$v_u,v_d$. This illustration demonstrates very clearly that the HERA data constrain the couplings of the $Z$ boson to the $u$ quark significantly better than the couplings to the $d$ quark. All measurements are compatible with the SM. The parameterisation uncertainties mostly arise from the $D_{\bar{U}}$ parameter. As this parameter is constrained to be positive, the axial-vector couplings can only increase due to these uncertainties.

The results from ZEUS-EW-Z are compared to other measurements from LEP+SLC [@ZLEPSLC], the Tevatron [@ZD0Old; @ZCDF] and from HERAI (H1) [@ZH1] in Figs. \[fig:av-all\] and \[fig:comparison\]. The PDG14 value obtained from these measurements is also given in Fig. \[fig:comparison\]. The ZEUS results on the axial-vector and vector couplings to $u$-type quarks are the most precise published single values.

Electroweak mixing angle and mass of the boson
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The SM cross sections depend on $\sin^2\theta_W$ through three mechanisms:

1.  through $\chi_z$, see Eq. \[eqn:chiz\];

2.  through the normalisation factor from Eqs. \[eqn:xsec\_CC1\] and \[eqn:xsec\_CC2\] with $G_F$ rewritten as described in Eq. \[eqn:GF\];

3.  through the vector couplings of the $Z$ to the quarks.

The (13+1)-parameter fit ZEUS-EW-S with $M_W$ fixed to the PDG14 value exploits all three dependencies. It yields a value for the on-shell $\sin^2\theta_W$ of

