Session RL: Hadrons: GPD's and TMD's

x-dependent proton GPDs in lattice QCD

We present a novel calculation of the proton chiral-even unpolarized and helicity quark generalized parton distributions (GPDs), as extracted from numerical simulations of lattice QCD. We use the quasi-distribution method, which relies on matrix elements of fast-moving hadrons, and non-local operators. This method was developed for parton distribution functions (PDFs) and was recently extended for the study of GPDs. We obtain results for nucleon momentum up to 1.67 GeV, and momentum-transfer squared up to 1 GeV$^2$. The calculation is performed on one ensemble of two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover term, reproducing a pion mass of 260 MeV. The renormalized quasi-GPDs are given in the $\overline{\rm MS}$ scheme, evolved at a scale of 2 GeV, and are matched to light-cone GPDs using one-loop perturbation theory within Large Momentum Effective Theory.   

Deeply Virtual Compton Scattering cross section measurements with CLAS12

The deeply virtual Compton scattering (DVCS) is an electroproduction process of the real photon off the nucleon, mediated by the virtual photon. The proton DVCS events are experimentally characterized by exclusive detections of the electron, proton, and photon final states in certain kinematic conditions. Thanks to the large acceptance of the CLAS12 detector and high luminosity 10.6 GeV CEBAF electron beam of Jefferson Lab, about a million DVCS events have been collected with the liquid hydrogen target in a wide range of kinematics region. Extracting DVCS differential cross sections is a powerful analysis method to study proton's 3-dimensional imaging and the proton's generalized parton distributions (GPD), and is thus important. We will present preliminary proton DVCS differential cross sections after a careful review of the detector properties, which is the requirement for the cross section study and underway.   

Ioffe time behavior of Parton Distribution Functions and Generalized Parton Distributions

Ioffe time essentially quantifies the distance along the lightcone that the quark fields that enter the correlator describing the Parton Distribution Function (PDF) are separated by. In this sense, it is a natural candidate for clearly separating the short and long distance physics. We study how the behavior of the parton distribution in Ioffe time can be mapped out given its Mellin moments. Pseudo PDFs describe the nucleon matrix elements of quark field operators separated by a space like distance $z$. These are calculable in lattice QCD and as $z^2$ approaches zero, pseudo PDFs approach the actual PDFs. Complimentary to lattice efforts, we study the behavior of of pseudo PDFs as a function of $z$ in a spectator diquark model. We also extend the study to Generalized Parton Distributions (GPDs), which involves taking into account an extra degree of freedom because of the non diagonal nature of the hadronic matrix element in the case of GPDs.   

Ultraviolet divergences and evolution in weighted transverse moments

I will discuss the problem of ultraviolet divergences in the definitions of cross sections weighted by transverse momentum. A common integral relation connecting certain types of TMD pdfs to twist-3 collinear correlation function will be shown to receive unsuppressed corrections. I will explain how this is connected to questions about the form of QCD evolution appropriate for transversely weighted observables.   

Modeling the DVCS Cross Section with Deep Learning

Imaging the 3D partonic structure of the nucleon is a fundamental goal of every major nuclear experimental program, such as the Electron Ion Collider (EIC). Ji first proposed Deeply Virtual Compton Scattering (DVCS) as a probe for understanding the spatial distribution of the partons by fourier transform of the exchanged momentum transfer between the initial and final proton. The extraction of observables from deeply virtual exclusive reactions in a clear and concise formalism was a necessity. We recently presented a completely covariant description of the DVCS process that can be extended to any kinematics, either fixed target or collider. In our helicity formalism, we extract observables such that the dependence on Q2 is clear. Using a generalization of the Rosenbluth method, we present an extraction of Compton Form Factors from current JLab DVCS data. With our formalism and pseudo-data of an EIC generated by state of the art machine learning techniques, we show predictions of what such a machine will do for our understanding of the physical properties of the proton.   

