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This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions., Comment: 471 pages, many figures

We develop a framework to establish benchmarks for machine learning and deep neural networks analyses of exclusive scattering cross sections (FemtoNet). Within this framework we present an extraction of Compton form factors for deeply virtual Compton scattering from an unpolarized proton target. Critical to this effort is a study of the effects of physics constraint built into machine learning (ML) algorithms. We use the Bethe-Heitler process, which is the QED radiative background to deeply virtual Compton scattering, to test our ML models and, in particular, their ability to generalize information extracted from data. We then use these techniques on the full cross section and compare the results to analytic model calculations. We propose a quantification technique, the random targets method, to begin understanding the separation of aleatoric and epistemic uncertainties as they are manifest in exclusive scattering analyses. We propose a set of both physics driven and machine learning based benchmarks providing a stepping stone towards applying explainable machine learning techniques with controllable uncertainties in a wide range of deeply virtual exclusive processes., 16 pages, 12 figures

This volume is a collection of contributions for the 7-week program "Probing Nucleons and Nuclei in High Energy Collisions" that was held at the Institute for Nuclear Theory in Seattle, WA, USA, from October 1 until November 16, 2018. The program was dedicated to the physics of the Electron Ion Collider (EIC), the world's first polarized electron-nucleon (ep) and electron-nucleus (eA) collider to be constructed in the USA. These proceedings are organized by chapters, corresponding to the weeks of the program: Week I, Generalized parton distributions; Week II, Transverse spin and TMDs; Week III, Longitudinal spin; Week IV, Symposium week; Weeks V & VI, eA collisions; Week VII, pA and AA collisions. We hope these proceedings will be useful to readers as a compilation of EIC-related science at the end of the second decade of the XXI century., Electron Ion Collider, INT 18-3 Program. Published by World Scientific. Duplicates content of arXiv:1912.10965, arXiv:1912.10724, arXiv:1910.03006, arXiv:1910.07982, arXiv:1912.13397, arXiv:1910.01979, arXiv:2001.07862, arXiv:2001.03700, arXiv:1910.01030, arXiv:1910.01273, arXiv:1912.13020, arXiv:1910.06003, arXiv:2001.03655, arXiv:1909.12591, arXiv:1909.09809, arXiv:1910.04806, arXiv:2001.05978

We address the validity of the momentum sum rule for deep inelastic nuclear structure functions., 5 pages, 5 figures

It is now widely recognized that large Bjorken $x$ data play an important role in global analyses of Parton Distribution Functions (PDFs) even at collider energies, through perturbative QCD evolution. For values of the scale of the reaction, $Q^2$, in the multi-GeV region the structure functions at large $x$ present resonance structure. Notwithstanding, these data can be incorporated in the analyses by using quark-hadron duality or approximate scaling of the structure function data averaged over their resonance structure. Several averaging methods have been proposed using either the PDFs Mellin moments, or their truncated moments. We propose an alternative method using Bernstein polynomials integrals, or Bernstein moments. Bernstein moments render a smooth form of the structure function in the resonance region. Furthermore, being based on a different averaging criterion than the methods adopted so far, they provide a new framework for understanding the possible mechanisms giving origin to the phenomenon of quark-hadron duality., 16 pages, 9 figures

Spin and transverse momentum dependent parton distributions - Generalized Parton Distributions (GPDs) - are at the interface between the QCD structure of the hadrons and observable quantities. The GPDs are linear superpositions within helicity amplitudes. The amplitudes are probed in high energy leptoproduction processes through angular dependent cross sections and polarization asymmetries. Phenomenological extraction of the amplitudes and the distributions is a challenging task. We present observables that connect particularly with the chiral odd quark-nucleon helicity amplitudes for Deeply Virtual $\pi^0$ Production., Comment: Talk presented at CIPANP2015. 15 pages, LaTeX, 7 figures

Using a physically motivated parameterization based on the reggeized diquark model we perform a flavor separation of the chiral-odd generalized parton distributions obtained from both $\pi^0$ and $\eta$ exclusive electroproduction. In our approach we exploit a connection between the chiral-even and chiral-odd reduced helicity amplitudes using Parity transformations that are relevant for a class of models that includes two-component models. We compare our results for $\eta$ production to the previously obtained $\pi^0$ results, and we make predictions for the transverse single spin asymmetry components which will be measured within the Jefferson Lab 12 GeV program., Comment: 23 pages, 12 figures

We present and discuss a new method to extract parton distribution functions from hard scattering processes based on an alternative type of neural network, the Self-Organizing Map. Quantitative results including a detailed treatment of uncertainties are presented within a Next to Leading Order analysis of inclusive electron proton deep inelastic scattering data., 16 pages, 12 figures

We show how deeply virtual pseudoscalar meson production experiments single out the contribution of the four chiral odd quark-proton GPDs which are related to the so far elusive transversity distribution function, $h_1$. Furthermore, in the kinematical ranges of the proposed EIC, electroproduction of strange and charmed mesons will allow one to uniquely pin down the non-perturbative charmed component in the nucleon structure function, and at the same time provide new insights in the connection of the quark/gluon degrees of freedom with the meson-baryon description. The use of dispersion relations as well as the naive extension of the parton model to the ERBL region are critically analyzed., 5 pages, 2 figures, unexpurgated version of the contribution submitted to the section "Spatial imaging of quarks and gluons" (tentative title) of the INT 10-3 program write-up

