### 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 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 α^{2}
_{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.

Original language | English |
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Article number | 113 |

Journal | Journal of High Energy Physics |

Volume | 2011 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2011 Sep 28 |

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### Keywords

- Heavy quark physics
- QCD

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

_{s}

*Journal of High Energy Physics*,

*2011*(1), [113]. https://doi.org/10.1007/JHEP01(2011)113