Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process $e^{+}{e}^{-}\to {\gamma }^{⁎}/Z^{⁎}$ for the first three logarithmic contributions from $O({\alpha }^3{L}^3),O({\alpha }^3{L}^2),O({\alpha }^{3}L)$ to $O({\alpha }^5{L}^5),O({\alpha }^5{L}^4),O({\alpha }^5{L}^3)$ and compare their effects to the leading contribution $O({\alpha }^6{L}^6)$ and one more subleading term $O({\alpha }^6{L}^5)$. The calculation is performed in the limit of large center of mass energies squared $s\gg m_e^2$. These terms supplement the known corrections to $O({\alpha }^2)$, which were completed recently. Given the high precision at future colliders operating at very large luminosity, these corrections are important for concise theoretical predictions. The present calculation needs the calculation of one more two–loop massive operator matrix element in QED. The radiators are obtained as solutions of the associated Callen–Symanzik equations in the massive case. The radiators can be expressed in terms of harmonic polylogarithms to weight w = 6 of argument z and $(1-z)$ and in Mellin N space by generalized harmonic sums. Numerical results are presented on the position of the Z peak and corrections to the Z width, ${\mathrm{\Gamma }}_Z$. The corrections calculated result into a final theoretical accuracy for $\delta M_Z$ and $\delta {\mathrm{\Gamma }}_Z$ which is estimated to be of $O(30\text{keV})$ at an anticipated systematic accuracy at the FCC_ee of $\sim 100\text{keV}$. This precision cannot be reached, however, by including only the corrections up to $O({\alpha }^3)$.

使用大规模算子矩阵元素的方法，我们计算了过程的次导QED初始状态辐射校正 ${Ë}^{+}{Ë}^{-}\to {\gamma }^{⁎}/{ž}^{⁎}$ 来自的前三个对数贡献 $Ø（{\alpha }^3{\mathrm{大号}}^3），Ø（{\alpha }^3{\mathrm{大号}}^2），Ø（{\alpha }^3\mathrm{大号}）$ 至 $Ø（{\alpha }^5{\mathrm{大号}}^5），Ø（{\alpha }^5{\mathrm{大号}}^4），Ø（{\alpha }^5{\mathrm{大号}}^3）$ 并将其影响与主要贡献进行比较 $Ø（{\alpha }^6{\mathrm{大号}}^6）$ 还有一个副词 $Ø（{\alpha }^6{\mathrm{大号}}^5）$。计算是在大的质能中心平方的极限内进行的$s\gg {米}_{Ë}^2$。这些术语补充了已知的更正$Ø（{\alpha }^2）$，这是最近完成的。鉴于未来对撞机在非常高的光度下工作时的高精度，这些修正对于简明的理论预测非常重要。当前的计算需要在QED中再计算一个二环大规模算子矩阵元素。在大量情况下，获得辐射体作为相关联的Callen–Symanzik方程的解。辐射体可以用谐波多对数表示，即参数z的权重w = 6和$（\mathrm{1个}-ž）$并在Mellin N空间中通过广义谐波和。数值结果显示在Z峰的位置以及Z宽度的校正上，${\mathrm{\Gamma }}_{ž}$。校正后的计算结果为最终的理论精度$\delta {\mathrm{中号}}_{ž}$ 和 $\delta {\mathrm{\Gamma }}_{ž}$ 估计是 $Ø（30\text{keV}）$ 以FCC_ee的预期系统准确性 $〜100\text{keV}$。但是，仅包含不超过$Ø（{\alpha }^3）$。