Neutral gluon polarization tensor in a color magnetic background at finite temperature

Abstract

In the framework of SU(2) gluodynamics, we derive the tensor structure of the neutral gluon polarization tensor in an Abelian homogeneous magnetic field at finite temperature and calculate it in one-loop approximation in the Lorentz background field gauge. The imaginary time formalism and the Schwinger operator method are used. The latter is extended to the finite temperature case. The polarization tensor turns out to be non transversal. It can be written as a sum of ten tensor structures with corresponding form factors. Seven tensor structures are transversal, three are not. We represent the form factors in terms of double parametric integrals and the temperature sum which can be computed numerically. As applications we calculate the Debye mass and the magnetic mass of neutral gluons in the background field at high temperature. A comparison with the results of other authors is done.

Vacuum Superconductivity, Conventional Superconductivity and Schwinger Pair Production

“…The condensation of the ρ mesons in QCD is similar to the Nielsen-Olesen instability of the pure gluonic vacuum in Yang-Mills theory 27 (also at finite temperature 28 ) and to the magnetic-field-induced Ambjørn-Olesen condensation of the W -bosons in the standard electroweak model 29 . Both the ρ mesons in QCD, the gluons in Yang-Mills theory, and the W bosons in the electroweak model have the anomalously large g-factor, g ≈ 2.…”

Vacuum Superconductivity, Conventional Superconductivity and Schwinger Pair Production

“…As the field becomes stronger than the critical value (1), the ground state energy of the charged ρ mesons gets purely imaginary thus signaling a tachyonic instability of the ground state of the vacuum towards the ρ-meson condensation. The condensation of the ρ mesons in QCD is similar to the Nielsen-Olesen instability of the pure gluonic vacuum in Yang-Mills theory 26 (also at finite temperature 27 ) and to the magnetic-field-induced Ambjørn-Olesen condensation of the W -bosons in the standard electroweak model 28 . Both the ρ mesons in QCD, the gluons in Yang-Mills theory, and the W bosons in the electroweak model have the anomalously large g-factor, g ≈ 2.…”

Groundstate projection of the charged SU(2) polarization tensor in a chromomagnetic background field

“…In opposite, in a magnetic background field, there is no fictitious pole already at the one-loop level at any temperature. As shown in [12], the projection of the right-hand side of the Schwinger-Dyson equation, D À1 ðk 2 Þ ¼ k 2 À Å 2 , does not change sign. For example, for high T, the projection on the ground state takes the form hD À1 ðk 2 Þi ¼ k 2 ð1 þ 5:7T= ffiffiffiffiffiffi ffi gB p Þ.…”

“…The Debye mass becomes a function of the magnetic field, m D ¼ m D ðT ¼ 0ÞfðT= ffiffiffiffiffiffi ffi gB p Þ, where fðT= ffiffiffiffiffiffi ffi gB p Þ is some function turning into unity for B ! 0, but reducing m D for any finite B (see [12] for the neutral and [13] for the charged gluons). For the magnetic mass, a different picture is observed.…”

“…For the magnetic mass, a different picture is observed. For the color neutral gluon, in [12] the magnetic mass m m was found to vanish, m m ¼ 0, and the account for polarization tensor results merely in a renormalization of the external field like in QED.…”