AbstractMatching 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 $$\sin ^2\theta _W^{{\textit{eff}}}$$
sin
2
θ
W
eff
mixing angle for EW interactions, have evolved. In our discussion, we use four versions of 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 Monte Carlo program for $$e^+e^- \rightarrow f {\bar{f}} n(\gamma )$$
e
+
e
-
→
f
f
¯
n
(
γ
)
and available for the as well. re-weighs generated events for introduction of EW effects. To this end, is first invoked, and its results are stored in data file and later used. Documentation of 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 $$e^+e^-$$
e
+
e
-
colliders. The $$\tau $$
τ
lepton polarization $$P_{\tau }$$
P
τ
, forward–backward asymmetry $$A_{{\textit{FB}}}$$
A
FB
and parton-level total cross section $$\sigma ^{{\textit{tot}}}$$
σ
tot
are used to monitor the size of EW effects and effective $$\sin ^2\theta _W^{{\textit{eff}}}$$
sin
2
θ
W
eff
picture limitations for precision physics. Collected results include: (i) Effective Born approximations and $$\sin ^2\theta _W^{{\textit{eff}}}$$
sin
2
θ
W
eff
, (ii) differences between versions of EW libraries and (iii) parametric uncertainties due to, for example, $$m_t$$
m
t
or $$\Delta \alpha _h^{(5)}(s)$$
Δ
α
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.
Lorentz invariant relative velocity and relativistic binary collisions
