Field-dependent renormalisation of baryogenesis condition in thermal inflation model

Abstract

The Affleck-Dine (AD) mechanism in thermal inflation model is reviewed. To realize baryogenesis, one condition, softly supersymmetry breaking quadratic mass of slepton and $H_u$ being negative, is imposed on a large field value. To examine its feasibility in low energy, it is necessary to translate the condition in terms of a low scale parameter. A difficulty arises because the condition is imposed on the field value while the goal is to translate it to a low energy scale. Using a simple toy model, I illustrate that after a renormalisation group improvement, under a specific renormalisation condition canceling large logarithms, a field value dependent renormalisation can be achieved and that it is equivalent to solving renormalisation equation of running parameters. I solve those equations and obtain the renormalised parameters in the baryogenesis condition using the perturbation in Yukawa couplings. Furthermore, Reliability of such perturbative expansion is discussed.