The QED initial state corrections to the forward-backward asymmetry of e$^{+}$ e$^{-}$ → γ$^{∗}$/Z$^{0∗}$ to higher orders

The QED initial state corrections are calculated to the forward-backward asymmetry for e$^{+}$ e$^{-}$ → γ$^{∗}$/Z$^{0∗}$ in the leading logarithmic approximation to O(α$^{6}$L$^{6}$) extending the known corrections up to O(α$^{2}$L$^{2}$) in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-N and momentum fraction z-space. Numerical results are presented for various energies around the Z-peak by also including energy cuts. These corrections are of relevance for the precision measurements at the FCC_ee.