The exclusive vision of rare K and B decays and of the quark mixing in the standard model

The most common predictions for rare K and B decay branching ratios in the Standard Model in the literature are based on the CKM elements vertical bar V-cb vertical bar and vertical bar V-ub vertical bar resulting from global fits, that are in the ballpark of their inclusive and exclusive determinations, respectively. In the present paper we follow another route, which to our knowledge has not been explored for Delta M-s,M-d and rare K and B decays by anybody to date. We assume, in contrast to the prevailing inclusive expectations for vertical bar V-cb vertical bar, that the future true values of vertical bar V-cb vertical bar and vertical bar V-ub vertical bar will be both from exclusive determinations; in practice we use the most recent averages from FLAG. With the precisely known vertical bar V-us vertical bar the resulting rare decay branching ratios, epsilon(K) , Delta M-d , Delta M-s and S-psi KS depend then only on the angles beta and gamma in the unitarity triangle that moreover are correlated through the CKM unitarity. An unusual pattern of SM predictions results from this study with some existing tensions being dwarfed and new tensions being born. In particular using HPQCD B-s,d(0) - (B) over bar (0)(s,d) hadronic matrix elements a 3.1 sigma tension in Delta M-s independently of gamma is found. For 60 degrees <= gamma <= 75 degrees the tension in Delta M-d between 4.0 sigma and 1.1 sigma is found and in the case of epsilon(K) between 5.2 sigma and 2.1 sigma. Moreover, the room for new physics in K+ -> pi(+)nu(nu) over bar, K-L -> pi(0)nu(nu) over bar and B -> K(K*)nu(nu) over bar decays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which vertical bar V-cb vertical bar in the former scenario is replaced by the most recent inclusive vertical bar V-cb vertical bar and present the dependence of all observables considered by us in both scenarios as functions of gamma . As a byproduct we compare the determination of vertical bar V-cb vertical bar from Delta M-s, Delta M-d , epsilon(K) and S psi(KS) using B-s,d(0) -(B) over bar (0)(s,d) hadronic matrix elements from LQCD with 2 + 1 + 1 flavours, 2 + 1 flavours and their average. Only for the 2 + 1 + 1 case values for beta and gamma exist for which the same value of vertical bar V-cb vertical bar is found: vertical bar V-cb vertical bar = 42.6(4) x 10(-3), gamma = 64.6(16)degrees and beta = 22.2(7)degrees. This in turn implies a 2.7 sigma anomaly in B-s -> mu(+)mu(-).