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It is often taken for granted that Generalized Parton Distributions (GPDs) are defined in the "symmetric" frame, where the transferred momentum is symmetrically distributed between the incoming/outgoing hadrons. However, such frames pose computational challenges for the lattice QCD practitioners. In these proceedings, we lay the foundation for lattice QCD calculations of GPDs in "asymmetric" frames, where the transferred momentum is not symmetrically distributed between the incoming/outgoing hadrons. The novelty of our work relies on the parameterization of the matrix elements in terms of Lorentz-invariant amplitudes, which not only helps in establishing relations between the said frames but also helps in isolating higher-twist contaminations. As an example, we focus on the unpolarized GPDs for spin-1/2 particles., Comment: 10 pages, 1 figure, contribution to the 39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany

We calculate the gravitational form factors of the electron at one loop in quantum electrodynamics, decomposing these into contributions from the electron and photon parts of the energy-momentum tensor. Ultraviolet divergences are removed through renormalization in the $\overline{\text{MS}}$ scheme. Infrared divergences are isolated and results are given in both dimensional regularization and photon-mass regularization. The form factors contain information about the electron's energy and angular momentum structure in QED, as well as its mass radius. Whenever possible, we compare our results with the existing literature., 8 pages, 1 figure

In this work, we present a numerical investigation of a novel Lorentz-covariant parametrization to extract $x$-dependent GPDs using off-forward matrix elements of momentum-boosted hadrons coupled to non-local operators. The novelty of the method is the implementation of an asymmetric frame for the momentum transfer between the initial and final hadron state and the parametrization of the matrix elements into Lorentz-invariant amplitudes. The amplitudes can then be related to the standard light-cone GPDs. GPDs are defined in the symmetric frame, which requires a separate calculation for each value of the momentum transfer, increasing the computational cost significantly. The proposed method is powerful, as one can extract the GPDs at multiple values of the momentum transfer at the computational cost of a single value. For this proof-of-concept calculation, we use one ensemble of $N_f=2+1+1$ twisted mass fermions and a clover improvement with a pion mass of 260 MeV to calculate the proton unpolarized GPDs., 10 pages, 5 figures, contribution to the 39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany

We present a new global QCD analysis of unpolarized parton distribution functions (PDFs) and nuclear effects including for the first time data from the SeaQuest and Marathon experiments in addition to high-energy weak-boson-production data from the Tevatron and Large Hadron Collider. Simultaneously extracting the PDFs and nuclear effects, we examine the impact of the SeaQuest and Marathon data on the light-quark sea asymmetry and the EMC ratios of deuterium, helium, and tritium.

We present the results for the Energy-Momentum Tensor (EMT) form factor D(t) at one-loop accuracy in quantum electrodynamics for an electron state. We report the the results in the case of both zero and nonzero photon mass. Moreover, individual electron and photon contributions to the EMT are investigated.

The quasi-PDF approach, proposed by X. Ji in 2013, has made it possible to directly extract light-cone PDFs from lattice QCD. This approach relies on the extraction of matrix elements of space-like operators for fast-moving hadrons. Quasi-PDFs can be related to the light-cone PDFs through a perturbatively calculable matching coefficient. We explore the formalism of matching, for the very first time, for the twist-3 PDFs g_{T}(x)gT(x), e(x)e(x) and h_{L}(x)hL(x). In this work, we address the non-trivialities involved in the extraction of the matching coefficient due to the presence of (singular) zero-mode contributions.

We present the results of a global QCD analysis of helicity parton distribution functions (PDFs) that includes the latest polarized W-lepton production data from the STAR collaboration at the Relativistic Heavy-Ion Collider (RHIC). This data allows the first extraction of a nonzero helicity light-quark sea asymmetry within a simultaneous global QCD analysis of unpolarized and helicity PDFs.

The worm-gear transverse momentum dependent (TMD) function g1T is one of the eight leading-twist TMDs and has the probabilistic interpretation of finding a longitudinally polarized quark inside a transversely polarized hadron. In this work, we present the first simultaneous extraction of g1T from all the available experimental measurements. The study involves the analysis of COMPASS, HERMES, and Jefferson Lab data on semi-inclusive deep-inelastic scattering using Monte Carlo techniques. We also compare g1T obtained from this experimental data with different theoretical approaches, such as the large-Nc approximation, the Wandzura-Wilczek-type approximation, and lattice QCD.

