Regular Article - Theoretical Physics
The exclusive vision of rare K and B decays and of the quark mixing in the standard model
TUM Institute for Advanced Study, Lichtenbergstr. 2a, 85747, Garching, Germany
2 Physik Department, TU München, James-Franck-Straße, 85748, Garching, Germany
Accepted: 2 July 2022
Published online: 15 July 2022
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 and 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 and rare K and B decays by anybody to date. We assume, in contrast to the prevailing inclusive expectations for , that the future true values of and will be both from exclusive determinations; in practice we use the most recent averages from FLAG. With the precisely known the resulting rare decay branching ratios, , , and depend then only on the angles and 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 hadronic matrix elements a tension in independently of is found. For the tension in between and is found and in the case of between and . Moreover, the room for new physics in , and decays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which in the former scenario is replaced by the most recent inclusive and present the dependence of all observables considered by us in both scenarios as functions of . As a byproduct we compare the determination of from , , and using hadronic matrix elements from LQCD with flavours, flavours and their average. Only for the case values for and exist for which the same value of is found: , and . This in turn implies a anomaly in .
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