The O( α 2) initial state QED corrections to e + e ? annihilation to a neutral vector boson revisited

摘要

We calculate the non-singlet, the pure singlet contribution, and their interference term, atO(α2)due to electron-pair initial state radiation toe+e?annihilation into a neutral vector boson in a direct analytic computation without any approximation. The correction is represented in terms of iterated incomplete elliptic integrals. Performing the limits?me2we find discrepancies with the earlier results of Ref. and confirm results obtained in Ref. where the effective method of massive operator matrix elements has been used, which works for all but the power corrections inm2/s. In this way, we also confirm the validity of the factorization of massive partons in the Drell–Yan process. We also add non-logarithmic terms atO(α2)which have not been considered in . The corrections are of central importance for precision analyses ine+e?annihilation intoγ?/Z?at high luminosity.