Traditionally, lattice QCD computations of generalized parton distributions (GPDs) have been carried out in a symmetric frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. However, such frames are inconvenient since they require a separate calculation for each value of the momentum transfer, increasing significantly the computational cost. In this work, by focusing on the quasi-distribution approach, we lay the foundation for faster and more effective lattice QCD calculations of GPDs exploiting asymmetric frames, with freedom in the transferred momentum distribution. An important ingredient of our approach is the Lorentz covariant parameterization of the matrix elements in terms of Lorentz-invariant amplitudes, which allows one to relate matrix elements in different frames. We also use this amplitude approach to propose a new definition of quasi-GPDs that is frame-independent and, more importantly, may lead to smaller power corrections in the matching relations to the light-cone GPDs. We demonstrate the efficacy of the formalism through numerical calculations using one ensemble of $N_f$=2+1+1 twisted mass fermions with a clover improvement. The value of the light-quark masses lead to a pion mass of about 260 MeV. Concentrating on the proton, and limiting ourselves to a vanishing longitudinal momentum transfer to the target, we extract the invariant amplitudes from matrix element calculations in both the symmetric and asymmetric frame, and obtain results for the twist-2 light-cone GPDs for unpolarized quarks, that is, $H$ and $E$., Comment: 39 pages, 19 figures, matches with published version

We perform a global QCD analysis of unpolarized parton distributions within a Bayesian Monte Carlo framework, including the new $W$-lepton production data from the STAR Collaboration at RHIC and Drell-Yan di-muon data from the SeaQuest experiment at Fermilab. We assess the impact of these two new measurements on the light antiquark sea in the proton, and the $\bar{d}-\bar{u}$ asymmetry in particular. The SeaQuest data are found to significantly reduce the uncertainty on the $\bar{d}/\bar{u}$ ratio at large parton momentum fractions $x$, strongly favoring an enhanced $\bar{d}$ sea up to $x \approx 0.4$, in general agreement with nonperturbative calculations based on chiral symmetry breaking in QCD., 10 pages, 8 figures

The electron-graviton interaction can be described in terms of the gravitational form factors of the QED energy momentum tensor. Here we focus on the form factor D(t), and we examine its properties and its interpretation in terms of internal forces at one-loop accuracy in QED. We perform the calculation by keeping separate the contributions due to the electron and the photon parts of the energy momentum tensor. We also study the case of a nonzero photon mass. Furthermore, we discuss similarities with and differences to the form factor D(t) of hadronic bound states., 18 pages, 6 figures; accepted for publication in Phys. Lett. B

Recently the concept of quasi parton distributions (quasi-PDFs) for hadrons has been proposed. Quasi-PDFs are defined through spatial correlation functions and as such can be computed numerically using quantum chromodynamics on a four-dimensional lattice. As the hadron momentum is increased, the quasi-PDFs converge to the corresponding standard PDFs that appear in factorization theorems for many high-energy scattering processes. Here we investigate this new concept in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator model. For infinite hadron momentum, the analytical results of the quasi-GPDs agree with those of the standard GPDs. Our main focus is to examine how well the quasi-GPDs agree with the standard GPDs for finite hadron momenta. We also study the sensitivity of the results on the parameters of the model. In general, our model calculation suggests that quasi-GPDs could be a viable tool for getting information about standard GPDs., Comment: 14 pages; version to be published in PLB

Positron beams, both polarized and unpolarized, are identified as essential ingredients for the experimental programs at the next generation of lepton accelerators. In the context of the hadronic physics program at Jefferson Lab (JLab), positron beams are complementary, even essential, tools for a precise understanding of the electromagnetic structure of nucleons and nuclei, in both the elastic and deep-inelastic regimes. For instance, elastic scattering of polarized and unpolarized electrons and positrons from the nucleon enables a model independent determination of its electromagnetic form factors. Also, the deeply-virtual scattering of polarized and unpolarized electrons and positrons allows unambiguous separation of the different contributions to the cross section of the lepto-production of photons and of lepton-pairs, enabling an accurate determination of the nucleons and nuclei generalized parton distributions, and providing an access to the gravitational form factors. Furthermore, positron beams offer the possibility of alternative tests of the Standard Model of particle physics through the search of a dark photon, the precise measurement of electroweak couplings, and the investigation of charged lepton flavor violation. This document discusses the perspectives of an experimental program with high duty-cycle positron beams at JLab., Comment: 18 pages, 7 figures This version superseeds the previous version which scientific content was decomposed into several more elaborated articles. All of these articles will be collected in the EPJ A Topical Issue about "Positron beam and physics at Jefferson Lab (e+@Jlab)"

