Date of Award

Fall 12-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Program/Concentration

Physics

Committee Director

Raúl A. Briceño

Committee Director

Arkaitz Rodas

Committee Member

Alex Gurevich

Committee Member

Lawrence Weinstein

Committee Member

Sachin Shetty

Abstract

In this dissertation, we develop and apply a relativistic framework for studying three-body scattering amplitudes, their analytic structure, and the emergence of universal phenomena such as the Efimov effect. The work integrates three complementary components.

First, we introduce a systematically improvable numerical method for solving relativistic three-body integral equations in momentum space. By discretizing the continuum problem into finite matrix equations and extrapolating to the continuum limit, we obtain stable partial-wave amplitudes in the presence of a two-body bound state. Two complementary treatments of the pole contribution are implemented and shown to reproduce previous finite volume results, with controlled estimates of systematic uncertainties.

Second, we provide a general prescription for analytically continuing these integral equations into the complex energy plane. Using contour-deformation techniques guided by the singularity structure of the kernel, we compute amplitudes below elastic thresholds and on multiple Riemann sheets. This allows us to determine three-body bound and virtual states consistent with earlier finite-volume studies, and to identify departures from the standard two-body finite-volume formalism due to left-hand cuts.

Finally, we apply this framework to study Efimov physics in a fully relativistic setting. By tuning the interaction toward unitarity, we observe the characteristic discrete scaling symmetry of Efimov trimers and recover the expected geometric energy pattern. Tracking trimer poles across physical and unphysical Riemann sheets, we reveal rich trajectories connecting virtual states, bound states, and resonances. We also uncover cyclic behavior of higher Efimov resonances and propose a partial resolution to the associated “missing states” puzzle in terms of the multi-sheeted structure induced by the logarithmic three-body unitarity cut.

Overall, this work establishes a coherent relativistic approach to the three-body problem, clarifies its analytic structure, and demonstrates its ability to capture universal features relevant to nuclear, hadronic, and atomic few-body systems.

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DOI

10.25777/5fmr-xk29

ISBN

9798276039626

ORCID

0000-0003-2163-2026

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