Session FC: Mini-Symposium on Theoretical Approaches to Nucleon Structure

Theoretical approaches to nucleon structure

How do quarks and gluons, the basic degrees of freedom of the Standard Model of particle physics, interact to form protons and neutrons, the basic building blocks of most of the visible Universe? In spite of significant progress, the answer to this question is still unclear. Nucleons are strongly-coupled, highly nonlinear systems for which simple perturbative approaches fail and our understanding of their structure is far from complete. I will review recent theoretical approaches to nucleon structure, from both nonperturbative and perturbative quantum chromodynamics (QCD). In particular, I will highlight some recent advances in direct calculations from lattice QCD, in which QCD is formulated on a Euclidean hypercube, and discuss the complementarity and relative strengths of perturbative and lattice techniques. I will finish by providing an overview of various quantities for which lattice calculations and phenomenological results can (potentially) be compared.   

First Renormalized Parton Distribution Functions from Lattice QCD

We present the first lattice-QCD results on the nonperturbatively renormalized parton distribution functions (PDFs). Using X.D. Ji's large-momentum effective theory (LaMET) framework, lattice-QCD hadron structure calculations are able to overcome the longstanding problem of determining the Bjorken-$x$ dependence of PDFs. This has led to numerous additional theoretical works and exciting progress. In this talk, we will address a recent development that implements a step missing from prior lattice-QCD calculations: renormalization, its effects on the nucleon matrix elements, and the resultant changes to the calculated distributions.   

Partonic Orbital Angular Momentum and Lorentz Invariance Relations

We show that Generalized Transverse Momentum Distributions (GTMDs) and twist three Generalized Parton Distributions (GPDs) can be connected through Lorentz Invariant Relations. The equations of motion along with the Lorentz Invariance Relations allow one to explicitly write the separate contributions to twist three GPDs from leading twist GPDs, a quark gluon quark correlation term and, in some cases, a mass term. In particular, the GTMD $F_{14}$ or the correlation of an unpolarized quark in a longitudinally polarized proton, is known to describe the quarks’ Orbital Angular Momentum (OAM). In a separate approach, the twist three GPD $\tilde{E}_{2T}$ tilde was also be shown to connect to OAM. We show that these two definitions are connected by a Lorentz Invariance Relation. A similar relation is found for the GTMD $G_{11}$ which describes quark spin orbit correlations in the proton can be connected to the twist three GPDs $E_{2T}'$ and $\tilde{H}_{2T}'$. These relations show how twist three GPDs through an implicit quark gluon interaction reproduce the effects of intrinsic transverse momentum in the GTMDs.   

Generalized TMDs in Hadronic Collisions

Generalized transverse momentum dependent parton distributions (GTMDs) are the most general parton correlation functions of hadrons. For a long time it was not clear if/how GTMDs can be measured. We argue that the exclusive double Drell-Yan process and $\eta_c$ production in hadronic collisions do give access to GTMDs. We also discuss how specific GTMDs can be measured by means of polarization observables.