Power corrections to leading logs and their application to heavy quark decays

Abstract

When a heavy virtual particle of mass M contributes to a process at low energies E ⪡ M, the anomalous dependence on M of the amplitude can be obtained by integrating out the heavy particle and constructing an effective hamiltonian. If there are two heavy particles of masses E ⪡ m ⪡ M one proceeds analogously, integrating them out in succession. But if m and M are comparable, the full dependence on both masses can produce a substantial correction. We consider the problem of keeping in the effective hamiltonian the full anomalous dependence on both heavy masses. We solve it by expanding perturbatively both in the gauge coupling constant and in the ratio of masses m/ M. The method we present has application in the static quark effective theory, in the context of which we compute corrections of order m c / m b to the form factors for B-meson to D-meson transitions.