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 the nucleon, x μ 2 = 4 GeV 2 8 $${\left\langle x\right\rangle}_{\mu^2=4\kern0.5em {\mathrm{GeV}}^2}^{\left((8)\right.}$$ . In particular, we fully take the disconnected contributions into account in our analysis for which we use a generalization of the technique developed in [1]. We investigate systematic effects with particular emphasis on the excited states contamination. We find that in the renormalization free ratio x 3 x 8 $$\frac{{\left\langle x\right\rangle}^{(3)}}{{\left\langle x\right\rangle}^{(8)}}$$ (with 〈x〉 (3) the non-singlet moment) the excited state contributions cancel to a large extent 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, x 3 x 8 = 0.39 1 4 $$\frac{{\left\langle x\right\rangle}^{(3)}}{{\left\langle x\right\rangle}^{(8)}}=0.39(1)(4)$$