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.
Highlights
To target in lattice QCD (LQCD) calculations
After introducing the lattice ensemble employed in this work, we proceed in section 3 with a recapitulation of the Distillation spatial smearing program, a recent extension of the method to high-momentum observables, and argue why its utilization is essential in such structure calculations
Motivated by the demonstrable success of the union of the distillation paradigm and the momentum smearing idea [60], we apply for the first time the distillation spatial smearing program to the extraction of PDFs from lattice QCD
Summary
Consider the non-local quark bilinear ψ (z) γαΦ(zf) ({z, 0}) ψ (0) connected with a straight z-separated Wilson line Φ(zf) ({z, 0}) in the fundamental representation of SU(3). Prior to taking the continuum limit, the UV divergences must be regularized and removed In perturbation theory, such divergences appear first, as power-like z/a [37] terms in the gauge-link selfenergy corrections, with a being a UV regulator. The choice to construct the RG invariant reduced pseudo-ITD with M 0, z2 is especially straightforward, as M 0, z2 is the bare vector charge ZV−1 in the light-cone limit thereby leaving the OPE unaltered. Following removal of the UV divergences produced by the space-like Wilson line, the remaining singularities in (2.4) stem from ln(−z2) contributions in QCD. These terms generate the perturbative evolution of the collinear PDFs and complicate the naive z2 → 0.
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