Abstract
Using the formalism of parton virtuality distribution functions (VDFs) we establish a connection between the transverse momentum dependent distributions (TMDs) F(x,k⊥2) and quasi-distributions (PQDs) Q(y,p3) introduced recently by X. Ji for lattice QCD extraction of parton distributions f(x). We build models for PQDs from the VDF-based models for soft TMDs, and analyze the p3 dependence of the resulting PQDs. We observe a strong nonperturbative evolution of PQDs for small and moderately large values of p3 reflecting the transverse momentum dependence of TMDs. Thus, the study of PQDs on the lattice in the domain of strong nonperturbative effects opens a new perspective for investigation of the 3-dimensional hadron structure.
Highlights
The parton distribution functions (PDFs) f (x), being related to matrix elements of nonlocal operators near the light cone z2 = 0 are notoriously difficult objects for a calculation using the lattice gauge theory
Differ from PDFs f (x), but tend to them in the p3 → ∞ limit, displaying a usual perturbative evolution [2,3,4,5] with respect to p3 for large p3
Our goal in the present paper is to study nonperturbative evolution of parton quasi-distributions using the formalism of virtuality distribution functions proposed and developed in our recent papers [28,29], where it was applied to the transverse momentum dependent pion distribution amplitude and the exclusive γ ∗γ → π 0 process
Summary
Our goal in the present paper is to study nonperturbative evolution of parton quasi-distributions using the formalism of virtuality distribution functions proposed and developed in our recent papers [28,29], where it was applied to the transverse momentum dependent pion distribution amplitude and the exclusive γ ∗γ → π 0 process.
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