as Table \[tab:matrix\]. The small correlation between PDF parameters and couplings is a sign that the PDFs are not absorbing any significant non-SM effects which could show up in the electroweak couplings. A comparison of the PDFs of ZEUS-EW-Z to the PDFs of HERAPDF2.0 is shown in Fig. \[fig:ZEUS-EW-Z-HPDF\]. The PDFs agree well within uncertainties.

The predictions of ZEUS-EW-Z are compared to the ZEUS reduced NC cross sections in Figs. \[fig:NCpp\] and \[fig:NCep\] for $e^+p$ and $e^-p$ scattering, respectively. In both cases, data with positive and negative beam polarisation are shown separately. ZEUS-EW-Z describes the data well.

The values of the couplings were determined in the simultaneous fit as $$\begin{aligned}
\nonumber
a_u & = & +0.50~ ^{+0.09}_{-0.05} \,{\rm {\scriptstyle{(experimental/fit)}}}~ 
        ^{+0.04}_{-0.02}\,{\rm {\scriptstyle{(model)}}}~ 
        ^{+0.08}_{-0.01}\,{\rm {\scriptstyle{(parameterisation)}}} ~,\\
\nonumber
a_d & = & -0.56~ ^{+0.34}_{-0.14}\,{\rm {\scriptstyle{(experimental/fit)}}}~ 
        ^{+0.11}_{-0.05}\,{\rm {\scriptstyle{(model)}}}~ 
        ^{+0.20}_{-0.00}\,{\rm {\scriptstyle{(parameterisation)}}} ~,\\
\nonumber
v_u & = & +0.14~ ^{+0.08}_{-0.08}\,{\rm {\scriptstyle{(experimental/fit)}}}~ 
        ^{+0.01}_{-0.02}\,{\rm {\scriptstyle{(model)}}}~
        ^{+0.00}_{-0.03}\,{\rm {\scriptstyle{(parameterisation)}}}  ~,\\
\nonumber
v_d & = & -0.41~ ^{+0.24}_{-0.16}\,{\rm {\scriptstyle{(experimental/fit)}}}~ 
        ^{+0.04}_{-0.07}\,{\rm {\scriptstyle{(model)}}}~ 
        ^{+0.00}_{-0.08}\,{\rm {\scriptstyle{(parameterisation)}}} ~.\end{aligned}$$

They are also listed in Table \[tab:Z\] with their experimental/fit and total uncertainties and compared to SM predictions. Also listed are values obtained in a fit where the only free parameters were the $Z$ couplings and the 