THE QUESTION OF CP NONINVARIANCE— AS SEEN THROUGH THE EYES OF NEUTRAL BEAUTY

We present a detailed review of the expected phenomenology of CP violation in neutral B l&D] meson decays. When stating predictions as obtained from the standard model, we emphasize the basic concepts involved and give general expressions; the numbers that we quote are meant to illustrate the method and provide guidelines, not to be precise predictions. PROLOGUE Among the many statements that can and have been made on CP violation, three stand out since they are unassailable without being trivial: A breakdown of CP invariance has been directly observed in nature, namely in KL decays. CP violation, despite its shy appearance on the stage of physics, represents a truly fundamental phenomenon-as it has been duly recognized from the 9E beginning. We cannot claim to have developed a real understanding of this phenomenon. This -in view of the first two points-is highly unsatisfactory, if-not outright embarrassing; it actually refers to two different levels: *Work supported by the Department of Energy, contract DEAC03-76SF00515. SHeisenberg fellow. To be published in the Review Book of CP Violation C. Jarlskog, Editor, World Scientific, Singapore (a) Considerable progress has been made in ‘Theoretical Engineering;” we have developed a rather clear picture on the various generic ways of ‘. . imbedding CP violation into a given t+eory.‘l But we have been unable to decide which of these mechanisms is the source, or even the dominant source, of the observed CP violation. (b) Considering the fundamental importance of CP violation one yearns for a deeper understanding that goes beyond the question of which mechanism describes the data properly. We do not -have anything specific to say concerning point (b); however, we believe that it can hardly find a satisfactory answer if point (a) remains unanswered. Furthermore, we feel strongly that CP violation has to be found outside the decays of neutral kaons before light can be shed on the underlying source. Beauty hadrons carry excellent promise to exhibit large observable CP asymmetries in their decays. This holds, in particular, in the KobayashiMaskawa (KM) ansatz2] where it is the interplay of three quark families that makes the phases of the weak couplings and thus CP violation observable. Beauty decays are then the process of choice: b quarks belong to the third family, yet have to decay into members of the lower families; even the top quarks are drawn 1. into this affair via B”-r mixing. This argument can of course be made in a more precise way: the unitarity of the KM matrix V yields, among others, the following three relations which are evidently invariant under changes in the phase convention adopted for the quark fields V(ud)V*(td) + V(us)V*(ts) + V(ub)V*(tb) = 0 , (1) V(ub)V*(ud) + V(cb)V*(cd) + V(tb)V*(td) = 0 , (2) 2 V(cd)V*(td) + V(cs)V*(ts) + V(cb)V*(tb) = 0 . (3) -Up to small corrections of order sin2 8,, these equations can be rewritten in a simplified fashion: 2 V*(td) + XV*(ts) + V(ub) N 0 , V(ub) XV(cb) + V*(td) H 0 , -AV*(td) + V*(ts) + V(cb) N 0 , (4) (5) (6) where X-sin@, . These equations represent triangle relations in the complex plane and-as first pointed out by Bjorken, L.-L. Chau and Jarlskog25]-are quite accessible to geometric intuition: (i) Different parametrizations of the KM matrix correspond just to different rotations of these triangles. (ii) The two triangles defined by Eqs. (4) and (5) actually agree to this order in X since obviously V* (ts) N -V(cb). This triangle is shown in Fig. 1 with a shape that is “typical” as explained later. (iii) The triangle defined by Eq. (6) is quite a squashed one since IV(ts)I N IV(cb)l > XIV(td)l. 5928Al hV(cb) Fig. 1. Triangle depicting dominant relative phases in KM ansatz with three families. 3 Figure 1 contains the main observation: there are sizeable relative phases between V(ub), V(cb) and V(td). They can all be probed with high sensitivity in beauty decays (where V (td) drives Bd zd mixing). . In K and D decays, on the other hand, the situation is much less favorable: V (cs) contains a CP violating phase, but only at order X4; V(td) is quite crucial for EK and c’, yet its numerical impact is greatly reduced by the smallness of V(td)V* (ts); furthermore, the dynamical “accident” (as far as CP violation is concerned) of the AI = l/2 rule reduces CP asymmetries like c’ by an additional order of magnitude. For more detailed considerations it is still useful to employ an explicit form of the KM matrix d S b lix2 x AX3 (p irj (1 :A”}) : VKM = -A 1 ‘x2 2 irjA2X4 AX2(1 + +X2) AX3(1 p iv) -AX2 I t ’ 1 (7) where we have used the Wolfenstein expansion up to order X4(X6) for the real (imaginary) parts of the charged current couplings. 1. Meaningful bounds now exist on all these parameters; one typically finds A = 1.1 f0.2 from 78 , (8) 0.08 s p2 +v2 2 1.0 from B -+pFr(r) , Iv noncharm, (9) p < 0 from Bd Bd mixing . (10) To derive more specific numbers one has to proceed with considerable care and caution. For at present no precise scheme exists for describing weak decays that has been derived from first principles; instead one is limited to employing various phenomenological prescriptions whose reliability is not well established. Furthermore they introduce systematic correlations among the numerical values for the KM parameters as they are inferred from the data. Accordingly, one has to apply these schemes consistently. c