Sphaleron Erasure of Primordial Baryogenesis

Abstract

If the present baryon-asymmetry is due to a Planck or GUT-scale matter asymmetry then baryon- or lepton-number violating processes are constrained by the condition that they do not subsequently erase this asymmetry. We present a revision of the analysis of sphaleron baryon-number violating processes in the standard model including lepton-mass effects. We find the surprising result that a GUT-scale matter-asymmetry can survive the $B$ and $L$ violating sphaleron interactions even though ($B- L$) is conserved and equals zero for all temperatures. We extend the analysis to cover the minimal supersymmetric standard model (MSSM) and also derive the constraints on the R-parity violating couplings in extensions of the MSSM. In the case of the baryon number violating dimension 4 operators we find, contrary to current wisdom, that the resulting bounds can be avoided completely because of a residual lepton-flavour number conservation; in the case of lepton number violating operators we find the bounds are flavour dependent and can be avoided completely in definite flavour channels. We also consider how the bounds are modified in the case there is a Grand Unified extension of the supersymmetric model which introduces new lepton flavour violating couplings.