Exclusive non-leptonic B meson decays from QCD

Exclusive non-leptonic decays play a crucial part in the on-going programme to clarify the sources of CP violation and rare flavour-changing phenomena. As regards CP violation this is illustrated by the fact that there exists a fair knowledge of the length of each of the sides of the unitarity triangle from semi-leptonic B decays and BB̄ mixing. Since recently, the angle β (more precisely, sin 2β) is determined fairly accurately by the time-dependent CP asymmetry in the nonleptonic decay Bd → J/ψKS and related ones. However, the direct measurement of the other angle γ, the phase of V ∗ ub in the standard phase convention, remains a challenge to theory and experiment. Although γ is determined indirectly through the other measurements, the complementary direct determination is important, since meson mixing and rare non-leptonic decays could be affected by new flavour-changing interactions. The angle γ can be determined from decays with some kind of interference of b → cūD (no phase) and b → uc̄D (phase γ) tree transitions and their conjugates (D = d, s) or from decays with interference of b→ uūD (tree, phase γ) and b→ Dqq̄ (penguin, phase 0 (D = s), β (D = d)). There exist a few methods that allow one to obtain γ in a theoretically clean way, which means that no calculation of strong interaction effects is needed, but these methods are all difficult to realize experimentally at present. The more general