"Non-leptonic decays of B mesons have been studied extensively since the 90s, when experimental progress made it possible to produce B mesons in large numbers and controlled conditions. These studies have been essential in testing and understanding the flavor and CP sector of the Standard Model. However, theory predictions are difficult to produce. The experimental program at LHC and Belle-II opens now the door to a more systematic study of exclusive non-leptonic B decays with more than 2 particles in the final state. The theoretical study of such decay modes is the subject of this project. The objective has been to put in place a framework and a set of calculations that will contribute to the theoretical understanding of these decay modes and to the interpretation of the wealth of experimental data.
This framework relies on the property of ""factorization"" of short and long-distance physics, and allows to write decay amplitudes in terms of simpler non-perturbative matrix elements. One of the main outputs of the research performed here has been the calculation of the non-perturbative matrix elements genuine of three-body non-leptonic decays in the borders of the kinematic phase space (B--> 2-meson form factors). One of the conclusions is that the method of light-cone sum rules with B-meson distribution amplitudes is the ideal approach so far. These calculations have been performed for the pi-pi and the K-pi systems, and it has been identified that the correction due to the width of the K* in B decays with K* mesons in the final states is as large as 20% at the level of the decay rate. This conclusion seems very relevant in applications to semileptonic rare decays, and will also be the case in non-leptonic decays as soon as experimental precision is improved. In addition, contributions from resonances at higher K-pi invariant masses are also found to be relevant for the determination of the B-->K* form factors. Another new element that we have introduced in this project is the possibility to use LHCb measurements at high K-pi invariant masses to gain knowledge on the K*.
Non-leptonic B decays are also used systematically to determine CKM parameters, which are fundamental constants related to flavor. As another output of this project, it has been realized that in the situation of generic physics beyond the Standard Model (SM), when new degrees of freedom are above the electroweak scale, the way we use non-leptonic B decays to gain access to these fundamental parameters has to be revised. We have presented a proposal for CKM determinations beyond the SM, and the avenue of revisiting the role of non-leptonic decays has been opened. Regarding the predictions for CP violation, the challenge remains in gaining control over different partial waves, and on the structure of CP-violating asymmetries far from the edges of the kinematic phase space. Thus, more work is needed in this direction, where hopefully future experimental studies will shed some light.
Finally, a symbiotic relationship between non-leptonic and rare B decays has been explored, in the quest towards a theoretical approach to ""non-local"" form factors. The conclusion is that a detailed experimental study of non-leptonic B decays such as B-->K* X(1--), where X(1--) is a generic hadronic final state with spin 1, and negative parity and charge conjugation, will be a strong handle for predictions of semileptonic FCNC decays."
