Second-order power corrections in the heavy-quark effective theory. I. Formalism and meson form factors

Abstract

In the heavy-quark effective theory, hadronic matrix elements of currents between two hadrons containing a heavy quark are expanded in inverse powers of the heavy-quark masses, with coefficients that are functions of the kinematic variable $v·v^{\prime }$. For the ground-state pseudoscalar and vector mesons, this expansion is constructed at order $\frac{1}{m_Q^2}$. A minimal set of universal form factors is defined in terms of matrix elements of higher-dimensional operators in the effective theory. The zero recoil normalization conditions following from vector current conservation are derived. Several phenomenological applications of the general results are discussed in detail. It is argued that at zero recoil the semileptonic decay rates for $B\to D\ell \nu$ and $B\to D^{*}\ell \nu$ receive only small second-order corrections, which are unlikely to exceed the level of a few percent. This supports the usefulness of the heavy-quark expansion for a reliable determination of $V_{\mathrm{cb}}$.g