Exact solution of the Dirac equation with CP violation - Prokopec, Tomislav; Schmidt, Michael G.; Weenink, Jan (Physical review. D, Particles, fields, gravitation, and cosmology, 2013)
We consider Yukawa theory in which the fermion mass is induced by a Higgs-like scalar. In our model the fermion mass exhibits a temporal dependence, which naturally occurs in the early Universe setting. Assuming that the complex fermion mass changes as a tanh-kink, we construct an exact, helicity-conserving, CP-violating solution for the positive- and negative-frequency fermionic mode functions, which is valid in both the weak and strong CP violation cases. Using this solution we then study the fermionic currents in both the initial vacuum and finite-density/-temperature setting. Our result shows that—due to a potentially large state squeezing—fermionic currents can exhibit a large oscillatory magnification. Having in mind applications to electroweak baryogenesis, we then compare our exact results with those obtained in a gradient approximation. Even though the gradient approximation does not capture the oscillatory effects of squeezing, it describes quite well the averaged current, obtained by performing a mode sum. Our main conclusion is that while the agreement with the semiclassical force is quite good in the thick-wall regime, the difference is sufficiently significant to motivate a more detailed quantitative study of baryogenesis sources in the thin-wall regime in more realistic settings.
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