Abstract
In the vev insertion approximation (VIA) the spacetime dependent part of the mass matrix is treated as a perturbation. We calculate the source terms for baryogenesis expanding both the self-energy and propagator to first order in mass insertions, which gives the same results as the usual approach of calculating the self-energy at second order and using zeroth order propagators. This procedure shows explicitly the equivalence between including the mass in the free or in the interaction Lagrangian. The VIA source then originates from the same term in the kinetic equation as the semi-classical source, but at leading order in the derivative expansion (the expansion in diamond operators). On top, another type of derivative expansion is done, which we estimate to be valid for a bubble width larger than the inverse thermal width. This cuts off the divergence in the VIA source in the limit that the thermal width vanishes.
Highlights
Degenerate mass limit) in the limit that the thermal width is taken to zero, while it is not clear what the physical origin of this enhancement is [38]
The vev insertion approximation (VIA) source can be derived from the Schwinger-Dyson equations, which in turn can be reformulated in terms of the Kadanoff-Baym (KB) equations
Our approach agrees with the known results, but has the advantage that it shows clearly the equivalence of expanding the transport equations in terms of mass perturbations or in self-energies
Summary
For simplicity we will consider a scalar model in this paper, which avoids complication with spin projections, but we expect the results can be rather straightforwardly generalized to fermionic models as well. Consider a two-flavor scalar model with CP violating couplings to the bubble background [39, 40]. The flavor-diagonal masses m2L,R are constant, while the off-diagonal mass δm2 = |δm2|eiθ depends on the bounce solution vb = vb(z) describing the bubble wall. In VIA the offdiagonal term is treated as an interaction, and the mass and flavor eigenstates coincide for the free Lagrangian. Φ interacts with the degrees of freedom in the plasma. These plasma effects are incorporated dressing the Green’s functions with a non-zero selfenergy.
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