We report the first-ever calculation of the isovector flavor combination of the chiral-odd twist-3 parton distribution $h_L(x)$ for the proton from lattice QCD. We employ gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3 fm and lattice spacing of 0.093 fm. The values of the quark masses lead to a pion mass of $260$ MeV. We use a source-sink time separation of 1.12 fm to control contamination from excited states. Our calculation is based on the quasi-distribution approach, with three values for the proton momentum: 0.83 GeV, 1.25 GeV, and 1.67 GeV. The lattice data are renormalized non-perturbatively using the RI$'$ scheme, and the final result for $h_L(x)$ is presented in the $\overline{\rm MS}$ scheme at the scale of 2 GeV. Furthermore, we compute in the same setup the transversity distribution, $h_1(x)$, which allows us, in particular, to compare $h_L(x)$ to its Wandzura-Wilczek approximation. We also combine results for the isovector and isoscalar flavor combinations to disentangle the individual quark contributions for $h_1(x)$ and $h_L(x)$, and address the Wandzura-Wilczek approximation in that case as well., Comment: 18 pages, 13 figures

In these proceedings, we summarize the main results from the first-ever calculations of the chiral-even and chiral-odd twist-3 parton distributions, $g_T(x)$ and $h_L(x)$, of the proton from lattice QCD. We use an $N_f=2+1+1$ ensemble of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3~fm, the lattice spacing is 0.093~fm, and the pion mass is $260$~MeV. The matrix elements are obtained with a source-sink time separation of 1.12~fm to control contamination from excited states. The calculation is based on the quasi-PDF approach and employs three values for the proton momentum: 0.83~GeV, 1.25~GeV, and 1.67~GeV. The lattice data are renormalized non-perturbatively using the RI$'$ scheme, and the final results are presented in the $\overline{\rm MS}$ scheme at the scale of 2~GeV. Furthermore, we compute in the same setup the helicity, $g_1(x)$, and transversity, $h_1(x)$, distributions, which are used to compare $g_T(x)$ and $h_L(x)$ to their Wandzura-Wilczek approximations. For $h_L(x)$, we combine results for the isovector and isoscalar flavor combinations to disentangle the individual up- and down-quark contributions., Comment: Talk at the 38th International Symposium on Lattice Field Theory (LATTICE 2021), 26th-30th July, 2021, Zoom/Gather@Massachusetts Institute of Technology

We present a comprehensive impact study of future Electron-Ion Collider (EIC) data for parity-conserving and parity-violating polarization asymmetries on quark and gluon helicity distributions in the proton. The study, which is based on the JAM Monte Carlo global QCD analysis framework, explores the role of the extrapolation uncertainty and SU(3) flavor symmetry constraints in the simulated double-spin asymmetry, $A_{LL}$, at small parton momentum fractions $x$ and its effect on the extracted parton polarizations. We find that different assumptions about $A_{LL}$ extrapolations and SU(3) symmetry can have significant consequences for the integrated quark and gluon polarizations, for polarized proton, deuteron and $^3$He beams. For the parity-violating asymmetry, $A_{UL}$, we study the potential impact on the polarized strange quark distribution with different extrapolations of $A_{UL}$, finding the constraining power to be ultimately limited by the EIC machine luminosity., Comment: 23 pages, 7 figures

Twist-3 partonic distributions contain important information that characterizes nucleon's structure. In this work, we show our lattice exploration of the twist-3 PDFs $g_T(x)$, and $h_L(x)$. We also present our preliminary results on the twist-3 GPD $\tilde{G}_2(x)$. We use the quasi-distribution approach to connect the lattice-extracted matrix elements, renormalized in the RI/MOM scheme, to light-cone distributions, applying the matching procedure that we developed in parallel. We also calculate the twist-2 counterparts of $g_T(x)$ and $h_L(x)$, i.e. $g_1(x)$, and $h_1(x)$, and test the Wandzura-Wilczek approximation., Comment: 6 pages, 4 figures, submission to SciPost Proceedings (DIS 2021)

