论文标题
对数的QED QED初始状态更正为$ e^+e^ - \rightarrowγ^*/{z^{0}}}^*$ to $ o（α^6 l^5）$
Subleading Logarithmic QED Initial State Corrections to $e^+e^- \rightarrow γ^*/{Z^{0}}^*$ to $O(α^6 L^5)$
论文作者
论文摘要
使用大量操作员矩阵元素的方法，我们计算出对过程$ o（α^3 l^3），o（α^3 l^2），o（α^3 l^2），O（α^3 l^3 l l）$ o（α^3 l^3）的前三个对数贡献$ e^+e^+e^+e^ - \rightArrowγ^*/z^*$的初始态辐射校正。 l^4），o（α^5 l^3）$，并将其效果与领先的贡献$ O（α^6 l^6）$和另一个subleading项$ o（α^6 l^5）$进行比较。计算以大型质量中心平方的限制进行，$ s \ gg m_e^2 $。这些术语将已知的校正补充到最近完成的$ O（α^2）$。考虑到以非常大的亮度运行的未来山着人的高精度，这些校正对于简洁的理论预测很重要。当前的计算需要在QED中进行另外两个环的大规模运算符矩阵元素的计算。在大规模的情况下，辐射器作为相关的Callen-symanzik方程的溶液获得。散热器可以用谐波属性来表达，以$ z $和$ z $和$ z $和$ z $的权重{\ sf w = 6}，以及通过通用的谐波总和在梅林$ n $ space中。 $ z $峰的位置和校正$ z $ width（$γ_z$）的位置显示了数值结果。校正计算为$Δm_z$和$Δγ_z$的最终理论准确性，估计在\ sim 100 kev的FCC \ _ee上以预期的系统准确性为O（30 KeV）。但是，仅包括最多$ o（α^3）$的校正来达到此精度。
Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process $e^+e^- \rightarrow γ^*/Z^*$ for the first three logarithmic contributions from $O(α^3 L^3), O(α^3 L^2), O(α^3 L)$ to $O(α^5 L^5), O(α^5 L^4), O(α^5 L^3)$ and compare their effects to the leading contribution $O(α^6 L^6)$ and one more subleading term $O(α^6 L^5)$. 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 $O(α^2)$, 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 {\sf 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, $Γ_Z$. The corrections calculated result into a final theoretical accuracy for $δM_Z$ and $δΓ_Z$ which is estimated to be of O(30 keV) at an anticipated systematic accuracy at the FCC\_ee of \sim 100 keV. This precision cannot be reached, however, by including only the corrections up to $O(α^3)$.
