We consider rare semileptonic decays of a heavy D-meson into a light vector meson in the framework of QCD factorization. In contrast to the corresponding B-meson decays, the naive factorization hypothesis does not even serve as a first approximation. Rather, the decay amplitudes appear to be dominated by non-factorizable dynamics, e.g. through annihilation topologies, which are particularly sensitive to long-distance hadronic contributions. We therefore pay particular attention to intermediate vector-meson resonances appearing in quark-loop and annihilation topologies. Compared to the analogous B-meson decays, we identify a number of effects that result in very large theoretical uncertainties for differential decay rates. Some of these effects are found to cancel in the ratio of partially integrated decay rates for transversely and longitudinally polarized ρ mesons. On the phenomenological side this implies a very limited potential to constrain physics beyond the Standard Model by means of these decays.

Abstract:The standard theoretical framework to deal with weak decays of heavy mesons is the so-called weak effective Hamiltonian. It involves the short-distance Wilson coefficients, which depend on the renormalisation scale µ.

We study the semileptonic decayBs → K * + −ν , which is induced by b → u −ν transitions at the quark level. We take into account the standard model (SM) operator from W -boson exchange as well as possible extensions from physics beyond the SM. The secondary decay K * + → Kπ can be used to study a number of angular observables, which are worked out in terms of short-distance Wilson coefficients and hadronic form factors. Our analysis allows for an independent extraction of the Cabibbo-Kobayashi-Maskawa matrix element |V ub | and for the determination of certain ratios ofBs → K * form factors. Moreover, a future precision measurement of the forward-backward asymmetry in theBs → K * + −ν decay can be used to unambiguously verify the left-handed nature of the transition operator as predicted by the SM. We provide numerical estimates for the relevant angular observables and the resulting decay distributions on the basis of available formfactor information from lattice and sum-rule estimates. In addition, we pay particular attention to suitable combinations of angular observables in the decaysBs → K * + (→ Kπ) −ν andB → K * 0 (→ Kπ) + − , and find that they provide complementary constraints on the relevant b → s shortdistance coefficients. As a by-product, we perform a SM fit on the basis of selected experimental decay rates and hadronic input functions, which results in |V ub | = (4.07 ± 0.20) · 10 −3 .