Towards high-precision parton distributions from lattice QCD via distillation

Abstract

We apply the Distillation spatial smearing program to the extraction of the unpolarized isovector valence PDF of the nucleon. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD). The impact of higher-twist effects is subsequently explored by extending the Wilson line length present in our non-local operators to one half the spatial extent of the lattice ensemble considered. The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. Through development of a novel prescription to obtain the PDF from the pITD, we establish a concerning deviation of the pITD from the expected DGLAP evolution of the pseudo-PDF. The presence of DGLAP evolution is observed once more following introduction of a discretization term into the PDF extractions. Observance and correction of this discrepancy further highlights the utility of distillation in such structure studies.

Lattice QCD Calculations of Parton Physics

“…The distillation framework [61] is a further example of smearing with the important benefit that it enables a momentum projection to be performed at each point in a two-point or three-point function, thereby providing a more complete sampling of the lattice than is possible with the Jacobi or Wuppertal frameworks. The efficacy of combining the more complete sampling of the lattice made possible by distillation with the ability to reach higher momenta using momentum smearing [62] has been demonstrated in the recent calculation of the unpolarized PDF using distillation [63], which showed improved precision in comparison with an earlier work employing Jacobi smearing [64].…”

Continuum limit of parton distribution functions from the pseudo-distribution approach on the lattice

“…In Ref. [105], it was found that discretization effects lead to the violation of the DGLAP evolution of PDFs. The authors of the aforementioned work only used a single lattice spacing, but parametrized the cutoff effects using Jacobi polynomials under the assumption that they have the form a/|z| multiplied by a function of ν.…”

“…We recall here the methodology of this test proposed in Ref. [105]. It consists of fitting the real part of ITDs at fixed z to a cosine Fourier transform of a phenomenologically-inspired ansatz for the valence PDF:…”

“…We take βM = 3, as in Ref. [105], but also consider another setup with βM for each ensemble taken as its fitted value in the PDF reconstruction with z max = 0.5 fm, i.e. 1.72 for A60, 1.76 for B55, 1.54 for D45 and 1.27 in the continuum (see Tabs.…”

Complementarity of experimental and lattice QCD data on pion parton distributions

“…The LaMET and SDF approaches provide complementary methods for extracting PDFs from lattice calculations, with different systematic uncertainties. The success of these approaches has encouraged significant effort aimed at constraining PDFs through lattice QCD, using a variety of methods and lattice actions [48,[59][60][61][62][63][64][65][66][67][68][69][70][71][72][73]. These methods generally provide more information about PDFs than does the traditional approach of calculating the Mellin moments of PDFs from matrix elements of local operators.…”