Single Higgs Boson Production at Electron-Positron Colliders in Gauge-Higgs Unification

We examine contributions to single Higgs boson production processes via $Z'$ and $W'$ bosons in the $SU(3)_C\times SO(5)_W\times U(1)_X$ gauge-Higgs unification (GHU) model. In particular, we analyze the cross sections of three single Higgs boson production processes $e^-e^+\to Zh$, $e^-e^+\to \nu\bar{\nu}h$, and $e^-e^+\to e^-e^+h$ in the SM and the GHU model. For the Higgs strahlung process $e^-e^+\to Zh$, we show that for a parameter region satisfying the current experimental constraints, a maximum deviation from the SM is about up to 6% for the center-of-mass energy of the initial electron and positron $\sqrt{s}=250$ GeV and that from the SM is about up to 20% for $\sqrt{s}=500$ GeV, depending on the initial polarization of electron and positron. The deviation from the SM is monotonically increasing with respect to $\sqrt{s}$ for $\sqrt{s}\lesssim 1$ TeV. By using the Higgs strahlung process, it is possible to explore up to the region of tens of TeV in terms of the Kaluza-Klein (KK) mass. We also show that the sign of the bulk mass of a lepton multiplet in the GHU model can be determined by examining the deviation of the left-right symmetry of the $e^-e^+\to Zh$ process from the SM. The contributions to the cross sections of the $e^-e^+\to \nu\bar{\nu}h$ and $e^-e^+\to e^-e^+h$ processes via the $Z'$ and $W'$ bosons are relatively small compared to that for $e^-e^+\to Zh$ at least for $\sqrt{s}\leq 1$ TeV. As is the same as in the SM, the $e^-e^+\to\nu\bar{\nu}h$ process gives a main contribution to the single Higgs boson production processes for $\sqrt{s}\gtrsim 500$ GeV, but large deviations from the SM are only observed on energy scales close to the masses of the first KK gauge bosons or higher.