Relativistic corrections to the axial vector and vector currents in the (b)over-barc meson system at order alpha(s)

Abstract

We compute the short distance coefficients for the NRQCD factorization formulas of the meson-to-vacuum matrix elements for the axial vector and vector parts of the charged weak current in the S-wave spin-singlet and -triplet (b) over barc mesons, respectively. The computation is carried out to order alpha(s) including relativistic corrections of all orders in q(2n), where q is the relative momentum of the (b) over bar and c in the meson rest frame. The relativistic corrections at order alpha(s) are new. The results reveal that the relativistic corrections to the leptonic decay rate of the B-c meson at order alpha(s) or less converge rapidly, which shows a strong contrast to the uncomfortably large corrections of order a(s)(2) |q|(0). The short distance coefficients listed in this paper can be employed to compute the resummation of relativistic corrections to the phenomenological measurables that involve B-c and B-c* production and decay.