The elements of the CKM matrix are fundamental parameters of the Standard Model. Substantial experimental and theory efforts are under way, aimed at determining them ever more precisely and accurately. Interestingly, some tensions between different approaches have persisted over many years, in particular, between determinations from inclusive and exclusive semi-leptonic meson decays, respectively. This talk addresses new ideas aimed at resolving these tensions. In particular, I will discuss how fundamental principles like analyticity and unitarity can be used to improve existing, and enable new computations in lattice QCD. The ideas will be demonstrated for the analysis of simulations of exclusive as well as inclusive semileptonic $B_s$-meson decay. In the former case, the use of Bayesian inference allows for formulating a model- and truncation independent parameterisation of hadronic form factors. In the latter case, the properties of the QCD transfer matrix are used to tackle the computation of the inclusive decay rate for the first time.
Ankita Budhraja, Juraj Klaric, Johannes Michel, Maria Laura Piscopo