Quasi-parton distribution functions: A study in the diquark spectator model

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 PzPz is very large. Since taking the Pz→∞Pz→∞ limit is not feasible in lattice simulations, it is essential to provide guidance for which values of PzPz 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 f1f1, helicity distribution g1g1, and transversity distribution h1h1). 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 GeVPz≳1.5–2 GeV. On the other hand, for large x∼1x∼1 much larger Pz>4 GeVPz>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.