Meson distribution amplitudes - applications to weak radiative B decays and B transition form factors

This thesis examines the applications and determinations of meson light-cone distribution amplitudes. The investigation of such processes, in the context of $B$ physics, provides one with a rich and extensive way of determining the Standard Model parameters of the CKM matrix, which are essential in describing CP violation, and searching for tell-tale signs of new physics beyond the Standard Model. We investigate the twist-2 and twist-3 distribution amplitudes of light vector mesons and fully examine $\mathrm{S}\mathrm{U}(3{)}_{\mathrm{F}}$-breaking effects and include leading G-parity violating terms. Numerical values of the leading non-perturbative hadronic parameters are determined from QCD sum rules. The distribution amplitude results find direct application in the radiative $B$ decays to light vector mesons $B\to V\gamma$. We examine the phenomenologically most important observables in this decay mode using the formalism of QCD factorisation. We also include long-distance photon emission and soft quark loop effects, which formally lie outside the QCD factorisation formalism. The analysis encompasses all the modes $B_{u,d} \to \rho, \omega, K^$and$B_{s} \to \phi, \bar{K}^$\mathrm{.}Wealsocalculatethe$B \to \etapb$ transition form factor using QCD sum rules on the light-cone. We include the singlet contribution originating from the $\mathrm{U}(1{)}_{\mathrm{A}}$ anomaly and bring the calculation consistently within the $\eta$-$\text{etap}$ mixing framework.