Abstract
The parton quasidistribution functions approach provides a path to computing parton distribution functions (PDFs) using lattice QCD. This approach requires matrix elements of a power-divergent operator in a nucleon at high momentum and one generically expects discretization effects starting at first order in the lattice spacing $a$. Therefore, it is important to demonstrate that the continuum limit can be reliably taken and to understand the size and shape of lattice artifacts. In this work, we report a calculation of isovector unpolarized and helicity PDFs using lattice ensembles with ${N}_{f}=2+1+1$ Wilson twisted mass fermions, a pion mass of approximately 370 MeV, and three different lattice spacings. Our results show a significant dependence on $a$, and the continuum extrapolation produces a better agreement with phenomenology. The latter is particularly true for the antiquark distribution at small momentum fraction $x$, where the extrapolation changes its sign.
Highlights
The calculation of parton distribution functions (PDFs) using lattice QCD has seen renewed interest in recent years [1,2,3,4], driven in part by the introduction of the quasi-PDF method [5,6]
We report a calculation of isovector unpolarized and helicity PDFs using lattice ensembles with Nf 1⁄4 2 þ 1 þ 1 Wilson twisted mass fermions, a pion mass of approximately 370 MeV, and three different lattice spacings
As the signal-to-noise problem is much milder in a nucleon at rest, this requires a relatively inexpensive additional calculation: see Table V. This ratio is similar to the reduced Ioffe-time distribution used in the pseudo-PDF approach for parton distributions [77]. It is a different observable than the MMSrenormalized matrix elements used for quasi-PDFs, it provides the opportunity to study the approach to the continuum limit in a clean, controlled setting
Summary
The calculation of parton distribution functions (PDFs) using lattice QCD has seen renewed interest in recent years [1,2,3,4], driven in part by the introduction of the quasi-PDF method [5,6] This method requires nucleon matrix elements of a nonlocal operator containing a Wilson line, which must be computed on the lattice. Not eliminate all discretization effects linear in the lattice spacing a [45,46,47] This means that in a lattice setup where most observables have only Oða2Þ lattice artifacts, quasiPDFs can have OðaÞ contributions. We present a study of the approach to the continuum limit of isovector nucleon unpolarized and helicity parton distributions using three lattice ensembles, each having a different lattice spacing but with otherwise similar parameters.
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