Revisiting the implications of CPT and unitarity for baryogenesis and leptogenesis

In the context of GUT baryogenesis models, a well-known theorem asserts that CPT conservation and the unitarity of S-matrix require that the lowest order contribution that leads to the generation of a non-zero net CP-violation via the decay of a heavy particle must be to $\mathcal{O}({\alpha_\slashed{B}}^3)$, where $\alpha_\slashed{B}$ is a baryon number (B) violating coupling. We revisit this theorem (which holds for lepton number (L) violation, and hence for leptogenesis as well) and examine its implications for models where the particle content allows the heavy particle to also decay via modes which conserve B (or L) in addition to modes which do not. We systematically expand the S-matrix order by order in B\slash L-violating couplings, and show, in such cases, that the net CP-violation is non-zero even to $\mathcal{O}({\alpha_\slashed{B}}^2)$, without actually contradicting the theorem. By replacing a B/L violating coupling (usually constrained to be small) by a relatively unconstrained B/L conserving one, our result may allow for sufficient CP violation in models where it may otherwise have been difficult to generate the observed baryon asymmetry. As an explicit application of this result, we construct a model in low-scale leptogenesis.