Abstract
A set of quasi-parton distribution functions (quasi-PDFs) have been recently proposed by Ji. Defined as the matrix elements of equal-time spatial correlations, they can be computed on the lattice and should reduce to the standard PDFs when the proton momentum Pz is very large. Since taking the Pz→∞ limit is not feasible in lattice simulations, it is essential to provide guidance for which values of Pz the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs for all leading-twist distributions (unpolarized distribution f1, helicity distribution g1, and transversity distribution h1). We find that, for intermediate parton momentum fractions x, quasi-PDFs are good approximations to standard PDFs (within 20–30%) when Pz≳1.5–2 GeV. On the other hand, for large x∼1 much larger Pz>4 GeV is necessary to obtain a satisfactory agreement between the two sets. We further test the Soffer positivity bound, and find that it does not hold in general for quasi-PDFs.
Highlights
Parton distribution functions (PDFs) are of fundamental importance to science
We use previously fitted parameters for the spectator diquark model, which lead to reasonable standard PDFs, consistent with those extracted from the global analysis
The Soffer bound breaks down for relatively small Pz values for the u quark. What this tells us for the usual lattice QCD simulations is that while the standard PDFs might still satisfy the positivity bounds, such as Soffer bound on the lattice [33], these positivity bounds in general do not hold for quasi-PDFs, and, one should avoid using them in lattice simulations
Summary
Parton distribution functions (PDFs) are of fundamental importance to science. PDFs provide invaluable information on the proton’s partonic structure [1, 2] and are essential ingredients in theoretical predictions and description of the data from high energy scattering experiments [3, 4]. We compute both the quasi-PDFs and the standard PDFs, to study/explore for what values of Pz they are good approximations of each other This can provide guidance for future lattice QCD calculations. We study the behaviors of both quasi-PDFs and the standard PDFs for all three leading-twist distributions, and for both up and down quarks
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
