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

Abstract

We perform a lattice computation of the flavour octet contribution to the average quark momentum in a nucleon, $\text{la}x{\text{ra}}_{{\mu }^2=4{\text{gev}}^2}^{(8)}$. 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 $\frac{\text{la}x{\text{ra}}^{(3)}}{\text{la}x{\text{ra}}^{(8)}}$ (with $\text{la}x{\text{ra}}^{(3)}$ 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, $\frac{\text{la}x{\text{ra}}^{(3)}}{\text{la}x{\text{ra}}^{(8)}}=0.39(1)(4)$.

Comments: 18 pages, 7 figures