We propose to investigate a largely unexplored sector that is unique to the formulation of hard exclusive processes in terms of GPDs, namely the electroproduction of strange and charmed mesons in the kinematical ranges of Jefferson Lab's 12 GeV upgrade, and of the proposed Electron Ion Collider (EIC). In this contribution we focus on charmed meson production that is unique to the EIC. Exclusive strange and charmed meson production provides new insights in the connection of the quark/gluon degrees of freedom with the meson-baryon description, both in the unpolarized and polarized sectors. However, as particularly evident in polarized scattering, the underlying mechanisms are still far from being fully understood. We present an approach in terms of generalized parton distributions. As an application, we show that through exclusive electroproduction of pseudoscalar charmed mesons one can uniquely single out the non-perturbative charmed component in the nucleon structure function., 8 pages, 3 figures, to appear in proceedings of Workshop on Exclusive Reactions at High Momentum Transfer (IV), Jefferson Lab, May 18-21, 2010

We describe a new method to extract parton distribution functions both in the unpolarized and the polarized case, based on a type of neural networks, the Self-Organizing Maps. Initial quantitative results of our Next to Leading Order analysis are presented for the unpolarized case., 5 pages, 1 figure, to appear in the proceedings of "XVIII International Workshop on Deep-Inelastic Scattering and Related Subjects April 19 -23, 2010 Convitto della Calza, Firenze, Italy"

Exclusive meson leptoproduction from nucleons in the deeply virtual exchanged boson limit can be described by generalized parton distributions (GPDs). Including spin dependence in the description requires 8 independent quark-parton and gluon-parton functions. The chiral even subset of 4 quark-nucleon GPDs are related to nucleon form factors and to parton distribution functions. The chiral odd set of 4 quark-nucleon GPDs are related to transversity, the tensor charge, and other quantities related to transversity. Different meson or photon production processes access different combinations of GPDs. This is analyzed in terms of t-channel exchange quantum numbers, $J^{PC}$ and it is shown that pseudoscalar production can isolate chiral odd GPDs. There is a sensitive dependence in various cross sections and asymmetries on the tensor charge of the nucleon and other transversity parameters. We also consider, briefly, the analyticity of the GPDs and the problems with the partonic interpretation in the ERBL region., 5 pages, 1 figure, presentation at DIS 2010, Firenze, Italy

Exclusive $\pi^0$ electroproduction from nucleons at large $Q^2$ can be described by Generalized Parton Distributions (GPDs), particularly the chiral odd subset related to transversity. These GPDs can be accessed experimentally from various cross sections and asymmetries. We calculate these GPDs in a spectator model, constrained by boundary functions. Alternatively, in a hadronic picture the meson production amplitudes correspond to C-odd Regge exchanges with final state interactions. The helicity structure provides relations between the partonic and the hadronic, Regge description of C-odd, chiral-odd processes. Calculations show how the tensor charge and other transversity parameters can be, Comment: 5 pages, 3 figures, to appear in the proceedings of DIS 2009, 26-30 April 2009, Madrid

Exclusive $\pi^o$ electroproduction from nucleons is suggested for extracting the tensor charge and other quantities related to transversity from experimental data. This process isolates C-parity odd and chiral odd combinations of t-channel exchange quantum numbers. In a hadronic picture it connects the meson production amplitudes to C-odd Regge exchanges with final state interactions. In a description based on partonic degrees of freedom, the helicity structure for this C-odd process relates to the quark helicity flip, or chiral odd generalized parton distributions. This differs markedly from deeply virtual Compton scattering, and both vector meson and charged $\pi$ electroproduction, where the axial charge can enter the amplitudes. Contrarily the tensor charge enters the $\pi^o$ process. The connection through the helicity description of the process to both the partonic and hadronic perspectives is studied and exploited in model calculations to indicate how the tensor charge and other transversity parameters can be related to cross section and spin asymmetry measurements over a broad range of kinematics., Comment: 40 pages, 14 figures Revised text clarifying main points, fixing typos, adding references

Exclusive $\pi^o$ electroproduction and related processes are suggested to investigate the chiral odd transversity distributions of quarks in the transversely polarized nucleon, $h_1(x)$, and its first moment, the tensor charge. The connection between a description based on partonic degrees of freedom, given in terms of generalized parton distributions, and Regge phenomenology is explored., Comment: Proceedings of XII International Conference on Hadron Spectroscopy, October 8-13, 2007, Laboratori Nazionali di Frascati (Rome) Italy

We present recent progress on the study of the deep inelastic structure of nuclei that improves our current understanding of the mechanisms of nuclear modifications of parton distribution functions., 5 pages, 2 figures, talk presented at "Les Rencontres de Physique de la Vallee d'Aoste", La Thuile, March 5-11, 2006