Effective chemical potential in spontaneous baryogenesis
  Models of spontaneous baryogenesis have an interaction term
$\partial_\mu\theta j^\mu_B$ in the Lagrangian, where $j^\mu_B$ is the baryonic
current and $\theta$ can be a pseudo-Nambu-Goldstone boson. Since the time
component of this term, $\dot{\theta} j^0_B$, equals $\dot{\theta} n_B$ 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} $n_B \sim \dot{\theta} T^2$. 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.
But, 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 $\dot{\theta} T^2$. Our arguments are very different from that
in the standard literature on spontaneous baryogenesis.
