Session D08: Nucleon Structure and Nucleon Spin I

The Universal Nature of Transversity PDFs and the Tensor Charges of the Nucleon

The transversity parton distribution functions (PDFs), which quantify the degree of transverse polarization of quarks within a transversely polarized nucleon, have been a focus of QCD phenomenology for decades. Two approaches to extracting these functions are through transverse momentum dependent (TMD) and/or collinear twist-3 (CT3) observables as well as the use of collinear factorization with dihadron fragmentation functions (DiFFs). The transversity PDFs are also of interest since they allow one to calculate the tensor charges of the nucleon. The tensor charges are important in low-energy beyond the Standard Model studies and also have been computed very precisely in lattice QCD. In this talk, I will report on new developments in the theory and phenomenology of DiFFs in extracting the transversity PDFs and discuss their compatibility with the TMD/CT3 approach as well as lattice QCD computations of the nucleon tensor charges.   

Electron-proton elastic scattering at high momentum transfer at the Electron-Ion Collider

Unpolarized electron-proton elastic scattering measurements at high momentum transfer (Q²) using the future Electron-Ion Collider (EIC) will allow for more precise extractions of the proton electromagnetic form factors as well as provide constraints on possible hard two-photon exchange effects. I will present a detailed feasibility study on making these measurements at the EIC, taking into account detector effects, beam-luminosity and beam-crossing effects, as well as QED radiative effects. The results show that electron-proton elastic cross sections can be measured at the EIC in the momentum transfer range of 6 (GeV/c)² < Q² < 40 (GeV/c)², which would be the highest-ever Q² values measured.   

GTMDs within the Bag Model

GTMDs are studied within the framework of the MIT bag model. We display our results for these GTMDs and compare our work with previous model results concerning GPDs.   

Numerical Computation of Left-Right Asymmetries in Single-Inclusive Pion Production from Lepton-Nucleon Collisions

During collisions between leptons and transversely polarized nucleons at high energy, the left-right asymmetric formation of hadrons can be probed. These so-called transverse single-spin asymmetries A_N are the subject of our work. One issue for lower-energy fixed-target experiments is the possible need for next-to-leading order (NLO) corrections.  Therefore, to create plausible predictions of these asymmetries, we aim to include NLO corrections to the spin-averaged cross section that enters the denominator of A_N.  Comparison with data then may indicate the size of NLO corrections for the transversely polarized cross section in the numerator, which have not been fully worked out yet. We use recent phenomenological extractions of quark-gluon-quark (Sivers- and Collins-like) functions in our analysis to describe data from HERMES as well as present predictions for JLab12, COMPASS, and future Electron-Ion Collider experiments.   

Transverse Momentum Moments

We establish robust relations between Transverse Momentum Dependent distributions (TMDs) and collinear functions. We define weighted integrals of TMDs which we call Transverse Momentum Moments (TMMs). We demonstrate that TMMs are related to collinear distributions via calculable scheme-coefficients 

and we derive expressions for them up 

to three loops. We prove that TMMs obey the same evolution equations as the corresponding collinear quantities. We discuss in details the zeroth, the first, and the second TMMs and provide phenomenological results for those based on the current extractions of TMDs. Results of this paper open new avenues for theoretical and phenomenological investigation of the three-dimensional and collinear hadron structures.     

Observables for scattering on targets with arbitrary spin

Starting from the Weinberg formalism for fields for arbitrary spin, we discuss a construction for the decomposition of matrix elements of QCD operators (local currents, quark/gluon bilinears) for targets with arbitrary spin. This procedure is advantageous for the systematic study of the structure of hadrons and nuclei, particularly in the case of spin-dependent observables. As higher spin targets exhibit new features in their hadronic structure, the investigation of these properties can enhance our understanding of the strong force.

The construction allows for a unified framework to discuss spin > 1/2 very similar to the spin 1/2 case, without subsidiary conditions for the wave functions. Different types of spinors (canonical, helicity, light-front helicity) can be easily accommodated.  Its numerical implementation is simple and can be entirely reduced to objects familiar from the rotation group.  An sl(2,C) multipole decomposition naturally appears and allows for a physical interpretation of non-perturbative objects multiplying spinor bilinears.

To demonstrate the efficacy of this method, we apply it to the description of  a spin 1 target, such as the deuteron. We discuss extensions of the formalism to hard exclusive processes on the deuteron and beyond.   

Study of proton structure using heavy meson pair photoproduction

In this talk, we present our theoretical studies of the inclusive and exclusive photoproduction of heavy quarkonia and open-charm meson pairs, and demonstrate that these channels could be used as novel probes of the hadronic structure. For exclusive production at moderate energies, these channels allow to probe the generalized parton distributions (GPDs) of the proton in the Efremov-Radyushkin-Brodsky-Lepage region. At very high energies, due to onset of saturation effects, the process dynamics are described in the color glass condensate (color dipole) framework, and the suggested channels potentially could be used for detailed studies of the forward dipole scattering amplitude. The inclusive production of the same meson pairs gives access to quadrupole, sextupole, and octupole forward scattering amplitudes. We found that the associated charmonia-bottomonia photoproduction could be used as a potential gateway for the study of the quadrupole scattering amplitude. At present, the suggested channels can be studied in ultraperipheral collisions at LHC, and in the future, it will be possible to study such processes at the Electron Ion Collider (EIC).   

Phenomenology of TMD distributions in Drell-Yan and Z0 boson production with the Hadron Structure Oriented approach

We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to TMD phenomenology applied to Drell-Yan like processes, including lepton pair production at moderate Q² and Z₀ boson production. We compare and contrast general features of our methodology with other common practices and emphasize the improvements from our approach that we view as essential for applications where extracting details of nonperturbative transverse hadron structure is a major goal. These include the HSO’s preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution, explicit preservation of the integral relationship between TMD and collinear pdfs, and the ability to meaningfully compare different theoretical models of nonperturbative transverse momentum dependence. In our examples, we show that there is significant sensitivity at moderate Q² to both the form of the nonperturbative transverse momentum dependence and the parametrization of collinear

parton densities. However, we also find that evolving to Q² = M_Z² without fitting results in a satisfactory postdiction of existing data for Z₀ production, nearly independently of the modeling of nonperturbative transverse momentum dependence. We argue that this demonstrates that moderate Q measurements should be given greater weight than high Q measurements in extractions of nonperturbative transverse momentum dependence. We also obtain new extractions of the nonper-

turbative Collins-Soper kernel within the HSO approach. We discuss its features and compare with some earlier extractions.