Different decompositions (sum rules) for the proton mass have been proposed in the literature. All of them are related to the energy-momentum tensor in quantum chromodynamics. We review and revisit these decompositions by paying special attention to recent developments with regard to the renormalization of the energy-momentum tensor. The connection between the sum rules is discussed as well. We present numerical results for the various terms of the mass decompositions up to 3 loops in the strong coupling, and consider their scheme dependence. We also elaborate on the role played by the trace anomaly and the sigma terms., 28 pages; V2: some discussion added, matches PRD version

In this work, we present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution function $g_T(x)$ for the proton from lattice QCD. We use an ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3~fm, lattice spacing of 0.093~fm, and reproduces a pion mass of $260$ MeV. We use the quasi-distribution approach and employ three values of the proton momentum boost, 0.83 GeV, 1.25 GeV, and 1.67 GeV. We use a source-sink separation of 1.12~fm to suppress excited-states contamination. The lattice data are renormalized non-perturbatively. We calculate the matching equation within Large Momentum Effective Theory, which is applied to the lattice data in order to obtain $g_T$. The final distribution is presented in the $\overline{\rm MS}$ scheme at a scale of 2 GeV. We also calculate the helicity distribution $g_1$ to test the Wandzura-Wilczek approximation for $g_T$. We find that the approximation works well for a broad range of $x$. This work demonstrates the feasibility of accessing twist-3 parton distribution functions from novel methods within lattice QCD and can provide essential insights into the structure of hadrons., 10 pages, 6 figures, version accepted for publication

Perturbative matching relates the parton quasidistributions, defined by Euclidean correlators at finite hadron momenta, to the light-cone distributions which are accessible in experiments. Previous matching calculations have exclusively focused on twist-2 distributions. In this work, we address, for the first time, the one-loop matching for the twist-3 parton distribution function ${g}_{T}(x)$. The results have been obtained using three different infrared regulators, while dimensional regularization has been adopted to deal with the ultraviolet divergences. We present the renormalized expressions of the matching coefficient for ${g}_{T}(x)$ in the $\overline{\mathrm{MS}}$ and modified $\overline{\mathrm{MS}}$ schemes. We also discuss the role played by a zero-mode contribution. Our results have already been used for the extraction of ${g}_{T}(x)$ from lattice QCD calculations.

The perturbative procedure of matching was proposed to connect parton quasi-distributions that are calculable in lattice QCD to the corresponding light-cone distributions which enter physical processes. Such a matching procedure has so far been limited to the twist-2 distributions. Recently, we addressed the matching for the twist-3 PDF $g_T(x)$. In this work, we extend our perturbative calculations to the remaining twist-3 PDFs, $e(x)$ and $h_{L}(x)$. In particular, we discuss the non-trivialities involved in the calculation of the singular zero-mode contributions for the quasi-PDFs., 20 pages, 2 figures, results for zero-mode contributions partly revised, associated discussion modified

Generalized TMDs (GTMDs) of hadrons are the most general two-parton correlation functions. The Fourier transforms of GTMDs are partonic Wigner functions. Both GTMDs and Wigner functions were only briefly mentioned in the EIC White Paper1, but in the meantime, several interesting developments have happened in this field. In this write-up, we give a very brief overview of these objects and address the question whether they can play an important role for the EIC science case. To answer this question we discuss the presently known physics content of GTMDs and Wigner functions, as well as observables that are sensitive to these quantities.

Studying light-cone parton distribution functions (PDFs) through Euclidean correlators in lattice QCD is currently a very active field of research. In particular, the parton quasi-distributions (quasi-PDFs) have attracted a lot of attention. Quasi-PDFs converge to their respective standard distributions in the limit of infinite hadron momentum. We explore the quasi-distribution approach for twist-2 generalized parton distributions (GPDs) in a frequently used diquark spectator model. Our main focus is to test how well the quasi-distributions agree with their light-cone counterparts for finite hadron momenta. We also discuss model-independent results for moments of quasi-distributions.

Exploring hadron structure with generalized parton distributions (GPDs) and related concepts is an essential part of the physics program of the planned Electron-Ion Collider (EIC). We discuss new topics in GPD physics (theory, experiment, interpretation) that have emerged in the last years and could be included in the EIC program. This includes: (a) D-term and QCD forces in the nucleon; (b) Transversity GPDs in pseudoscalar meson production and high-mass pair production; (c) Pion and kaon form factors and GPDs; (d) Transition distribution amplitudes and backward meson production; (e) Neutron GPDs and nuclear modifications; (f) Nuclear GPDs and quark/gluon imaging of nuclei; (g) Twist-3 GPDs and quark-gluon correlations; (h) Wigner functions and potential observables. We also comment on future theoretical developments needed for the GPD program at EIC and emerging connections with other areas of nuclear physics. [Conveners’ summary, Week 1 of INT Program INT-18-3].

