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Articles Cosmology Baryon Number Generation in the Early Universe (1980)
Baryon Number Generation in the Early Universe (1980) |
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Constraints on CP Violation
In eq. (2.1.9) we showed that to obtain a 
-violating difference between partial cross sections of the form
cannot (except when 
mixing is possible, as discussed in subsect. 2.4) occur in the Born approximation, and requires loop corrections with absorptive (imaginary) parts. Here, we first show that a difference between cross sections summed over all final states 
with baryon number 
cannot occur unless the loop corrections are also 
-violating. We write
where 
is a -violating Born amplitude (which is necessarily conserving) and 
represents a correction (analogous to rescattering) which introduces violation, but is taken to be -conserving. Then
Since is baryon conserving, it must obey the unitarity constraint
when summed only over the accessible states 
of a given baryon number. Using this result, eq (B.4) becomes
since is -conserving. Hence to obtain a -violating difference of the form (B.2) after summing over states 
the hamiltonian responsible for the loop correction (hence ) must violate baryon number. This constraint severely restricts baryon generation in gauge models, as discussed in ref. [11,29].
