The accepted theory of the strong nuclear force that holds atomic nuclei together, called QCD (Quantum Chromodynamics) has been known for 35 years, but is extraordinarily difficult to use and is poorly understood in precisely the regions where it is most prominent; for example, we know that protons and neutrons (collectively, "nucleons") are made of smaller constituents named quarks and gluons, but exactly how they are assembled into nucleons remains murky at best. In this grant, Belitsky and Lebed will use a variety of high-powered mathematical tools, often ones borrowed from string theory, to make headway in this complicated landscape.

Belitsky is an expert in the theory of generalized parton distributions, which are the most precisely defined observables possible for nucleons, while Lebed is an expert on large Nc QCD, in which solving QCD becomes paradoxically simpler to solve by adding more degrees of freedom than occur in nature. In addition, Belitsky has become adept in a powerful technique called integrability, in which QCD and similar theories can be mathematically related to the physics of systems like ferromagnets and other "spin-chains". Meanwhile, Lebed is studying "holographic QCD," which is based upon an idea from string theory, that QCD and related strongly-interacting theories can be related to weakly-interacting gravity on a curved space. Each of Belitsky and Lebed will mentor a Ph.D. student in these project areas.

Project Report

This grant funded the research of Principal Investigator Andrei Belitsky and Co-Principal Investigator Richard Lebed for a three-year period (plus contributed to funding the research for an additional year via a no-cost extension). Included in this funding were support for Belitsky graduate students Roman Pasechnik, Joel Lynn, and Yao Ji, for Lebed graduate students Lang Yu and Russell TerBeek, and for postdoctoral researcher Van Eric Mayes. A number of other students were mentored by Belitsky and Lebed on research related to this project, including graduate students Xiang Chen and Lifang Xia and undergraduate student Christopher Sheridan. One of the major ingredients of the research endeavor funded under the current grant was channeled towards unraveling the intricate structure of the building blocks of matter, known as nucleons. These research efforts relied on several novel approaches to strongly-interacting systems such as large-Nc expansion and parton correlation functions by Lebed and Belitsky, respectively. The former framework includes allowing the number of quark colors to change from the known value of 3 in our universe to an arbitrarily large number Nc. One of the project findings is that the exact nature of the 1/Nc expansion can be performed in more than one way and still give results that agree with experiment. The study of microscopic partonic characteristics of strongly interacting particles was based on the concept of generalized parton distributions and a paradigm of Wigner distributions that laid the ground for a unified description of the internal structure of the proton as measured in a variety of high-energy reactions. These concepts were pivotal to warrant the current state of the art in the field that emerged as the main force driving for the science of the energy upgrade of the CEBAF in Jefferson Laboratory. This project was recently funded at the $310M level for upgrade of the experimental equipment in Halls A, B, C and construction of a brand new experimental Hall D. Over the period of the last several years, Belitsky devoted his efforts in this field towards refinement of theoretical description of differential cross sections for exclusive electro-production of particles which are major probes that give access to generalized parton distributions. Moreover, several other topics in particle physics were studied by Lebed, such as the atom formed from the heavy electron partner called the muon and its antiparticle (in which two novel and distinct ways of producing this heretofore undiscovered atom were described); the construction of models of particle physics in which the number, multiplicities, and masses of particles are successfully explained by the manner of intersection of fundamental strings that inhabit not only our three spatial and one time dimension, but a number of additional microscopically "compactified" dimensions; the construction of models of particle physics in which at least some of the known particles are accompanied by "Lee-Wick" partners that can, for very short amounts of time, violate the principle of cause and effect, and whose discovery (according to the funded work) is very possible at the Large Hadron Collider. Another aspect of Belitsky’s research was focused on develop a viable analytical framework to tackle quark confinement from first principles. A change of paradigm is needed to attack this problem when all conventional methods fail. since the early days of QCD, it was anticipated that it can reformulated as a string theory. But explicit formulation of this program was lacking until about fifteen years ago when the program was realized through the so-called gauge/string duality or Maldacena’s holography. The model is a very distant cousin of QCD and thus development of formalisms and techniques to solve its dynamics will teach us how to attack the real world phenomena. The maximally supersymmetric gauge theory theory, having Quantum Chromodynamics as its subsector, inherits its integrability property found in 1998 and moreover gets extended to all order in gauge coupling. The approach that Belitsky was pursuing was based on encoding the integrable structures on the theory in a generalization of the Baxter equations that was developed by him a few years ago. This framework allowed the authors to successfully obtain predictions for observables, with the cusp anomalous dimension being one example, that provide analytical interpolation between weak and strong coupling, thus fulfilling a long-standing goal of having an analytical framework for studies of strongly coupled gauge theories. More recent studies address the new duality between the S-matrix of the theory and expectation values of superholonomies. Under the aegis of this funding, Lebed was also involved in substantial public outreach. For example, he delivered a talk titled "Particle Physics: The Second Century" to the Arizona Science Circle, a group of highly-motivated high school students gathered from throughout the Phoenix metropolitan area. He also gave an interview to The Phoenix New Times weekly magazine on the discovery of the Higgs boson at the Large Hadron Collider.

National Science Foundation (NSF)
Division of Physics (PHY)
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Bradley D. Keister
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Arizona State University
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