Outcome from Spontaneous CP Violation for B Decays
  In the aspon model solution of the strong $CP$ problem, there is a gauged $U(1)$ symmetry, spontaneously broken by the same vacuum expectation value which breaks $CP$, whose massive gauge boson provides an additional mechanism of weak $CP$ violation. We calculate the $CP$ asymmetries in $B$ decays for the aspon model and show that they are typically smaller than those predicted from the standard model. A linear relation between the $CP$ asymmetries of different decay processes is obtained. 
A. W. Ackley, P. H. Frampton, B. Kayser, and C. N. Leung