Constraint of broken charge-conjugation invariance on the baryon asymmetry in grand unified theories

Abstract

The correct prediction for the baryon asymmetry is an important constraint on grand unified models. We examine a large class of models in which a group charge-conjugation operator $C$ can be defined. The existence of this operator $C$ tends to suppress the possible baryon asymmetry by a factor of $\frac{{V}^{2}}{{{m}_{X}}^{2}}$, where $V$ is related to the scale of $C$-invariance breaking and ${m}_{X}$ is the mass of the particles whose decays generate the baryon asymmetry. [These constraints do not apply to the standard $\mathrm{SU}(N)$ grand unified models because they do not possess a group charge-conjugation operator.] By making a few simplifying assumptions, we show that models where the $C$ operator exists fall into two classes. In one class of models, $C$-invariance breaking leads to a mild suppression of the baryon asymmetry and consistency with present-day observations is easily obtained. In a second class of models, the baryon asymmetry is suppressed by $\frac{{{M}_{N}}^{2}}{{{m}_{X}}^{2}}$, where $N$ is a superheavy Majorana neutrino. In such models, the observed baryon asymmetry requires that ${m}_{N}\ensuremath{\gtrsim}{10}^{10}$ GeV; implications for the masses of the ordinary light neutrinos are considered.