C1a : Inclusive semileptonic, rare and radiative decays of $B$ mesons

In project C1a various aspects of the Heavy Quark Expansion are used to provide precision predictions for inclusive B-meson decays. Both higher order perturbative corrections and non-perturbative matrix elements will be computed. This will lead to a more precise determination of fundamental flavour-physics parameters such as the Cabibbo-Kobayashi-Maskawa matrix element $V_{cb}$.

1. Quark Masses: improve relation between $m_{\rm kin}$ and pole mass; establish N$^3$LO relation between kinetic and $\overline{\rm MS}$ mass; include finite charm quark mass effects;
2. Heavy Quark Expansion for charged currents: QCD corrections to higher orders in the $1/m_Q$ expansion; QED Corrections for the precision determination
3. on $V_{cb}$; improvement of the inclusive $V_{ub}$ determination; improvement of the HQE parameters;
4. Inclusive Decays ${\mathbf{\bar B \to X_s \gamma}}$ and ${\mathbf{\bar B \to X_{s,(d)} \, \ell^+\ell^-}}$: 4-loop $Q_{1/2}-Q_7$ interference contribution; QED bremstrahlung corrections; constraining ``New Physics'' from FCNC $B$ Decays;
5. Increase precision of ${\mathbf{\bar B \to X_{s,(d)} \, \ell^+\ell^-}}$: treatment of resonances and analysis of $m_{X_s}$ cut effects; constraints on New Physics and interplay with exclusive modes; contributions of multi-parton final states;
6. Higher-order behaviour of the HQE: structures of the HQE at higher order and resummations; realistic models for Duality Violations;
7. Non-leptonic $B$ meson decays up to NNLO