Abstract
We study the Landau gauge gluon propagators in dense two-color QCD at quark chemical potential, $\mu_q$, in the range from 0.5 to 1.0 GeV not reachable by the perturbative method at weak coupling. In order to take into account the non-perturbative effects, at tree level we use a massive Yang-Mills model for the Yang-Mills theory (or the Curci-Ferrari model) which has successfully described the lattice results of the gluon and ghost propagators in the Landau gauge. We couple quarks to this theory and compute the one-loop polarization effects in medium. The presence of the gluon mass significantly tempers the medium effects and uncertainties associated with the strong coupling constant $\alpha_s$. The diquark condensate in two-color QCD is color-singlet, for which neither electric nor magnetic screening masses should appear at the scale less than the diquark gap. The presence of the gap helps to explain the lattice results which are not very sensitive to the quark density. Meanwhile we also found the limitation of the one-loop estimate as well as the lack of some physics in perturbative medium corrections.
Highlights
A highly compressed matter of quantum chromodynamics (QCD) is expected to transform from a hadronic to a quark matter when baryons overlap; quarks start to directly contribute to equations of state as well as transport properties of the matter [1]
Considering the size of hadrons of ∼0.5–1 fm the transition should occur around the baryon density nB ∼ 5–10n0 (n0 ≃ 0.16 fm−3: nuclear saturation density) or quark chemical potential μq 1⁄4 0.5–0.8 GeV [2,3]
We have studied the in-medium gluon propagator in QC2D by employing the CF model as an effective theory at the energy less than ∼1 GeV
Summary
A highly compressed matter of quantum chromodynamics (QCD) is expected to transform from a hadronic to a quark matter when baryons overlap; quarks (and gluons) start to directly contribute to equations of state as well as transport properties of the matter [1]. We combine the in-medium effects with nonperturbative vacuum gluon propagators For the latter, the Landau gauge studies in lattice QCD [27,28] and functional approaches [29,30,31,32] for pure Yang Mills (YM) theory have reported the generation of effective mass of mg ∼ 0.4–0.7 GeV at soft Euclidean momenta [33,34,35] for early studies) Based on this finding seminal works assumed the massive Landau gauge YM, or the Curci-Ferrari (CF) model [36] as an effective theory and performed the 1-loop calculations for gluon and ghost propagators, finding the remarkable agreement with the lattice results in vacuum [37,38] and reasonable agreement at finite temperature [39,40]. We will come back to this point after performing one-loop calculations with quarks
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