Orthopositronium lifetime at O(alpha) and O(alpha^3 ln(alpha)) in closed form

TL;DR

This paper provides detailed calculations of the O(alpha) and O(alpha^3 ln(alpha)) radiative corrections to orthopositronium lifetime, revealing new constants and transformation formulas for polylogarithms, advancing precision in quantum electrodynamics.

Contribution

It presents the detailed derivation of closed-form expressions for higher-order radiative corrections to orthopositronium decay rate, including new constants and polylogarithm transformations.

Findings

Analytical expressions for O(alpha) and O(alpha^3 ln(alpha)) corrections

Identification of new mathematical constants involved

Transformation formulas for weight-four polylogarithms

Abstract

Recently, the O(alpha) and O(alpha^3 ln(alpha)) radiative corrections to the orthopositronium lifetime have been presented in closed analytical form, in terms of basic irrational numbers that can be evaluated numerically to arbitrary precision [Phys. Rev. Lett. 101, 193401 (2008)]. Here, we present the details of this calculation and reveal the nature of these new constants. We also list explicit transformation formulas for generalized polylogarithms of weight four, which may be useful for other applications.