Effects of subleading operators in the heavy quark effective theory

Abstract

The heavy quark effective theory is a powerful approach for calculating form factors for hadronic processes involving heavy (c and b) quarks. In this note, we investigate the leading order effects of the finite charm quark mass on semileptonic B decays and c c production. We find that the matrix elements of dimension-four operators suppressed by one power of Λ QCD m c in the weak hadronic current may be parameterized by a single new non-perturbative function and one unknown dimensionful constant. Dimension-five operators in the effective lagrarian which break the spin-flavour SU(4) of the lowest order lagrangian introduce corrections of the same order of magnitude; these require the introduction of three more non-perturbative form factors. However, when the initial and final velocities of the heavy quark are equal, the Λ QCD m c corrections vanish and the absolutely normalized lowest order predictions remain valid.