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

TL;DR

This study evaluates quasi-PDFs within a diquark spectator model, providing guidance on the proton momentum needed for quasi-PDFs to approximate standard PDFs, and examining their properties and bounds.

Contribution

It offers the first detailed analysis of quasi-PDFs for all leading-twist distributions in a diquark model, including their accuracy at various momenta and the validity of the Soffer bound.

Findings

Quasi-PDFs approximate standard PDFs within 20-30% for intermediate x at Pz ≥ 1.5-2 GeV.

Higher Pz (>4 GeV) is required for large x to match PDFs.

The Soffer positivity bound does not generally hold for quasi-PDFs.

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 $P_z$ is very large. Since taking the $P_z\to \infty$ limit is not feasible in lattice simulations, it is essential to provide guidance for what 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 $f_1$, helicity distribution $g_1$, and transversity distribution $h_1$). We find that, for intermediate parton momentum fractions $x$, quasi-PDFs are good approximations to standard PDFs (within $20-30%$) when $P_z\gtrsim 1.5-2$ GeV. On the other hand, for large $x\sim 1$ 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.