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

Preprint number: CP3-Origins-2015-4 DNRF90 and DIAS-2015-4
Authors: Constantia Alexandrou (University of Cyprus), Martha Constantinou (University of Cyprus), Simon Dinter (NIC, DESY), Vincent Drach (CP3-Origins & DIAS), Kyriacos Hadjiyiannakou (University of Cyprus), Karl Jansen (NIC, DESY), Giannis Koutsou (Cyprus Institute), and Alejandro Vaquero (Cyprus Institute)
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We perform a lattice computation of the flavour octet contribution to the average quark momentum in a nucleon, \(\langle x\rangle^{(8)} _{\mu^2 = 4~\mathrm{GeV}^2 }\). In particular, we fully take the disconnected contributions into account in our analysis for which we use a generalization of the technique developed in [1]. We investigate systematic effects with a particular emphasis on the excited states contamination. We find that in the renormalization free ratio \(\frac{\langle x \rangle^{(3)}}{\langle x \rangle^{(8)}}\) (with \(\langle x \rangle^{(3)}\) 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, \(\frac{\langle x \rangle^{(3)}}{\langle x \rangle^{(8)}} = 0.39(1)(4)\).