Quarks, Hadrons, & Nuclei

Most of the visible mass in the universe is due to nuclei and their interactions. However, our understanding of the emergent nuclear phenomena in terms of their constituent quarks and gluons through Quantum ChromoDynamics (QCD) has remained elusive. My research focuses on understanding QCD by studying few-body nuclear reactions, and developing non-perturbative methods to use in lattice QCD analyses. Particularly, I am interested in three-body scattering processes to understand the role of three-body nuclear forces. Additionally, I am investigating electroweak transitions of multi-hadron systems to gain insight on the structure of hadrons

Lattice QCD

Lattice QCD is a non-perturbative numerical technique where one discretizes the QCD path integral in finite Euclidean spacetime and evaluates it via numerical Monte Carlo sampling. In principle, hadron properties are then determined by computing appropriate correlation functions of quarks and gluons. Since most of the hadrons are unstable, we require a systematic approach to include the coupling of these hadrons to multi-particle scattering amplitudes. Accessing scattering amplitudes directly from lattice QCD is complicated by the fact that calculations are performed in a finite volume, forbidding any notion of an asymptotic state. However, one can indirectly determine scattering processes by constructing a non-perturbative mapping between the finite volume spectrum of particles in a box and the infinite volume scattering amplitude. This technique, known as L"uscher’s method, has been used to extract scattering amplitudes. Once the scattering amplitudes are determined, elements from scattering theory are used to obtain the spectral properties of the unstable resonances.

Reaction Theory

Our primary method for studying hadrons and their interactions is through reactions in particle accelerators. Reaction Theory is a framework to quantitatively construct observables which can be used to analyze such processes. We use fundamental principles of physics, such as causality and probability conservation, to construct analytic reaction amplitudes, which are the primary quantum observable which encodes the dynamics of the interactions between particles. My work in reaction theory spans constructing reaction amplitudes for phenomenological studies of few-body interactions as well as for the analysis of computational results from Lattice QCD

Three-Body Dynamics

Exploring the spectrum above three-body thresholds is a highly non-trivial problem, however in recent years both the lattice QCD and hadron phenomenology communities have been active in developing the theoretical tools to study three-body reaction amplitudes. Phenomenologically many excited states decay to three particles, such as the \(N^{\star}(1440)\) (commonly known as the Roper resonance) which is known to decay to \(\pi\pi N\) in both the \(\pi \Delta\) and \\(\sigma \pi\) channels. In addition, it has been shown that \(3N\) effects are responsible for up to 30% of the binding of light-nuclei. My research program aims to utilize lattice QCD, scattering theory, and effective field theories to study three-body nuclear systems such as these from QCD. Addressing the three-body problem requires two complimentary paths of study: Theoretical developments of finite-volume and scattering formalisms, and numerical applications to lattice QCD.

Electroweak Interactions of Hadrons

Quantifying the spectrum of low-lying QCD states is a necessary first step towards connecting QCD to few-body nuclear phenomena. To further this goal, we must build on top of spectroscopic studies by examining the substructure of hadrons in terms of their constituent quarks and gluons. Structural observables, such as electromagnetic form-factors or parton distributions functions, can be extracted from electroweak transitions of hadronic systems. Calculating such observables from Lattice QCD for stable hadrons such as the nucleon has seen tremendous progress, applications to excited states which couple strongly to few-body systems remains an open problem.