Hubble-induced mass from MSSM plasma

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.