Ebook: Three-Dimensional Partonic Structure of the Nucleon

The CLXXX Course, “Three-Dimensional Partonic Structure of the Nucleon”, of the “Enrico Fermi” School, held in Varenna from June 28 to July 8, 2011, was devoted to the study of the 3-dimensional structure of protons and neutrons (nucleons) and to the properties and motion of the nucleon internal constituents, quarks and gluons (partons).

This issue is central in many theoretical and experimental activities and has marked a real transition, in the last two decades, in our exploration of the ultimate structure of matter, addressing fundamental questions such as the orbital motion of quarks and gluons inside the nucleons, their spatial distribution and the correlation between spin and intrinsic motion. A real 3-dimensional imaging of the nucleon as a composite object, both in momentum and coordinate space, is slowly emerging.

Several dedicated experiments are either running (COMPASS, JLab and RHIC) or analyzing previously collected data (HERMES). Other experimental facilities are under construction (J-PARC and the upgrading of JLab) or being planned (PANDA, PAX, ENC, EIC). All these have a central focus in the study of the 3-dimensional nucleon structure.

Enormous theoretical progress has been achieved in the last years with the new concepts of Transverse Momentum Dependent (TMDs) and Generalized Parton Distributions (GPDs). These can be studied respectively in inclusive and exclusive processes at the above-mentioned facilities by looking at spin asymmetries and azimuthal distribution of final hadrons or leptons. The collection and interpretation of data, with theorists and experimentalists working together, is and will be one of the major activities in hadron physics; the international scientific community working in the field is constantly growing.

The proposed School had the ambitious goal of educating postgraduate students, so that they could end up becoming specialists in hard scattering and partonic azimuthal distributions analysis and could be able to join CLAS, COMPASS, RHIC, J-PARC, PAX, PANDA, EIC, ENC and any of the dedicated experiments; or they could perform theoretical and phenomenological studies of TMDs and GPDs.

The School was attended by 40 students and 3 observers from 13 different Countries. Basic introductory lectures were delivered by 7 lecturers and more specialized topics covered by 7 seminar speakers. All of them are among the world experts in their own field. Special attention was given to the interaction among lecturers and students and to favor active participation. Lectures and seminars were focused on the conceptual theoretical ideas, the experimental techniques and the phenomenological interpretation of data. Special lectures and tutorials were dedicated to data analysis and model building, with the active participation of students.

The main topics discussed can be summarized as follows:

– Partonic distributions, fragmentation functions and factorization in QCD (collinear case).

– Theory of Transverse Momentum Dependent partonic distributions (TMDs).

– Theory of Generalized Partonic Distributions (GPDs).

– Experimental methods in studies of hard scattering processes.

– Extraction of TMDs and GPDs from data.

– Analysis tools for azimuthal asymmetries.

– Models for TMDs and numerical methods.

– Future experiments.

In conclusion the organizers of the Course warmly thank the Jefferson Science Associates, the Jefferson Laboratory, and the HadronPhysics2 European Project of the FP7 framework for their generous financial support; the Wolfram Research for supporting the School with complimentary licenses of Mathematica for Students. Special thanks are due to Barbara Alzani, Monica Bonetti, Roberta Comastri and Ramona Brigatti for their precious, continuous and invaluable help both during the preparation of the Course and its organization at Villa Monastero.

M. Anselmino, H. Avakian, D. Hasch and P. Schweitzer

In these lecture notes, I describe typical experimental equipment and methods, as well as analysis procedures, for measurements of inclusive Deep Inelastic (DIS) and Semi-Inclusive Deep Inelastic Scattering (SIDIS) of (polarized) leptons off (polarized) targets. While some of the topics I discuss have broader applicability (for instance, for measurements of exclusive processes, or for hadron-hadron interactions), I concentrate on lepton scattering experiments, with particular emphasis on experiments already completed or planned at the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab.

In these lectures we study how properties of hadrons like charge densities and parton distributions can be described within the framework of quantum chromodynamics and how they appear in high-energy scattering cross-sections. For the parton distributions, we specifically look at the role of transverse momenta of partons.

