The QED Initial State Corrections to the Forward-Backward Asymmetry of $e^{+}{e}^{-}\to {\gamma }^{\ast }/Z^{0\ast }$ to Higher Orders

Abstract

The QED initial state corrections are calculated to the forward-backward asymmetry for $e^{+}{e}^{-}\to {\gamma }^{\ast }/{Z^0}^{\ast }$ in the leading logarithmic approximation to $O({\alpha }^6{L}^6)$ extending the known corrections up to $O({\alpha }^2{L}^2)$ 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.

Dedicated to the Memory of Tini Veltman, who made it possible to probe the Standard Model at high precision

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• Forward-backward asymmetries of the heavy quark pair production in $e^{+}{e}^{-}$ collisions at $\mathcal{O}({\alpha }_s^2)$