Closed-form evaluation of integrals appearing in positronium decay.

A theoretical prediction for the total width of the positronium decay in quantum electrodynamics has been given by Kniehl et al. [“Irrational constants in positronium decays,” Nucl. Phys. B (Proc. Suppl.) 184, 14 (2008), arXiv:hep-ph/0811.0306] in the form of an expansion in Sommerfeld’s fine-structure constant. The coefficients of this expansion are given in the form of two-dimensional definite integrals, with an integrand involving the polylogarithm function. We provide here an analytic expression for the one-loop contribution to this problem. [ABSTRACT FROM AUTHOR]