Using NSPT for the Removal of Hypercubic Lattice Artifacts

The treatment of hypercubic lattice artifacts is essential for the calculation of non-perturbative renormalization constants of RI-MOM schemes. It has been shown that for the RI'-MOM scheme a large part of these artifacts can be calculated and subtracted with the help of diagrammatic Lattice Perturbation Theory (LPT). Such calculations are typically restricted to 1-loop order, but one may overcome this limitation and calculate hypercubic corrections for any operator and action beyond the 1-loop order using Numerical Stochastic Perturbation Theory (NSPT). In this study, we explore the practicability of such an approach and consider, as a first test, the case of Wilson fermion bilinear operators in a quenched theory. Our results allow us to compare boosted and unboosted perturbative corrections up to the 3-loop order.Comment: 7 pages, 6 figures, talk presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York, USA; PoS(LATTICE2014)29

<x>_{u-d} from lattice QCD at nearly physical quark masses

We determine the second Mellin moment of the isovector quark parton distribution function _{u-d} from lattice QCD with N_f=2 sea quark flavours, employing the non-perturbatively improved Wilson-Sheikholeslami-Wohlert action at a pseudoscalar mass of 157(6) MeV. The result is converted non-perturbatively to the RI'-MOM scheme and then perturbatively to the MSbar scheme at a scale mu = 2 GeV. As the quark mass is reduced we find the lattice prediction to approach the value extracted from experiments.Comment: 4 pages, 3 figures, v2: minor updates including journal ref