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1.3 The Three Types of CP Violation in B Decays 13

A second type of phase can appear in scattering or decay amplitudes even when the Lagrangian is real. Such phases do not violate CP, since they appear in Af and A¯f¯ with the same sign. Their origin is the possible contribution fr om intermediate on‐shell states in the decay process, that is an absorptive part of an amplitude that has contributions from coupled channels. Usually the dominant rescattering is due to strong interactions, hence the designation strong phases“ for the phase shiftts so induced. Again only the relative strong phases of diff erent terms in a scattering amplitude have physical content, an overall phase rotation ofthe entire amplitude has no physical consequences.

Thus it is useful to write each contribution to A in three parts: its magnitude Ai, its weak‐phase term eiφi, and its strong phase term eiδi. Then, if several amplitudes contribute to B0f, the amplitude Af (see (1.20)) and the CP conjugate amplitude A¯f¯ (see (1.21)) are given by:

Af=iAiei(δi+φi),A¯f¯=e2i(ξf-ξB)iAiei(δi-φi), (1.45)

where ξf and ξB are defined in 1.2.2. (If f is a CP eigenstate then e2iξf=±1 is its CP eigenvalue.) The convention‐independent quantity is then

|A¯f¯Af|=|ΣiAiei(δi-φi)ΣiAiei(δi+φi)|. (1.46)

When CP is conserved, the weak phases φi are all equal. Therefore, fr om Eq. (1.46) one sees that

|A¯f¯/Af|1 CP violation. (1.47)

This type of CP violation is here called CP violation in decay. It is oft en also called direct CP violation. It results fr om the CP‐violating interference among various terms in the decay amplitude. From Eq. (1.46) it can be seen that a CP violation of this type will not occur unless at least two terms that have diff erent weak phases acquire diff erent strong phases, since:

|A|2|A¯|2=2i,jAiAjsin(φiφj)sin(δiδj) . (1.48)

Any CP asymmetries in charged B decays,

af=I(B+f)I(B-f¯)I(B+f)+I(B-f¯), (1.49)

are fr om CP violation in decay. In terms ofthe decay amplitudes

af=1|A¯/A|21+|A¯/A|2. (1.50)

CP violation in decays can also occur for neutral meson decays, where it competes with the other two types of CP violation eff ects described below. There is as yet no unambiguous experimental

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