The $O({\alpha }^2)$ Initial State QED Corrections to $e^{+}{e}^{-}$ Annihilation to a Neutral Vector Boson Revisited

Abstract

We calculate the non-singlet, the pure singlet contribution, and their interference term, at $O({\alpha }^2)$ due to electron-pair initial state radiation to $e^{+}{e}^{-}$ 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 limit $s\gg m_e^2$ we find discrepancies with the earlier results of Ref.~\cite{Berends:1987ab} and confirm results obtained in Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator matrix elements has been used, which works for all but the power corrections in $m^2/s$. 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 at $O({\alpha }^2)$ which have not been considered in \cite{Berends:1987ab}. The corrections are of central importance for precision analyzes in $e^{+}{e}^{-}$ annihilation into ${\gamma }^{\ast }/Z^{\ast }$ at high luminosity.

4 pages Latex, 2 Figures, several style files

References in corpus (10)

• Mellin Moments of the {$O({\alpha }_s^3$)} Heavy Flavor Contributions to unpolarized Deep-Inelastic Scattering at $Q^2\gg m^2$ and Anomalous Dimensions
• A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• Iterated Binomial Sums and their Associated Iterated Integrals
• The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)
• Muon Colliders
• The Compact Linear e${}^{+}$e${}^{-}$ Collider (CLIC): Physics Potential
• Universal Higher Order Singlet QED Corrections to Unpolarized Lepton Scattering
• Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm

Cited by in corpus (2)

• The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
• Initial state radiation correction and its effect to data-taking scheme for ${\sigma }^{\mathrm{B}}(e^{+}{e}^{-}\to ZH)$ measurement