the third mechanism was found to be negligible by fixing the couplings to their SM values.

The PDFs of ZEUS-EW-S are compared to the PDFs of ZEUS-EW-Z in Fig. \[fig:ZEUS-EW-S\]. The two sets of PDFs agree very well. The predictions of ZEUS-EW-S are compared to the reduced CC cross sections in Figs. \[fig:CCpp\] and \[fig:CCep\] for $e^+p$ and $e^-p$ scattering, respectively. In both cases, data with positive and negative beam polarisation are shown separately; ZEUS-EW-S describes the data well.

The $\sin^2\theta_W(M_Z)$ value obtained with ZEUS-EW-S can be converted to a value of the effective weak mixing angle [@PDG14]. The result is given in Table \[tab:run-sin\] and is shown in Fig. \[fig:run-sin\] together with the SM prediction [@run-sin-pred2] for the running of $\sin^2\theta_W^{\rm eff}$. The prediction was computed using the boson and fermion masses and the couplings as listed in PDG14.

An additional three fits were performed with the data separated into three $Q^2$ bins from 200 to 1000, 1000 to 5000 and 5000 to 50000GeV$^2$, using all data available in each range. The scales of the measurement were taken as a log-average $Q^2$ value of the given bin. These bins were chosen such that the uncertainties are about equal; cross 