Probing gauge-Higgs Unification models at the ILC with quark-antiquark forward-backward asymmetry at center-of-mass energies above the Z mass

The International Linear Collider (ILC) will allow the precise study of $e^{-}e^{+}\rightarrow q\bar{q}$ interactions at different center-of-mass energies from the $Z$-pole to 1 TeV. In this paper, we discuss the experimental prospects for measuring differential observables in $e^{-}e^{+}\rightarrow b\bar{b}$ and $e^{-}e^{+}\rightarrow c\bar{c}$ at the ILC baseline energies, 250 and 500 GeV. The study is based on full simulation and reconstruction of the International Large Detector (ILD) concept. Two gauge-Higgs unification models predicting new high-mass resonances beyond the Standard Model are discussed. These models predict sizable deviations of the forward-backward observables at the ILC running above the $Z$ mass and with longitudinally polarized electron and positron beams. The ability of the ILC to probe these models via high-precision measurements of the forward-backward asymmetry is discussed. Alternative scenarios at other energies and beam polarization schemes are also discussed, extrapolating the estimated uncertainties from the two baseline scenarios.