Bayesian Analysis and Analytic Continuation of Scattering Amplitudes from Lattice QCD

TL;DR

This paper introduces a Bayesian and analytic continuation method for analyzing lattice QCD spectra to extract multi-hadron scattering amplitudes at real and complex energies, improving the understanding of resonant systems.

Contribution

It combines Bayesian reconstruction with Nevanlinna interpolation for a non-parametric analysis of scattering amplitudes, accounting for uncertainties and parametrization dependence.

Findings

Successfully applied to toy and real lattice-QCD data

Provides constraints on multi-hadron scattering amplitudes

Demonstrates effectiveness in resonant systems

Abstract

We present a novel procedure for analyzing the lattice-QCD spectrum via the finite-volume formalism to obtain constraints on multi-hadron scattering amplitudes at both real and complex energies. This approach combines a Bayesian reconstruction of the scattering amplitude on the real axis with Nevanlinna interpolation for analytic continuation to complex-valued energies. The method is non-parametric, inherently accounting for parametrization dependence within the uncertainty. We demonstrate the applicability of this approach using both toy data and real lattice-QCD data in resonant systems from the HadSpec and BaSc collaborations.