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

Abstract

We determine the second Mellin moment of the isovector quark parton distribution function <x>_{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.

Figures (3)

• Figure 1: Pion mass dependence of $\langle x\rangle_{u-d}^{\overline{\mathrm{MS}}}$ at $\mu=2$ GeV from $N_f=2$ (new, QCDSF Sternbeck:2012rwPleiter:2011gw, ETMC Alexandrou:2011nr) and $N_f=2+1$ (RBC-UKQCD Aoki:2010xg) lattice QCD simulations, together with expectations from PDF parametrizations (NNPDF Ball:2011uy, ABM Alekhin:2012ig, MSTW Martin:2009bu).
• Figure 2: Plateaus and fitted values (grey bands) of ratios of renormalized three-point over two-point functions at $\beta=5.29$ ($a^{-1}\approx 2.76$ GeV) for $\kappa=0.13632$ ($m_{\pi}\approx 290$ MeV) and $\kappa=0.13640$ ($m_{\pi}\approx 157$ MeV).
• Figure 3: Extrapolations of the generalized form factor $A_{20}^{u-d}(Q^2)$ to $Q=0$ for the three smallest mass points. The left-most points ($Q=0$) are determined directly from the forward matrix element.