First Determination of the Shear Forces Inside the Proton

Protons and neutrons, generally referred to as nucleons, are the fundamental building blocks of nuclei and make up nearly 100\% of the mass of normal matter in the universe. They are composed of elementary objects, quarks and gluons. The latter are the carrier of the strong force that governs the dynamics binding quarks and gluons together. It is well established that quarks do not exist in isolation but only in the confines of nucleons and mesons (hadrons) of finite size. The forces between quarks and the angular momentum distributions are largely unknown. The mechanical properties of the proton, including pressure, forces and mechanical size are encoded in the proton's matrix element of the energy-momentum tensor and are expressed in scalar gravitational form factors (GFFs). Recent theoretical development showed that the GFFs may be probed in deeply virtual Compton scattering (DVCS). In this process two photons couple to the proton and mimic the graviton-proton interaction, and hence probe its mechanical properties. Here we present the first extraction of shear forces and their spatial distribution inside the proton and compare the results with model prediction.   

Bounds on the Equation of State of Neutron Stars from the QCD Energy Momentum Tensor

The recent detection of gravitational waves from merging neutron star events has opened a new window on the many unknown aspects of their internal dynamics. A key role in this context is played by the transition from baryon to quark matter traced by the neutron star equation of state. The quark matter phase of neutron stars is thought to be governed by short range interactions among quark and gluons within Quantum Chromodynamics (QCD), the theory which describes the inner structure of the nucleon. Pressure, energy, as well as other mechanical properties of the nucleon are encoded in the QCD Energy Momentum Tensor. The QCD energy momentum tensor matrix elements are connected to the Mellin moments of the generalized parton distributions which can be measured in deeply virtual exclusive scattering experiments. As a consequence, we establish a connection between observables from high energy experiments and from the analysis of gravitational wave events. Both can be used to mutually constrain the respective sets of data. In particular, the emerging QCD-based picture is consistent with the GW170817 neutron star merger event once we allow a first-order phase transition from a low-density nuclear matter EoS to the newly-constructed high-density quark-gluon one.   

First global analysis of SSAs in SIDIS, Drell-Yan, e$^{\mathrm{+}}$e$^{\mathrm{-}}$ annihilation, and proton-proton collisions

The analysis of single transverse-spin asymmetries (SSAs) gives us tremendous insight into the internal structure of hadrons. For example, the Sivers and Collins effects in semi-inclusive deep-inelastic scattering (SIDIS), Sivers effect in Drell-Yan, and the Collins effect in electron-positron annihilation have been widely investigated over many years in order to perform 3D momentum-space tomography. In addition, observables like $A_{N}$ in proton-proton collisions are of interest due to their sensitivity to quark-gluon correlations. In this talk I will report on the first global fit of SSA data from SIDIS, Drell-Yan, e$^{\mathrm{+}}$e$^{\mathrm{-}}$ annihilation into hadron pairs, and proton-proton collisions. I will discuss the results of our analysis, including extraction of a unique set of universal non-perturbative functions that describe all observed SSAs, agreement with lattice QCD on the nucleon tensor charge, and also explore avenues for future research.   

A new Monte Carlo fit of unidentified charged hadron fragmentation functions

The theoretical description of transverse momentum differential semi-inclusive deep inelastic cross sections, particularly the description of the very large transverse momentum region where fixed order collinear perturbative QCD factorization applies, requires collinear fragmentation functions that are applicable at comparatively lower $Q$ where many semi-inclusive deep inelastic scattering experiments are performed. Recent phenomenological studies, however, have demonstrated tension in the large transverse momentum/moderate $Q$ region for a number of hard processes. As such, new global analyses focused on these particular kinematical regions are needed. Motivated by this, we present the results of a multi-step Monte Carlo (MC) fit of unidentified charged hadron fragmentation functions performed using various e+/e- data sets and the most recent SIDIS data from COMPASS.