Hard dense loops in a cold non-Abelian plasma

Abstract

Classical transport theory is used to study the response of a non-Abelian plasma at zero temperature and high chemical potential to weak color electromagnetic fields. In this article the parallelism between the transport phenomena occurring in a non-Abelian plasma at high temperature and high density is stressed. Particularly, it is shown that at high densities it is also possible to relate the transport equations to the zero-curvature condition of a Chern-Simons theory in three dimensions, even when quarks are not considered ultrarelativistic. The induced color current in the cold plasma can be expressed as an average over angles, which represent the directions of the velocity vectors of quarks having Fermi energy. From this color current it is possible to compute n-point gluonic amplitudes, with arbitrary n. It is argued that these amplitudes are the same as the ones computed in the high chemical potential limit of QCD, that are then called hard dense loops. The agreement between the two different formalisms is checked by computing the polarization tensor of QED due to finite density effects in the high density limit.

Erratum: Schwinger-Dyson approach to color superconductivity in dense QCD [Phys. Rev. D61, 056001 (2000)]

“…In the hard dense loop approximation, the result for the polarization tensor is given by [25][26][27],…”

“…The calculation of the polarization tensor was performed by others [25][26][27] and we are not going to repeat it here. Instead we present the final result and comment on its essential features.…”

Hard loops, soft loops, and high density effective field theory

“…In this section we review the calculation of hard dense loop contributions to QCD Greens functions [22,23,24]. The hard dense loop limit corresponds to soft external momenta, | p| ≪ µ.…”

Directional dependence of a color superconducting gap in two-flavor QCD in a magnetic field

“…In the case of a weak external field, the screening of the one-gluon interaction in dense medium can be described well by the usual hard-dense loop approximation [34][35][36]. In the Coulomb gauge, the Lorentz structure of the gluon propagator is given by [37,38] …”

“…In the most important regime for Cooper pairing dynamics, q 0 ≪ | q| ≪ m D , the approximate expressions for these screening functions read [34][35][36] …”