DISSERTATION DEFENSE
"Relativistic Three-Particle Scattering"
Md Habib E Islam (Digonto)
Old Dominion University
OCNPS 304 Physics Conference Room
November 18, 2025
1:00 pm – 3:00 pm
Abstract:
Three-hadron interactions play a central role in both conventional and exotic sectors of nuclear physics. Even long-studied states such as the Roper resonance, 𝑁∗(1440), require a proper treatment of their dominant three-body decay modes to uncover their internal structure, while many recently discovered exotic candidates involve multi-particle final states that cannot be fully understood within two-body dynamics alone. Lattice QCD (LQCD) provides a first-principles framework for studying such systems directly from quarks and gluons, but the theoretical and numerical tools needed to interpret three-body effects from finite-volume spectra are still being developed. My dissertation advances this program by constructing and solving relativistic three-body integral equations that connect LQCD spectra and phenomenological models to infinite-volume scattering amplitudes.
In this talk, I will present a systematically improvable numerical framework for solving the relativistic three-body integral equations in momentum space, including the consistent treatment of two-body bound-state poles and the extraction of stable partial-wave amplitudes. I will then describe a general prescription for analytically continuing the three-body amplitude into the complex energy plane using contour-deformation techniques tailored to the kernel’s singularity structure. This enables us to locate three-body bound, virtual, and resonant states on multiple Riemann sheets and to track their trajectories across thresholds. Using a toy model of three identical scalar bosons coupled by exchange interactions, I demonstrate the emergence of Efimov-like trimers and their evolution from bound states to virtual states and resonances, revealing universal scaling behavior expected from Efimov physics. Together, these results establish a coherent relativistic framework for three-body scattering that is directly relevant to ongoing studies of exotic hadrons, low-energy nuclear systems, and cold-atom few-body phenomena.