Abstract
In present work, we explore and experiment with an alternative approach to studying resonance properties in a finite volume. By analytic continuing the finite lattice size $L$ into a complex plane, the oscillating behavior of the finite volume Green's function is mapped onto an infinite volume Green's function that is corrected by exponentially decaying finite volume effect. The analytic continuation technique thus can be applied to study resonance properties directly in finite volume dynamical equations.
Highlights
The Dalitz plot is a powerful tool in particle physics to extract information from processes involving three-particle final states
Since many resonances emerge in few-hadron systems, the Dalitz plot plays an important role in the study of resonance dynamics from experimental data, e.g., the coupled-channel analysis of ρ and KÃ resonances dynamics in [8,9]
lattice quantum chromodynamics (LQCD) normally puts out discrete energy spectra of few-hadron systems, because of the finite volume inherent to the method, rather than reaction amplitudes, which are needed to generate the Dalitz plot
Summary
The Dalitz plot is a powerful tool in particle physics to extract information from processes involving three-particle final states. Two-step procedures seem like a compromise solution, and one may hope to have an ultimate formalism that grants the user direct access to infinitevolume reaction amplitudes from the LQCD energy levels, independently of interhadron interaction models. Deriving such relations beyond two-body systems poses great challenges. The model dependence of the interhadron potential can be assessed by how well it fits to the LQCD energy levels Scattering observables, such as the Dalitz plot, must be computed in a separate step.
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