Hubble-induced mass from MSSM plasma

We evaluate the effective mass of a scalar field φ coupled to thermal plasma through Planck-suppressed interactions. We find it useful to rescale the coupled fields so that all the φ-dependences are absorbed into the yukawa and gauge couplings, which allows us to read off the leading order contributions to the effective mass m_φ from the 2-loop free energy calculated with the rescaled couplings. We give an analytical expression for m _φ at a sufficiently high temperature in the case where φ is coupled to the MSSM chiral superfields through non-minimal Kähler potential. We find that |m_φ²| is about 10 ^-3H² ∼ 10^-2H² at the leading order in terms of the couplings for typical parameter sets, where H is the Hubble expansion rate in the radiation-dominated era.