Bhabha scattering in the gauge-Higgs unification

Abstract

We examine effects of $Z^{\prime }$ bosons in gauge-Higgs unification (GHU) models at ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to {\mathrm{e}}^{+}{\mathrm{e}}^{-}$ Bhabha scatterings. We evaluate differential cross sections in Bhabha scatterings including $Z^{\prime }$ bosons in two types of $\mathrm{SO}(5)\times \mathrm{U}(1)\times \mathrm{SU}(3)$ GHU models. We find that deviations of differential cross sections in the GHU models from those in the SM can be seen at $\sqrt{s}=250\mathrm{GeV}$. With $80\%$-longitudinally polarized electron and $30\%$-longitudinally polarized positron beams, the left-right asymmetries in the GHU A- and B-models are resolved at more than $3\ddot{I}ƒ$ at $L_{\mathrm{int}}=250{\mathrm{fb}}^{-1}$. We also show that Bhabha scattering with scattering angle less than 100 mrad can be safely used as luminosity measurements in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ colliders since the effects of $Z^{\prime }$ bosons are well suppressed for small scattering angle. We propose a new observable which can be measured at future TeV-scale ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ linear colliders.

22 pages, 8 figures, 3 tables (v2) comments added