These lectures give an introduction to the theory of generalized parton distributions, starting from the underlying concepts, highlighting their physical interest, and discussing the possibilities to study them experimentally.

The following lecture notes are an introduction to some aspects of transverse-momentum–dependent parton distribution functions (TMDs). Some parts of the present notes were not actually covered during the school, but are given here for reference.

Transverse-momentum-dependent distributions reveal three-dimensional partonic structure of the nucleon. In these lectures I am going to discuss the phenomenology of TMDs and give some examples of calculations.

We present a systematic study of the transverse-momentum–dependent parton distributions (TMDs) in the framework of quark models. In particular, we review the general formalism for modeling the quark TMDs using the representation in terms of overlap of nucleon light-cone wave functions. Such a formalism can be applied to a large class of quark models. We will discuss the building blocks of these different models, and we will use as explicit example for the calculation of the TMDs a light-cone constituent quark model. Within this model, we also propose a phenomenological study of different observables, trying to learn how model parameters related to particular assumptions on the nucleon structure can be tuned to describe available experimental data.

We present some of the latest developments in the field of Generalized Parton Distributions (GPD). Experimentally, a lot of data has been recently released from the DESY and Jefferson Lab (JLab) facilities. Theoretically, much progress has been made with the recent emergence of fitting codes and algorithms which provide some first 3-d imaging insights on the quark structure of the nucleon. In this paper, we concentrate our discussions on the deep virtual compton scattering process and to the quark sector.

The statistical tools discussed during these lectures can be applied in the analysis of the data from real experiments, for example in the extraction of single-spin or double-spin azimuthal asymmetries. The extraction might be relatively easy if there is a reasonable amount of statistics, there are no gaps in the acceptance or significant inefficiencies in the detectors. Otherwise, powerful statistical tools have to be applied. During the lectures, the least-squares, the unbinned (standard and extended) and binned maximum-likelihood methods of asymmetry extraction have been introduced. In this write up, only the method of standard maximum likelihood is discussed. Maximum likelihood is a technique for estimating the values of parameters given a finite sample of data. It is approximately unbiased and efficient.

This lecture discusses the COMPASS experiment at Cern performing deep inelastic scattering of polarised muons off polarised targets. The main results from the measurements performed since 2002 with longitudinal and transverse target polarisation are presented. The second part of the lecture discusses the plans and preparations for future measurements related to generalised parton distributions and transverse-momentum–dependent distribution functions. These experiments comprise deeply virtual Compton scattering as well as hard exclusive meson production in muon scattering off a liquid-hydrogen target on the one hand and Drell-Yan dimuon production using a negative pion beam and a transversely polarised proton target on the other hand. During the GPD muon experiment, precise data will also be taken on hadron production and transverse-momentum–dependent distributions with the unpolarised proton target.

An overview is presented of the upgrade of JLab's cw electron accelerator from the current maximum beam energy of 6 GeV to the upgraded maximum energy of 12 GeV. Construction of the 12 GeV upgrade project has started in 2008. A broad experimental program has been developed to map the nucleon's intrinsic correlated spin and momentum distribution through measurements of deeply exclusive and semi-inclusive processes, and to probe the quark and gluon confinement by studying the spectrum of mesons with exotic quantum numbers. Other programs include the forward parton distribution function at large x_B, the quark and gluon polarized distribution functions, measurements of electromagnetic form factors of the nucleon ground state and of nucleon resonance transitions at high Q², and the exploration of physics beyond the Standard Model in high-precision parity-violating processes. The higher beam energy is also well suited to explore quark hadronization properties using the nucleus as a laboratory.

The project of a polarised Electron Ion Collider (EIC) is currently discussed intensively in the high energy nuclear physics community. With such a facility, a real breakthrough in “spin physics” and the study of the three-dimensional structure of the nucleon is expected. This lecture reviews the physics case for an EIC, concentrating on the topics discussed at this school, as well as the technical challenges and envisaged realisations.

The participants of the School were assigned a “Fermi problem”. An analysis of the results is presented, and future developments are outlined.