Relativistic corrections to the axial vector and vector currents in the bar{b}c meson system at order alpha_s

TL;DR

This paper calculates relativistic corrections to the axial vector and vector currents in the B_c meson system at order alpha_s, showing rapid convergence of decay rate corrections and providing coefficients for phenomenological applications.

Contribution

It introduces the first calculation of relativistic corrections at order alpha_s for the meson-to-vacuum matrix elements in B_c mesons, including all orders in relative momentum.

Findings

Relativistic corrections at order alpha_s converge rapidly.

Corrections of order alpha_s^2|vec{q}|^0 are large and problematic.

Results enable improved predictions for B_c meson production and decay.

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 bar{b}c mesons, respectively. The computation is carried out to order alpha_s including relativistic corrections of all orders in vec{q}^{2n}, where vec{q} is the relative momentum of the bar{b} 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 alpha_s^2|vec{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.