Comments on the review of CP Violation in the Particle Data Book

Rephasing invariant formalism for the K 0 − ¯ K 0 system is recommended for the Particle Data Group. This formalism is accurate and prevents possible errors in generalizing the formalism to other systems, as well as in using CKM matrices not included in the Particle Data Book. The 1998 Particle Data Book (PDB) is already available on the Web site. In this brief note I will comment on an essential part of " CP Violation " (referred as CPVW) prepared by L. Wolfenstein. Compared with the old version[1] by Wolfenstein and Trippe, a crucial differentiation is made, for the study of the K 0 system, between the parameter˜ǫ in (12.3) (that is phase convention dependent) and ǫ in (12.5a) (that is phase convention independent). However a further improvement may help the CLEO group to avoid a mistake in assuming, for the B d system, a counterpart of Eq (12.5d), Reǫ B d ≈ 1 4 a ll [2], which is still in the new version of the PDB. All three recommended forms of the CKM matrix (RCKM)[3] in the Particle Data Book provide the same a ll of order 10 −4. But they give large and different Reǫ B d. Indeed, ǫ B d = (1+σ)−(1−σ)e iθ (1+σ)+(1−σ)e iθ , where θ = arg(V tb V * td) 2 , and σ = 1 2 B H |B L ∼ 10 −4. The phase θ can be arbitrarily changed by changing the phase of the b-quark field, for example. Consequently, ǫ B d can be as large as 1/σ ∼ 10 4. This is an example of how generalizing a formalism for the K 0 system under specific phase conventions (to be discussed later) leads to mistakes because for the B d system the same conventions (such as RCKM) do not lead to similar formulas.