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-v2 formulas are explicitly derived, and a strategy to calculate the higher-order relativistic corrections at order αs, is also given. The result may be very useful in calculating the order-v2n relativistic corrections to the leptonic decay width of the spin-triplet S-wave heavy quarkonium at order αs.
|Number of pages||5|
|Journal||Journal of the Korean Physical Society|
|Publication status||Published - 2007 Feb 1|
- Master integral
- Relativistic corrections
ASJC Scopus subject areas
- Physics and Astronomy(all)