Documentation of TauSpinner approach for electroweak corrections in LHC

The LHC Standard Model Z-boson couplings measurements approach the LEP legacy precision. The calculations of electroweak (EW) corrections available for the Monte Carlo generators become of relevance. Predictions of Z-boson production and decay require classes of QED/EW/QCD corrections and separatly from the production process QCD dynamics. At the LEP time electroweak form-factors and Improved Born Approximation were introduced for non QED genuine weak and line-shape corrections. This formalism was well suited for observables, so-called doubly-deconvoluted the Z-pole region where initial- and final-state QED real and virtual emissions were treated separately or were integrated over. The approach was convenient for implementation into Monte Carlo programs for LEP, Belle-BaBar and other future $$e^+e^-$$ colliders and for invariant mass of outgoing lepton pair from a few GeV to well above WW and even $$t{\bar{t}}$$ threshold. We attempt now to profit from that, for the LHC pp and 70–150 GeV window for the outgoing lepton pair invariant mass. Our technical focus is on the EW corrections for LHC $$Z \rightarrow \ell \ell $$ observables. For this purpose the TauSpinner package, for the reweighting of previously generated events, is enriched with the genuine EW corrections (QED effects subtracted) of the Dizet electroweak library, taken from the LEP era KKMC Monte Carlo. Complete genuine EW $$O(\alpha )$$ weak loop corrections and dominant higher-order terms are taken into account. For the efficiency and numerical stability look-up tables are used. For LHC observables: the Z-boson line-shape, the outgoing leptons forward-backward asymmetry, the effective leptonic weak mixing angles and finally for the spherical harmonic expansion coefficients of the lepton distributions, corrections are evaluated. Simplified calculations of Effective Born of modified EW couplings are compared with of Improved Born Approximation of complete set of EW form-factors. Approach uses LEP precision tests definitions and thus offers consistency checks. The package can be useful to evaluate of observables precision limits and to determine which corrections are then important for LHC and FCC projects phenomenology