Unraveling quark confinement

by Andrei Belitsky

The past century witnessed enormous progress in unraveling the origin, structure and evolution of the visible matter in the universe—the material that makes up stars, planets, and life forms.
   Our evolving understanding of the structure of matter in XX century was an interplay of theoretical and experimental advances that yielded several paradigm changes that revolutionized physics and technologies that emerged from it. The discovery of radioactive decays and Rutherford scattering experiments, which demonstrated the existence of atomic nucleus, were matched by powerful theoretical foundation: the Einstein’s theory of special relativity, stating that mass and energy were truly interchangeable, and the introduction of quantum mechanics. The realization that nuclear reactions provide the energy that drives the cosmos revolutionized our understanding of the universe. Finally the scattering of high-energy electron beam on nucleons led to the discovery of point-like, i.e., partonic, structure inside the proton and neutron and confirmed that these particles are made of more fundamental building blocks—quarks and gluons, which make up 99 percent of the mass of our everyday world.  The theory which encodes the strong interaction physics was realized to be a gauge field theory called quantum chromodynamics (QCD). Quarks are bound to each other by the strongest force in the universe so tightly that one quark cannot exist by itself. The carries of the force are gluons which are much like photons but come in eight different species and also can directly interact with each other. The latter property creates the main obstacle in solving QCD using the same tools as for its electromagnetic cousin as that contrary to the latter the former becomes strong when one attempts to separate hadronic constituents apart (see Fig. 2) thus making traditional perturbative methods invalid. The main focus of our studies in QCD is understanding the quark confinement and its implications for the structure of hadrons. We use diverse techniques for this purpose, both phenomenological and analytical.       
    One of the most fascinating possibilities of modern electron-scattering experiments is that they can measure the spatial distribution of quarks and gluons, providing actual three-dimensional images of the proton at the femtometer scale. The reconstruction of spatial images from scattering experiments by way of Fourier transform of the observed scattering pattern is a technique widely used in physics, e.g., in X-ray scattering from crystals. Recently, it was discovered how to extend this technique to the spatial distribution of quarks and gluons within the proton, using processes that probe the proton at a tiny resolution scale. Our major contribution in this line of endeavor was in the development of a novel approach to understanding quark confinement through the study of microscopic partonic characteristics of strongly interacting particle based on the concept of generalized parton distributions. This is a rich formalism that both unifies existing descriptions of proton structure and takes a giant leap into unknown territory. In brief, a generalized parton distribution is a relativistic equivalent of the quantum mechanical Wigner quasiprobability distribution and provides complete information about a quantum mechanical state, contrary to conventional probes. It encodes the quantum phase of their wave function not just their absolute value.    (CONTINUED ON PAGE 5)  

Unraveling quark confinement (continued from Page 2)

The forgoing decade witnessed substantial progress in unraveling the intriguing puzzle of hadron's structure through GPDs and endowed us with a phase-space picture of nucleon’s structure (see Fig. 3). Are the up quarks, the down quarks, and the gluons in the proton equally distributed in space? Are the quarks more polarized in the center than at the periphery? Answers to questions like these await and will revolutionize our knowledge of proton structure. Finally, encoded in the GPDs is yet another secret: the orbital angular momentum of the quarks and gluons. With the GPDs, we not only obtain still photographs of the quarks, but we catch them in action as well. Our work laid the ground in the establishment and development of a number of concepts and directions in the field. These results were pivotal to warrant the current state of the art of the field and brought the whole subject to the level when it grew into the main experimental project driving the science of the 12 GeV energy upgrade of the Continuous Electron Beam Accelerator Facility in Jefferson Laboratory, Virginia. This $310 million major national project was recently funded by the Office of Nuclear Science of the U.S. Department of Energy.  
 The above phenomenological approach to hadron’s structure has to be complimented by theoretical tools based on first principle calculations. To date, however, the bulk of our theoretical knowledge about QCD has been gained from methods relying on some kind of a perturbative expansion with respect to a small parameter.  This is the case for traditional renormalizable or nonrenormalizable effective field theories.  The major challenge has always been the need to devise nonperturbative techniques overcoming the limitations of perturbative considerations.  The numerical framework of lattice gauge theory, which uses discretized space-time, partially resolves these problems, but one still lacks reliable analytical methods.  Recently, a unifying concept becoming increasingly prominent is integrability. The idea of integrability for interacting particle systems in classical mechanics is associated with Liouville theorem, which states that a mechanical system is integrable provided it has as many conserved quantities as degrees of freedom. Integrability is manifested in diverse physical systems describing different physical phenomena.  Its story starts with the Heisenberg model (1929), which describes of a chain of atoms interacting via nearest-neighbor spin exchange.  The spectrum of the system was solved by Bethe in 1931 using an innovative method now called the coordinate Bethe ansatz.  Later, Liouville's idea was generalized (starting with Skyrme) to construct exact solutions to classical equations of motion of physical nonlinear systems in one space and one time dimension, e.g., the nonlinear sine-Gordon and Korteweg-de Fries wave equations.  Since then the scope of this idea has grown dramatically, and implications of this concept have now been extended to any classical or quantum system that possesses sufficiently many conserved charges such that all physical characteristics can be calculated exactly.  The conservation laws are generally associated with symmetries, and not necessarily Noetherian.  More than that, the symmetries may be hidden, and uncovering them is often a challenging mathematical problem.  And while in principle exact solutions exist, their explicit construction can be extremely nontrivial. However, if these complications are circumvented, quantum field theory breaks free from the limitations of perturbation theory, and previously concealed properties such as, for instance, strong-weak coupling dualities can be revealed. Nowadays, diverse methods have been formulated to identify and solve integrable systems.  For one, the original Heisenberg model, used to describe diverse aspects of ferromagnetism and superconductivity, has been generalized to that for a chain of particles with arbitrary spin, which turns out to be relevant to four-dimensional gauge theories including QCD as was demonstrated by Belitsky-Braun-Derkachov-Korchemsky-Manashov over a decade ago. Recently, a distant cousin of QCD - the so-called maximally supersymmetric field theory – a full-fledged four-dimensional theory was solved by means of generalization of techniques known as the Bethe Ansatz and Baxter equations to long-range interacting systems. Our current work is focused on the extension of this formalism to nonconformal theories like QCD. Successful implementation of these ideas will not only solve one of the most outstanding problems of modern gauge theories – quark confinement - but also will help to establish a close connection between condensed matter and particle physics.

For more information on Professor Andrei Belitsky and his research, click HERE.