Speaker
Description
Over the past several decades, lattice quantum chromodynamics (LQCD) has developed into a powerful non-
perturbative tool for extracting hadronic scattering amplitudes from first principles. The theoretical foundation
connecting finite-volume spectra to infinite-volume scattering observables was established by Luscher for two-body
elastic scattering and has since been extended to coupled two-body channels, nonzero boost, and, more recently,
three-body systems. Of particular phenomenological interest are resonances—such as the Roper excitation, the scalar
σ/f0(500), and the exotic Tcc—that couple strongly to both two- and three-body final states. Extracting resonance
parameters in such cases requires a unified, unitary framework for the coupled 2 ↔3 system.
Prior work on coupled two- and three-body systems has relied on a non-overlap condition on kinematic cutoff
functions, which enforces an artificial separation between the support of the two- and three-body cutoff functions.
While this condition simplifies certain algebraic steps, it introduces a non-analyticity directly in the kinematic region
of interest. This issue can be resolved by constructing a diagrammatic derivation of the finite-volume quantization
condition (QC) in which the two- and three-body cuts separate naturally, without any non-overlap constraint.
The present work develops the corresponding infinite-volume (IV) side of that construction. Our main result is a
set of coupled integral equations for the 2 and 3 body scattering amplitudes, derived directly from unitarity. We set up the notation, derive the K-matrix representation, and
obtain the coupled integral equations and their decomposed form; the constraint relating K-matrix
elements to one another is also derived there. Then we describe the connection between finite-volume QC and the pipeline from lattice spectra to scattering amplitudes.