Theoretical investigations of nuclear and particle phenomena probe the most fundamental laws governing what matter is and how it behaves. The "standard model" of elementary particle physics is sufficiently complete to permit, in principle, the prediction of the collective properties of QCD matter as well as phenomena involving hadronic, nuclear, and atomic interactions in terms of derived "effective" forces, in the same sense that chemical interactions can be derived from the rules of atomic physics. Duke nuclear and particle theorists develop techniques to study the internal structure of nucleons and nuclei and the phases of QCD matter.

Our research is funded by the U.S. Department of Energy (DOE) through regular research grants. In addition, we also participate in a SSI grant from the National Science Foundation and a Topical Collaboration Grant by the DOE. Our past research support includes international collaboration grants from the National Science Foundation, three DOE Outstanding Junior Investigator Awards as well as collaborative agreements with the RIKEN/BNL Research Center and Jefferson Laboratory.

We participate in international collaborations with many universities, including Osaka University (Japan), Nagoya University (Japan) and the Variable Energy Cyclotron Centre (Calcutta, India), as well as universities in Bern (Switzerland), Frankfurt (Germany) and Regensburg (Germany). We also interact closely with nuclear theory and experimental groups at North Carolina State and the University of North Carolina, with whom we run the bi-weekly Triangle Nuclear Theory Colloquium. Our work impacts the experimental progams at TUNL/HIGS, ORNL, NIST, LHC, RHIC, FAIR, Jefferson Lab, KEK and BES (Beijing).

### Research Topics

#### How do quarks interact?

How do the most fundamental particles known bind together to form nucleons? Matter is composed of atoms and molecules, atoms are made of electrons and nuclei, nuclei are built from nucleons, and the constituents of nucleons are quarks. The theory of the force responsible for the binding of quarks into nucleons is called Quantum Chromodynamics, or QCD. Though the binding forces at the first three levels of composition are quantitatively understood, those at the quark level are still very poorly understood. Duke theorists investigate QCD from three broad points of view: the derivation of effective quark interactions from first principles; the behavior of elementary particles under extreme conditions; and reactions of particles and nuclei at high densities and temperatures.

#### Lattice Gauge and Effective Field Theories (L/EFT)

The Lattice and Effective Field Theory group studies phenomena that arise from Quantum Chromodynamics (QCD), weak interactions, and electromagnetic interactions at both the hadron level (protons, neutrons, mesons and their excited states), the few nucleon level, and the quark level. We approach the subject using two complementary techniques, lattice field theories and effective field theories.

The symmetries of QCD impose important constraints on its solutions. Effective field theory (EFT) is a methodology that encodes the symmetries of QCD in terms of the relevant degrees of freedom for the process being studied. In this framework we perform systematic expansions in the small parameters that arise from ratios of disparate scales in the problem. We apply EFT methods to the physics of hadrons containing heavy quarks (bottom or charm) which are produced in many nuclear and particle physics experiments. For example, we proposed studying the production of heavy quarkonium within jets as a new way to test the underlying production mechanisms that motivated experimental studies at the LHC. In the last ten years, numerous exotic hadrons with unconventional quark content including heavy quarks have been discovered and we develop theories to explain the properties of these particles in support of expected measurements at LHC, FAIR (Darmstadt), and the BES (Beijing). At lower energies we use EFTs to study few nucleon reactions, including parity violation, as a probe of QCD. We have been able to provide a unifying description of few nucleon parity violating experiments, and use the enhanced symmetries of QCD in the large-number-of-colors limit to identify where the largest asymmetries might be measured. Our work on parity conserving few body asymmetries helps support the measurements of our TUNL/FEL/HIGS experimental colleagues as well as proposed experiments at the Oak Ridge SNS.

Since QCD is a complete theory in itself, we can also study methods to solve it non-perturbatively. The only known way to do this today is through a numerical approach that formulates QCD on a space-time lattice and performs the relevant calculations through a Monte Carlo sampling process. While many impressive calculations of QCD have been performed using such an approach, our group focusses on problems that are not solvable using traditional approaches. One example of a problem that requires nontraditional approaches is the physics of dense nuclear systems at low temperatures. The technical challenge, called the sign problem, arises due to the quantum mechanical nature of quarks and gluons. Similar challenges arise in other simpler quantum many body systems as well. The Duke Lattice and Effective Field Theory group is a leader in finding solutions to such challenges and has developed several new ideas to tackle the difficulties. Using our non-traditional ideas we have discovered new and efficient quantum Monte Carlo algorithms, computed universal properties of fermionic quantum critical points, and even discovered novel mechanisms of fermion mass generation that may be relevant to physics beyond the standard model of particle physics. Most recently we have combined our lattice and EFT efforts to study few body EFTs using lattice techniques.

#### Hot and Dense QCD: Quark-Gluon-Plasma and relativistic heavy ion collisions

For about 10 microseconds after its creation in the Big Bang, the universe was in a state called the Quark Gluon Plasma in which quarks and gluons roamed freely. Due to the universe's rapid expansion, this plasma cooled and went through a phase transition to form hadrons - most importantly nucleons – which constitute the building blocks of matter as we know it today. Little is directly known from experiments about the properties of the early Universe in its plasma phase - only in the last fifteen years have accelerators been able to recreate in the laboratory the conditions of temperature and density at which the QGP can exist, by heating and compressing nuclear matter through collisions of heavy nuclei. The Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory was specifically built to observe and study the QGP phase of matter, and similar experiments are now underway at the CERN Large Hadron Collider (LHC).

The central problem in studying the QGP in nuclear collisions is that its lifetime is so short that only the ashes of its decay (in the form of hadrons) can be detected. One of the main challenges of determining the QGP properties is therefore to find clear and unambiguous connections between the transient (quark-gluon) plasma state and the experimentally observable hadronic final state. This can only be accomplished by detailed computational modeling of the time-evolution of heavy-ion reactions and the subsequent calibration of the model’s multiple parameters to the available data taken at RHIC and LHC.

The determination of the properties of the QGP will provide a first comprehensive understanding of emergent phenomena in strongly interacting multi-particle systems governed by the fundamental forces of QCD. Beyond its immediate impact of addressing pressing questions in strong interaction physics, the research of the QCD group will also have the potential of generating significant insights in the fields of astrophysics, condensed matter physics and cosmology.

#### Group Activities and Further Information

The Triangle Nuclear Theory Colloquium (TNT) is a DOE-funded Colloquium series jointly organized and held at Duke University, the University of North Carolina at Chapel Hill (UNC) and the North Carolina State University (NC-State). The Colloquium is regularly attend by members of the High-Energy and Nuclear Theory groups of those three institutions.