for HERAPDF2.0, because the data sets from ZEUS and H1 were not combined and, in addition, polarisation was considered for the ZEUS data sets as listed in Table \[tab:pol\] doubling the cross-section values for these data sets.

All QCD parameters and settings entering the analysis were chosen as for HERAPDF2.0 unless explicitly stated. The experimental uncertainty, denoted “experimental/fit” in the following, is the uncertainty determined by the fit using the Hessian method. The model uncertainties were computed exactly as for HERAPDF2.0, except for the strange-sea contribution, which was assumed to be a fixed fraction of the $d$-type sea.

The PDFs parameterised are the gluon distribution, $xg$, and the quark distributions in the general form

$$xf(x) = A x^{B} (1-x)^{C} (1 + D x + E x^2)~~.
\label{eqn:pdf}$$

The quark distributions are the valence-quark distributions, $xu_v$, $xd_v$, and the $u$-type and $d$-type anti-quark distributions, $x\bar{U}$, $x\bar{D}$. The relations $x\bar{U} = x\bar{u}$ and $x\bar{D} = x\bar{d} +x\bar{s}$ are assumed at the starting scale. A detailed discussion on this parameterisation $ansatz$ can be found in the HERAPDF2.0 publication [@HERAPDF20]. A slight deviation from the HERAPDF2.0 analysis is the reduction from 14 to 13 PDF parameters as described below.

The parameterisation of the proton 