Finding signs of physics beyond the Standard Model is the main goal of particle physics. Flavour physics studies low-energy processes involving transitions between quarks of different flavours, that are among the most sensitive processes probing new physics.

In principle, flavour processes can probe energy scales much higher than those accessible in direct collider searches. In the next decades, experimental flavour physics will be dominated by two complementary experiments: the Large Hadron Collider (LHC) with the LHCb (and also the ATLAS and CMS) detectors, which have already produced a plethora of significant results probing the SM in the flavour sector, and the Belle-II experiment that will start its first physics run in early 2019. The two experiments are largely complementary. As a hadron collider, one of the unique features of LHC is the possibility to study heavy-flavour baryons; Belle-II, at an electron-positron machine, can instead uniquely probe processes with missing energy in the final state and measure absolute branching fractions.

On the theory side, flavour physics is particularly challenging as the study of low-energy processes involving quark flavour transitions necessarily deals with hadronic physics involving strong, non-perturbative interactions. Separating the short-distance dynamics ‒ including possible contributions from BSM physics ‒ from the long-distance QCD dynamics requires many different theoretical tools as well as data-driven methods in close collaboration with experimentalists. In addition to these “phenomenological” challenges, relating low-energy observations to dynamical models of BSM physics also requires sophisticated model building, considering also constraints outside of flavour physics, such as electroweak precision tests or direct searches for new particles.

In recent years, several tantalising hints for deviations from the SM have been observed in the flavour sector. Most notably, significant hints for a violation of lepton flavour universality in semi-leptonic B decays involving tau leptons (RD and RD*.), as well in FCNC B decays to muons and electrons (RK and RK*.) These two “anomalies” are experimentally unrelated but might find a unified description in terms of BSM physics. Solving this puzzle requires not only a strong experimental push, but also a concerted effort among experimentalists, phenomenologists, and model builders, to understand the uncertainties involved and the possible signals of new physics models hinted at.