mYM_g_gh']} except that thermal quark contributions in Equation \ref{['eq:F_q^T']} are added and the temperatures are now $T=100$ and 150 MeV. The effective quark mass is fixed to $M_q=400$ MeV. (Right) The temperature dependence of the Polyakov loop $\Phi$. The solid (dotted) lines are results for $M_q=400$ (500) MeV. The lattice results (renormalization scheme A in Ref. Boz:2019enj) are also plotted for comparison.
• Figure S5: The temperature dependence of the Polyakov loop and the effective quark mass $M_q$ for the set I (solid) and II (dotted) at $\mu_q = 0$ with $\Delta_{\rm ext} = 0$. For the lattice data with $m_\pi \simeq 637$ MeV, we use two renormalization schemes with $\Delta E_R = E_R - E_B = 220$ and $270$ MeV to convert the lattice data in scheme B; see Equation \ref{['eq:reno_L_B_to_A']}.