Past exam of the particle Astrophysics course of the University of Cambridge / 2012 / Paper 1 / 3 / c / Solution

The baryon excess requires a mechanism that produces different net baryon numbers from an initially symmetric ensemble. In the usual local, CPT-invariant framework, the Sakharov conditions are baryon-number violation, C and CP violation, and departure from thermal equilibrium. Baryon conservation would preserve zero net baryon number; exact conjugation symmetries equate the conjugate production processes; equilibrium inverse reactions and detailed balance erase a would-be asymmetry. These necessary conditions do not determine its magnitude.^[ref]

For example, let equal numbers of a heavy particle $X$ and its antiparticle decay into channels $i$ with baryon numbers $B_i$. Their mean net yield per pair isIt can be nonzero even though CPT requires equal total widths: the branching fractions differ among channels carrying different baryon numbers. A nonzero decay-rate asymmetry requires interference with both a CP-odd weak phase and an absorptive phase. If the expansion rate overtakes the inverse-reaction rate, decays can occur out of equilibrium; later baryon-violating washout must then be weak enough for the asymmetry to survive.

In electroweak baryogenesis, CP-asymmetric transport near a first-order phase-transition boundary can bias baryon-violating sphaleron transitions. CP violation alone is insufficient: the transition and washout dynamics also matter. In leptogenesis, out-of-equilibrium decays of heavy Majorana neutrinos can generate lepton asymmetry, part of which sphalerons convert into baryon asymmetry while conserving $B-L$. The CKM phase demonstrates CP violation in the Standard Model but does not by itself supply a successful cosmological mechanism. The key quantity is a surviving net charge yield, not merely the existence of a CP-violating reaction.