paper was performed at next-to-leading order (NLO) in pQCD.

The $ep$ cross sections measured at HERA were published after they were corrected for leading order (LO) quantum-electrodynamic (QED) radiative effects. These are dominated by initial- and final-state photon emission by the electron.

The neutral current (NC) cross section at all orders of pQCD for $e^ \pm p$ scattering can be written as [@MANDY]

$${\frac{d^{2}\sigma_{\rm NC}(e^{\pm}p)}{dx_{\rm Bj} dQ^{2}}} = 
  \frac{2 \pi \alpha^{2} }{x_{\rm Bj}Q^{4}}
  [Y_{+} \, \tilde{F_{2}}(x_{\rm Bj},Q^{2})  
  \mp Y_{-} \, x\tilde{F_{3}}(x_{\rm Bj},Q^{2})  
  - y^{2}\tilde {F_{L}}(x_{\rm Bj},Q^{2})],
\label{eqn:unpol_xsec}$$

where $\alpha$ is the fine-structure constant, $Y_{\pm} = 1 \pm (1 - y)^{2}$ and $\tilde{F_{2}}(x_{\rm Bj},Q^{2})$, $x\tilde{F_{3}}(x_{\rm Bj},Q^{2})$ and $\tilde{F_{L}}(x_{\rm Bj},Q^{2})$ are generalised structure functions. The sign in front of the $x\tilde{F_3}$ term is taken as positive for electrons and negative for positrons.

The $\tilde{F_{2}}$ term in Eq. \[eqn:unpol\_xsec\] is dominant at low $Q^{2}$, where only the photon exchange is important. The longitudinal structure function $\tilde{F_{L}}$ is only significant at very low $Q^{2}$ and irrelevant for this analysis. The $x\tilde{F_{3}}$ term starts to contribute significantly to the cross section at $Q^{2}$ values approaching the mass of the $Z$-boson squared, $M_Z^2$. The latter originates from $\gamma / Z$ interference and $Z$ exchange and results 