Thermal quarks and gluon propagators in two-color dense QCD

We study Landau gauge gluon propagators in two-color QCD at a finite quark chemical potential (${\mu }_q$) and temperature ($T$). We include medium polarization effects at the one loop by quarks into massive gluon propagators and compare the analytic results with the available lattice data. We particularly focus on the high density phase of color-singlet diquark condensates whose critical temperature is $\sim 100\mathrm{MeV}$ with a weak dependence on ${\mu }_q$. At zero temperature, the color singlet condensates protect the IR limit of electric and magnetic gluon propagators from the medium screening effects. At a finite temperature, this behavior remains true for the magnetic sector, but the electric screening mass should be generated by thermal, and hence gapless, particles which are unbound from the diquark condensates. Treating thermal excitations as quasiquarks, we found that the electric screening develops too fast as compared to the lattice results. Beyond the critical temperature for diquark condensates, the analytic results are consistent with the lattice results.

Figure 1

Thermal excitations at low and high temperature. At low temperature, a thermal gas is made by hadrons or quarks. At high enough temperature, the gas becomes dense and get percolated. The percolation may happen within the superfluid phase if the phase space for low energy excitations is sufficiently large, e.g., at high density.

Figure 2

A schematic phase diagram. The lines A, B, C indicate the domains analyzed in Secs. 3a, 3b, 3c. See also Fig. 10 in Ref. [30] and Fig. 2 in Ref. [46] based on the Polyakov loop.

Figure 3

The static propagators at ${\mu }_q=0.71\mathrm{GeV}$ and $T\simeq 44\mathrm{MeV}$, for ${\alpha }_s=1.0$. The upper (lower) panel is for electric (magnetic) propagators. For the electric propagators, we compare the ${\mathrm{\Delta }}_{T=0}=200\mathrm{MeV}$ and 10 MeV, while in the magnetic sector the dependence on ${\mathrm{\Delta }}_T$ is not visible for the range 10–200 MeV.

Figure 4

The ${\mu }_q$ dependence of the gluon propagators at spatial momenta $|\mathbf{k}|=0.0$, 0.55, 1.08 GeV and at a temperature $T\simeq 44\mathrm{MeV}$. The upper (lower) panel is for electric (magnetic) propagators. The plots with error bars correspond to the lattice data. From bold to thin lines, they correspond to the analytic results at ${\alpha }_s=0.0$, 0.5, 1.0, and the ${\mathrm{\Delta }}_{T=0}=0.2\mathrm{GeV}$ and ${\mathrm{\Delta }}_{T=44}\simeq 157\mathrm{MeV}$.

Figure 5

The same as Fig. 4 except that the temperature is $T\simeq 118\mathrm{MeV}$, and $m_E$ and $m_M$ change slightly. The temperature is higher than $T_{\mathrm{SF}}$, so ${\mathrm{\Delta }}_{T=118}=0$.

Figure 6

The $T$ dependence of the gluon propagators at spatial momenta $|\mathbf{k}|=0.0$, 0.55, 1.08 GeV and at ${\mu }_q\simeq 0.71\mathrm{GeV}$. The upper (lower) panel is for electric (magnetic) propagators. The plots with error bars correspond to the lattice data. From bold to thin lines, they correspond to the analytic results at ${\alpha }_s=0.0$, 0.5, 1.0, and the ${\mathrm{\Delta }}_{T=0}=0.2\mathrm{GeV}$.