Factorization theorems, effective field theory, and nonleptonic heavy meson decays

Abstract

The nonleptonic heavy meson decays $B\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\pi}(\ensuremath{\rho}), J/\ensuremath{\psi}{K}^{(*)}$, and $D\ensuremath{\rightarrow}{K}^{(*)}\ensuremath{\pi}$ are studied based on the three-scale perturbative QCD factorization theorem developed recently. In this formalism the Bauer-Stech-Wirbel parameters ${a}_{1}$ and ${a}_{2}$ are treated as the Wilson coefficients, whose evolution from the $W$ boson mass down to the characteristic scale of the decay processes is determined by effective field theory. The evolution from the characteristic scale to a lower hadronic scale is formulated by the Sudakov resummation. The scale-setting ambiguity, which exists in the conventional approach to nonleptonic heavy meson decays, is removed. Nonfactorizable and nonspectator contributions are taken into account as part of the hard decay subamplitudes. Our formalism is applicable to both bottom and charm decays, and predictions, including those for the ratios $R$ and ${R}_{L}$ associated with the $B\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{(*)}$ decays, are consistent with experimental data.