Subleading Logarithmic QED Initial State Corrections to $e^+e^- \rightarrow \gamma^*/{Z^{0}}^*$ to $O(\alpha^6 L^5)$

Understand

Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process $e^+e^- \rightarrow \gamma^*/Z^*$ 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.