arXiv 2003.142892020-03-31hep-phhep-th

$O(α^2)$初始状态QED对$e^+e^- \rightarrow γ^/Z_0^$的修正

The $O(α^2)$ Initial State QED Corrections to $e^+e^- \rightarrow γ^*/Z_0^*$

J. Blümlein, A. De Freitas, C. Raab, K. Schönwald

备注：: 32 pages Latex, several figures
DOI：: 10.1016/j.nuclphysb.2020.115055

摘要：

本文在不作任何近似的情况下，用直接解析计算的方法计算了$e^+ e^-$湮灭为中性矢量玻色子的完全$O(α^2)$初态辐射修正。的更正表示在迭代不完全（椭圆）积分的平方根值字母表。在极限$s \gg m_e^2$下，我们发现与文献[1]~[2]的结果不一致\cite{Berends:1987ab}并确认参考文献~中获得的结果\cite{Blumlein:2011mi}，其中使用了大量算子矩阵元素的有效方法，该方法适用于$m^2_e/s$中除幂校正之外的所有校正。这样，我们也证实了在Drell-Yan过程中大质量部分子因式分解的有效性。我们在$O(α^2)$处添加了以前计算中未考虑的非对数项。极限$s \gg m_e^2$的最终结果可以用尼尔森积分给出。

英文摘要：

We calculate the complete $O(α^2)$ 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 $O(α^2)$ 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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英文摘要：

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