Effective chemical potential in spontaneous baryogenesis

Abstract

Models of spontaneous baryogenesis have an interaction term ∂μθjBμ in the Lagrangian, where jBμ is the baryonic current and θ can be a pseudo-Nambu-Goldstone boson. Since the time component of this term, θjB0, equals θnB for a spatially homogeneous current, it is usually argued that this term implies a splitting in the energy of baryons and antibaryons, thereby providing an effective chemical potential for baryon number. In thermal equilibrium, one then obtains nB∼θT2. We however argue that a term of this form in the Lagrangian does not contribute to the single particle energies of baryons and antibaryons. We show this for both fermionic and scalar baryons. However, similar to some recent work, we find that despite the above result the baryon number density obtained from a Boltzmann equation analysis can be proportional to θT2. Our arguments are very different from that in the standard literature on spontaneous baryogenesis. © 2018 authors. Published by the American Physical Society.