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 P_z is very large. Since taking the P_z→∞ limit is not feasible in lattice simulations, it is essential to provide guidance for which values of P_z 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 P_z≥1.5-2 GeV. On the other hand, for large x~1 much larger P_z>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.