STANDARD MODEL CONTRIBUTIONS TO THE NEUTRINO INDEX OF REFRACTION IN THE EARLY UNIVERSE

With the standard electroweak interactions, the lowest-order coherent forward-scattering amplitudes of neutrinos in a CP-symmetric medium (such as the early Universe) are zero, and the index of refraction of a propagating neutrino can only arise from the expansion of gauge-boson propagators, from radiative corrections, and from new physics interactions. Motivated by nucleosynthesis constraints on a possible sterile neutrino (suggested by the solar-neutrino deficit and a possible 17-keV neutrino), we calculate the standard model contributions to the neutrino index of refraction in the early Universe, focusing on the period when the temperature was of the order of a few MeV. We find sizable radiative corrections to the tree-level result obtained by the expansion of the gauge-boson propagator. For nu(e) + e (eBAR) --> nu(e) + e (eBAR) the leading-log correction is about + 10%, while for nu(e) + nu(e) (nu(e)BAR) --> nu(e) + nu(e) (nu(e)BAR) the correction is about + 20%. Depending on the family mixing (if any), effects from different family scattering can be dominated by radiative corrections. The result for nu + gamma --> nu + gamma is zero at the one-loop level, even if neutrinos are massive. The cancellation of infrared divergence in a coherent process is also discussed.