Adequacy of Effective Born for electroweak effects and TauSpinner algorithms for LEP, Tevatron, HL-LHC and FCC simulated samples

Abstract: Matching and comparing measurements of past and future experiments calls for consistency checks of calculations used for their interpretation. New schemes of the field theory may optimize precision, but obscure comparisons with earlier results. Over years concepts of Improved Born, Effective Born, effective couplings, and sin^2theta_W^eff mixing angle for electroweak interactions, have evolved. We use four DIZET electroweak library versions; of today and of the last 30 years, wich were used for phenomenology of practically all HEP accelerator experiments. Versions differ by incremented with time updates of corrections. We rely on the codes archived with the KKMC Monte Carlo program for e^+e^- to f bar f n(gamma). Versions became recently available for the TauSpinner reweighting of simulated and stored events. Documentation of TauSpinner upgrade, to version 2.1.0, and of its arrangement for semi-automated electroweak (EW) effects benchmark plots are provided. Details which can be used to complete simulated sample with EW effects, are given. Focus is placed on numerical results and on approximations introduced in Improved Born to obtain Effective Born, to match with QCD corrections. The tau lepton polarization P_tau, forward backward asymmetry A_FB and parton level cross section sigma^tot are used to monitor electroweak effects and effective sin^2theta_W^eff limitations. Results include: (i) feasibility of Effective Born approximation and sin^2theta_W^eff, (ii) differences between versions of electroweak libraries and (iii) parametric ambiguities due to e.g. m_t or Delta alpha_h^5(s). Example results allow to evaluate adequacy of Effective Born with respect to Improved Born.