Studying light-cone PDFs through Euclidean correlators is currently an active field of research. In particular, the concept of quasi parton distributions (quasi-PDFs) is at the forefront of numerical calculations of the partonic structure of strongly interacting systems using lattice QCD. Quasi-PDFs converge to their respective standard distributions if the hadron momentum goes to infinity. We investigate this quasi-distribution approach for twist-2 generalized parton distributions (GPDs) in the widely-used diquark spectator model. We illustrate analytical and numerical results of quasi-GPDs and of quasi-PDFs. We test how well the quasi-distributions agree with their standard counterparts for finite hadron momenta. Furthermore, we explore higher-twist effects associated with the parton momentum and the longitudinal momentum transfer to the target. By discussing the sensitivity of our results to model parameters, we highlight robust features of the quasi-GPDs and quasi-PDFs that one may extract from this model study. We also elaborate on a model-independent analysis of moments of quasi-distributions including relation to Ji's spin sum rule. The moment analysis suggests a preferred definition of several quasi-distributions.

This chapter teaches students how to analyze movements in simple, balanced, and rounded binary form as well as small ternary themes. The analytical approach proposed here concentrates on the four formal functions featured in binary-form movements: initiation, continuation, digression, and conclusion. One of the main goals of this lesson plan is to make students more aware of the ubiquity of the binary form in different stylistic eras and to better prepare them for sonata-form analysis.

Different decompositions of the nucleon mass, in terms of the masses and energies of the underlying constituents, have been proposed in the literature. We explore the corresponding sum rules in quantum electrodynamics for an electron at one-loop order in perturbation theory. To this end we compute the form factors of the energy-momentum tensor, by paying particular attention to the renormalization of ultraviolet divergences, operator mixing and scheme dependence. We clarify the expressions of all the proposed sum rules in the electron rest frame in terms of renormalized operators. Furthermore, we consider the same sum rules in a moving frame, where they become energy decompositions. Finally, we discuss some implications of our study on the mass sum rules for the nucleon., 21 pages, 1 figure; V2: minor changes, references added, to appear in JHEP

We study transverse polarization of hyperons produced in unpolarized proton–proton collision, pp → Λ^↑X, based on the collinear twist-3 factorization. We focus on the twist-3 gluon fragmentation contribution to this process, which is potentially as important as the previously calculated contributions from the twist-3 distribution in the initial proton and the twist-3 quark-fragmentation for Λ^↑. After summarizing the complete set of the purely gluonic twist-3 fragmentation functions for Λ^↑, we provide a formalism of calculating its contribution to pp → Λ^↑X.

Generalized transverse momentum dependent parton distributions (GTMDs) are the most general parton correlation functions of hadrons. By considering the exclusive double Drell-Yan process it is shown for the first time how quark GTMDs can be measured. Specific GTMDs can be addressed by means of polarization observables., 6 pages, 1 figure, typos fixed

The field of fragmentation functions of light quarks and gluons is reviewed. In addition to integrated fragmentation functions, attention is paid to the dependence of fragmentation functions on transverse momenta and on polarization degrees of freedom. Higher-twist and di-hadron fragmentation functions are considered as well. Moreover, the review covers both theoretical and experimental developments in single-inclusive hadron production in electron-positron annihilation, deep-inelastic lepton-nucleon scattering, and proton-proton collisions., Comment: 103 pages, 31 figures, discussion and references added, accepted for publication in Progress in Particle and Nuclear Physics

We discuss the production of transversely polarized hyperons in unpolarized proton-proton collisions in the framework of the collinear twist-3 factorization. We focus on the contribution from the twist-3 fragmentation functions for the final hyperon, that represent the effect of multi-parton correlations in the fragmentation process. This contribution consists of the quark fragmentation one and the gluon fragmentation one. We present the twist-3 cross section for the former in the Leading Order (LO) with respect to the QCD coupling constant. We also present a new formalism to calculate the cross section for the latter contribution. These contributions are as important as that from the twist-3 distribution in the initial proton combined with the transversity fragmentation function for the final hyperon.