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

TL;DR

This paper calculates radiative corrections to the polarization tensor in SU(2) Yang-Mills theory at finite temperature, exploring implications for cosmic microwave background and galactic hydrogen cloud stability, with experimental and theoretical insights.

Contribution

It provides the first one-loop polarization tensor calculation for massless modes in SU(2) Yang-Mills thermodynamics, including two-loop pressure corrections and potential experimental tests.

Findings

Modified black-body spectrum at low momenta near CMB temperature

Proposed tabletop experiment to test SU(2)$_{CMB}$ hypothesis

Insights into galactic hydrogen cloud stability

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)$_{\tiny{CMB}}\stackrel{\tiny{today}}=U(1)_Y$, we discuss $\Pi$'s effect on the low-momentum part of the black-body spectrum at temperatures $\sim 2... 4$ $T_{\tiny{CMB}}$ where $T_{\tiny{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.