Relativistic corrections to the axial vector and vector currents in the b̄c meson system at order α_s

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 b̄c mesons, respectively. The computation is carried out to order α_s including relativistic corrections of all orders in q ²ⁿ, where q is the relative momentum of the b̄ and c in the meson rest frame. The relativistic corrections at order α_s are new. The results reveal that the relativistic corrections to the leptonic decay rate of the B_c meson at order α_s or less converge rapidly which shows a strong contrast to the uncomfortably large corrections of order α²_s|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.