Hubble-induced mass from MSSM plasma

TL;DR

This paper calculates the effective mass of a scalar field in the MSSM plasma during the radiation era, revealing it to be significantly smaller than the Hubble rate, with implications for early universe cosmology.

Contribution

It provides an analytical expression for the Hubble-induced mass of a scalar field coupled to MSSM plasma via Planck-suppressed interactions, using a novel rescaling method.

Findings

Effective mass squared is about 10^{-3} to 10^{-2} times H^2.

Rescaling fields simplifies the calculation of the effective mass.

Analytical formula derived for high-temperature regime.

Abstract

We evaluate the effective mass of a scalar field phi coupled to thermal plasma through Planck-suppressed interactions. We find it useful to rescale the coupled fields so that all the phi-dependences are absorbed into the yukawa and gauge couplings, which allows us to read off the leading order contributions to the effective mass \tilde m_{phi} from the 2-loop free energy calculated with the rescaled couplings. We give an analytical expression for \tilde m_{phi} at a sufficiently high temperature in the case where phi is coupled to the MSSM chiral superfields through non-minimal Kahler potential. We find that \tilde m_{phi}^2 is about 10^{-3} H^2 \sim 10^{-2} H^2 for typical parameter sets, where H is the Hubble expansion rate in the radiation-dominated era.