Radiative corrections to the pressure and the one-loop polarization tensor of massless modes in SU(2) Yang-Mills thermodynamics

Abstract

We compute the one-loop polarization tensor $\Pi$ for the on-shell, massless mode in a thermalized SU(2) Yang-Mills theory being in its deconfining phase. Postulating that SU(2)${}_{CMB}\stackrel{today}{=}U(1{)}_Y$, we discuss $\Pi$'s effect on the low-momentum part of the black-body spectrum at temperatures $\sim \mathrm{2...4}$ $T_{CMB}$ where $T_{CMB}\sim 2.73$K. A table-top experiment is proposed to test the above postulate. As an application, we point out a possible connection with the stability of dilute, cold, and old innergalactic atomic hydrogen clouds. We also compute the two-loop correction to the pressure arising from the instantaneous massless mode in unitary-Coulomb gauge, which formerly was neglected, and present improved estimates for subdominant corrections.

25 pages, 17 figs, v4: consequences of a modification of the evolution equation for the effectice coupling implemented, no qualitative change of the physics

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