### Abstract

We show that one-loop scalar integrals contributing to the order-v ^{2n} relativistic corrections to the QCD vertex corrections to the spin-triplet S-wave heavy-quark-antiquark pair annihilation into a virtual photon can be expressed in terms of a single master integral. With an algebraic reduction combined with the tensor-integral reduction method, we first simplify the scalar integrals as linear combinations of two-point functions. The two-point functions are reduced into a single master integral by using the recurrence relations derived from integration by parts. Order-v^{2} formulas are explicitly derived, and a strategy to calculate the higher-order relativistic corrections at order α_{s}, is also given. The result may be very useful in calculating the order-v^{2n} relativistic corrections to the leptonic decay width of the spin-triplet S-wave heavy quarkonium at order α_{s}.

Original language | English |
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Pages (from-to) | 398-402 |

Number of pages | 5 |

Journal | Journal of the Korean Physical Society |

Volume | 50 |

Issue number | 2 |

Publication status | Published - 2007 Feb 1 |

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### Keywords

- Master integral
- NRQCD
- Relativistic corrections

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

^{2n}relativistic corrections to Γ[J/ψ → e

^{+}e

^{-}].

*Journal of the Korean Physical Society*,

*50*(2), 398-402.