The project was articulated along three complementary lines: 1) the development of precise predictions for flavour-changing observables; 2) the development of Effective Field Theory (EFT) approaches to analyse the consistency of general theoretical hypotheses addressing the origin of the flavour hierarchies, and other open problems of the SM, with experimental data; 3) the constructions of ultraviolet (UV) complete models addressing both the origin of the flavour hierarchies and the recent flavour anomalies. We made substantial progress on all these lines.
Line 1 has been an essential step to improve, both in quantity and in quality, the extraction of theoretical information from experimental data. In this context, we have presented the first systematic analysis of QED corrections in B→Kℓ+ℓ- decays at the double-differential level, reducing the theoretical uncertainty on the Lepton Flavour Universality ratios below the 1% level. We have also developed a novel method that allow us to extract precise information about the underlying short-distance dynamics from any hadronic transition of the type b→sℓ+ℓ-, including processes with many hadrons in the final state.
Line 2 has been a key ingredient to facilitate the interpretation of data and, most important, to test general hypotheses about the underlying theory. We have developed the innovative concept of an EFT describing generic extensions of the SM where the new dynamics couples mainly to the third generation. We have shown how this effective theory represents a well-defined limit of the so-called Standard Model EFT (or SMEFT). By a detailed comparison with both low- and high-energy data, we have also shown that, within this EFT, the scale of physics beyond the SM can be as low as 1.5 TeV without additional model-dependent assumptions. This is a key result that corroborates one of the key hypotheses of this project, namely the existence of a connection between the flavour problem and the hierarchy problem. We have also shown how this EFT can be embedded into UV-complete extensions of the SM featuring flavour non-universal gauge groups, which are particularly interesting in view of line 3, and we have uncovered a series of interesting effects arising at the quantum in such models.
The most original part of the project is the last line, where we introduced and developed the concept of “flavour deconstruction”. By this term we mean extensions of the SM in which one or more of the three fundamental forces, associated with a given (flavour-universal) gauge group, arises as the low-energy limit of a UV theory with manifestly non-universal flavour forces. We have shown that via this hypothesis, postulating the first layer of flavour non-universality at the TeV scale, it is possible to construct consistent SM extensions that can address both the origin of the flavour hierarchies and the Higgs hierarchy problem. We have also shown how flavour deconstruction in four dimensions can be viewed as the limit of a five-dimensional theory, with a compact fifth dimension and an appropriate set of branches along this dimension.
