cases, the effect on the extracted EW parameters was negligible.

The published cross sections were not corrected for further electroweak effects by either ZEUS or H1. For the analysis presented here, electroweak effects were taken into account through $\Delta R$ as introduced in Eq. \[eq:rewrite1\]. It was computed with the program EPRC [@Spiesberger:95], where weak box-diagrams, $\gamma/Z$ interference and $Z$ and $W$ self-energies were taken into account. The running of $\alpha$, relevant for the CC cross sections, is also absorbed in $\Delta R$.

Couplings of the boson to the and quarks
========================================

To determine the axial-vector and vector couplings of the $Z$ to the $u$- and $d$-type quarks, $a_u, v_u, a_d, v_d$, the QCD predictions depending on the 13 PDF parameters plus the four couplings were fitted simultaneously to the data. The fit as well as the resulting set of PDFs are called ZEUS-EW-Z.

A comparison of the PDFs of ZEUS-EW-Z with full uncertainties to the central values of the PDFs of ZEUS-13p is shown in Fig. \[fig:ZEUS-EW-Z-13p\]. Within uncertainties, the PDFs of ZEUS-EW-Z agree well with ZEUS-13p. The freeing of the couplings in the fit has very little influence on the PDF parameters. The full correlation matrix is given 