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1.3 The Three Types of CP Violation in B Decays 15

In terms of|q/p|,

as1=1|q/p|41+|q/p|4, (1.54)

which follows from

-νX|H|Bphys0(t)=(q/p)g-(t)A*,+νX|H|B¯phys0(t)=(p/q)g-(t)A. (1.55)

As can be seen from the discussion in Section 1.2.3, eff ects of CP violation in mixing in neutral Bd decays, such as the asymmetries in semileptonic decays, are expected to be small, O(10-2) . Moreover, to calculate the deviation of q/p fr om a pure phase, one needs to calculate I12 and M12. This involves large hadronic uncertainties, in particular in the hadronization models for I12. The overall uncertainty is easily a factor of 23 in |q/p|1[10]. Thus even if such asymmetries are observed, it will be difficult to relate their rates to fundamental CKM parameters.

1.3.3 CP Violation in the Interference Between Decays With and Without Mixing

Finally, consider neutral B decays into final CP eigenstates, fCP[14, 15, 16]. Such states are accessible in both B0 and -B decays. The quantity of interest here that is independent of phase conventions and physically meaningful is λ ofEq. (1.42), λ=ηfCPqpA¯f¯CPAfCP. When CP is conserved, |q/p|=1, |A¯f¯CP/AfCP|=1, and furthermore, the relative phase between (q/p) and (A¯f¯CP/AfCP) vanishes. Therefore, Eq. (1.42) implies

λ±1 CP violation: (1.56)

Note that both CP violation in decay (1.47) and CP violation in mixing (1.52) lead to (1.56) through jj 1. However, it is possible that, to a good approximation, |q/p|=1 and |A¯/A|=1, yet there is CP violation:

|λ|=1,Imλ0. (1.57)

This type of CP violation is called CP violation in the intererence betw een decays with and without mixing here; sometimes this is abbreviated as ""interference between mixing and decay.“ As explained in Section 1.6, this type of CP violation has also been observed in the neutral kaon system.

For the neutral B system, CP violation in the interference between decays with and without mixing can be observed by comparing decays into final CP eigenstates of a time‐evolving neutral B state that begins at time zero as B0 to those ofthe state that begins as a B¯0:

a fCP=I(Bphys0(t)fCP)I(B¯phys0(t)fCP)I(Bphys0(t)fCP)+I(B¯phys0(t)fCP). (1.58)