First- and higher-order noninterference QED radiative corrections to the charge asymmetry at theZresonance

A variety of analytical and numerical results on the noninterference QED $O\left(\alpha \right)$ and $O\left({\alpha }^2\right)$ corrections to forward-backward (charge) asymmetry $A_{\mathrm{FB}}$ are presented. Three definitions of the scattering angle and six definitions of the $A_{\mathrm{FB}}$ are examined. For loose cutoffs, at the $Z$ position, the pure $O\left({\alpha }^2\right)$ noninterference correction is found to be $\delta A_{\mathrm{FB}}\simeq 8\times {10}^{-3\mathrm{}}$ with the theoretical uncertainty below ∼1 × ${10}^{-3\mathrm{}}$. All numerical and analytical calculations can be parametrized using a simple semianalytical formula: $A_{\mathrm{FB}}$ to within $\delta A_{\mathrm{FB}}\simeq 8\times {10}^{-3\mathrm{}}$ on the $Z$ resonance and ≃0.5 × ${10}^{-2\mathrm{}}$ off the resonance, $M_Z-5\mathrm{} \mathrm{GeV}<\sqrt{s}<M_Z+5\mathrm{} \mathrm{GeV}$; the differential distribution $\frac{d\sigma }{dcos\theta }$ to a relative precision of 5 × ${10}^{-3\mathrm{}}$. These results can be very useful for (i) quantitative parametrization of the exact Monte Carlo results, (ii) discussion of the electroweak corrections, and (iii) experimental data analysis.