标题： 重新审视$O(α^2)$初始态 QED 校正对$e^+e^-$粒子湮灭为中性玻色子的影响 显示英文标题

标题： Revisiting the $O(α^2)$ Initial State QED Corrections to $e^+e^-$ Annihilation into a Neutral Boson

摘要： 在$e^+ \, e^-$对撞机上，QED 初始态辐射构成了辐射修正的很大一部分。 它们的精确且快速的评估对于在高亮度下运行的 LEPT、ILC 和 FCC-ee 实验来说是一项重要的资产。 在$O(\alpha^2)$初始态修正的解析计算中，有一个长期存在的问题，即在极限$m_e^2 \ll s$下，Berends 等人 (1988) \cite{Berends:1987ab}的结果与 Blümlein 等人 (2011) \cite{Blumlein:2011mi}使用质量算符矩阵元直接推导出该极限的结果之间存在差异。 为了解决这个重要问题，我们通过直接对相空间进行积分，没有任何近似地重新计算了这一过程。 对于部分修正，我们找到了交叉截面的精确解，这些解以代表不完全椭圆积分及其迭代的平方根值字母的迭代积分为基础。 在极限$m_e^2 \ll s$下的展开揭示了先前计算中常数$O(\alpha^2)$项的错误，并与基于质量算符矩阵元的计算结果一致，这对实验分析程序有影响。 这一发现也明确证明了在高能极限下大质量初态粒子的分解，包括该过程中的$O(\alpha^2)$项。 显示英文摘要

摘要： At $e^+ \, e^-$ colliders the QED--initial state radiation forms a large part of the radiative corrections. Their precise and fast evaluation is an essential asset for the experiments at LEP, the ILC and the FCC-ee, operating at high luminosity. A long standing problem in the analytic calculation of the $O(\alpha^2)$ initial state corrections concerns a discrepancy which has been observed between the result of Berends et al. (1988) \cite{Berends:1987ab} in the limit $m_e^2 \ll s$ and the result by Bl{\"u}mlein et al. (2011) \cite{Blumlein:2011mi} using massive operator matrix elements deriving this limit directly. In order to resolve this important issue we recalculated this process by integrating directly over the phase space without any approximation. For parts of the corrections we find exact solutions of the cross section in terms of iterated integrals over square root valued letters representing incomplete elliptic integrals and iterations over them. The expansion in the limit $m_e^2 \ll s$ reveals errors in the constant $O(\alpha^2)$ term of the former calculation and yields agreement with the calculation based on massive operator matrix elements, which has impact on the experimental analysis programs. This finding also explicitly proofs the factorization of massive initial state particles in the high energy limit including the terms of $O(\alpha^2)$ for this process.