First moment of the flavour octet nucleon parton distribution function using lattice QCD

We perform a lattice computation of the flavour octet contribution to the average quark momentum in a nucleon, $\la x\ra^{(8)}_{\mu^2 = 4 \gev^2}$. In particular, we fully take the disconnected contributions into account in our analysis for which we use a generalization of the technique developed in \cite{Dinter:2012tt}. We investigate systematic effects with a particular emphasis on the excited states contamination. We find that in the renormalization free ratio $\frac{\la x \ra^{(3)}}{\la x \ra^{(8)}}$ (with $\la x \ra^{(3)}$ the non-singlet moment) the excited state contributions cancel to a large extend making this ratio a promising candidate for a comparison to phenomenological analyses. Our final result for this ratio is in agreement with the phenomenological value and we find, including systematic errors, $\frac{\la x \ra^{(3)}}{\la x \ra^{(8)}} = 0.39(1)(4)$.