Bhabha scattering at ILC250

This note intends to give an estimate on the sensitivity of the channel ee to ee at the future ILC250. At variance with other two fermion processes, the so-called Bhabha process is influenced by t-channel Z/photon exchange. In spite of the complexity of the resulting angular distribution of this process, one observes a good sensitivity to Zprime exchange, similar to those observed in annihilation channels. This feature is illustrated within the gauge-Higgs unification model, GHU, which shows an impressive indirect sensitivity to the mass of Zprime particles, up to about 20 TeV for the leptonic channels. Beam longitudinal polarisation and high luminosity are the key ingredients for this result. Measuring the Zprime ee coupling with the Bhabha process allows to measure separately Zprimemumu and Zprimetautau coupling, which serves for a precise test of lepton universality. Zprimebb and Zprimett couplings show good sensitivities to GHU. LHC and HE-LHC sensitivities are also discussed.