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The O(α²) Initial State QED Corrections to e^+e^- rightarrow γ^*/Z₀^*

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arxiv 2003.14289 v1 pith:HVRERODQ submitted 2020-03-31 hep-ph hep-th

The O(α²) Initial State QED Corrections to e^+e^- rightarrow γ^*/Z₀^*

J. Bl\"umlein , A. De Freitas , C. Raab , K. Sch\"onwald This is my paper
classification hep-ph hep-th
keywords correctionsalpharesultstermsbeenciteconfirminitial
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We calculate the complete $O(\alpha^2)$ initial state radiation corrections to $e^+ e^-$ annihilation into a neutral vector boson in a direct analytic computation without any approximation. The corrections are represented in terms of iterated incomplete (elliptic) integrals over alphabets of square--root valued letters. 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 $m^2_e/s$. In this way, we also confirm the validity of the factorization of massive partons in the Drell--Yan process. We add non--logarithmic terms at $O(\alpha^2)$ which have not been considered in previous calculations. The final results in the limit $s \gg m_e^2$ can be given in terms of Nielsen integrals.

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