Abstract
Matching and comparing the measurements of past and future experiments call for consistency checks of electroweak (EW) calculations used for their interpretation. On the other hand, new calculation schemes of the field theory can be beneficial for precision, even if they may obscure comparisons with earlier results. Over the years, concepts of Improved Born, Effective Born, as well as of effective couplings, in particular of sin ^2theta _W^{{textit{eff}}} mixing angle for EW interactions, have evolved. In our discussion, we use four versions of DIZET EW library for phenomenology of practically all HEP accelerator experiments over the last 30 years. We rely on the codes published and archived with the KKMC Monte Carlo program for e^+e^- rightarrow f {bar{f}} n(gamma ) and available for the TauSpinner as well. TauSpinner re-weighs generated events for introduction of EW effects. To this end, DIZET is first invoked, and its results are stored in data file and later used. Documentation of TauSpinner upgrade, to version 2.1.0, and that of its new arrangement for semi-automated benchmark plots are provided. In our paper, focus is placed on the numerical results, on the different approximations introduced in Improved Born to obtain Effective Born, which is simpler for applications of strong or QED processes in pp or e^+e^- colliders. The tau lepton polarization P_{tau }, forward–backward asymmetry A_{{textit{FB}}} and parton-level total cross section sigma ^{{textit{tot}}} are used to monitor the size of EW effects and effective sin ^2theta _W^{{textit{eff}}} picture limitations for precision physics. Collected results include: (i) Effective Born approximations and sin ^2theta _W^{{textit{eff}}}, (ii) differences between versions of EW libraries and (iii) parametric uncertainties due to, for example, m_t or Delta alpha _h^{(5)}(s). These results can be considered as benchmarks and also allow to evaluate the adequacy of Effective Born with respect to Improved Born. Definitions are addressed too.
Highlights
We focus on discussion/evaluation of: (i) the suitability of Effective versus Improved Born approximation, (ii) differences between results of DIZET library versions in use over the last 30 years, (iii) ambiguities due to parametric uncertainties or due to missing contributions
Let us turn our attention to the forward-backward asymmetry AFB
For the pp → Z /γ ∗ → l+l− process, energy range from 60 to 150 GeV was chosen which is of interest for EW effects
Summary
Born amplitudes remains intact and such re-definition usually does not break properties required for factorizing out strong interaction effects That is why, it was used for interpretation of LEP 2 data and is relatively easy to use for calculations of LHC, HL-LHC and FCC-hh phenomenology as well, where as we have pointed out, electroweak effects are not the main obstacle for precision. In an Improved Born (the most sophisticated picture developed at LEP 1 time) couplings are accompanied with energy- and angle-dependent, complex form factors This can damage strong interaction gauge invariance and would imply necessity of simultaneous. To address the above points, one needs to investigate first, if Improved or Effective Born can be localized and factorized with sufficient precision and kinematic details in calculations of strong interactions. The TauSpinner algorithms can be helpful in that respect and used to evaluate if for a given observable some classes of the corrections are necessary or can be ignored
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