Nevanlinna-Pick interpolation from uncertain data

Abstract

The calculation of inclusive processes that involve the production of many particles is a challenge for lattice QCD, a Euclidean-space method that is far removed from real-time, multiparticle production. A new approach to this problem based on Nevanlinna-Pick interpolation has been proposed by Bergamaschi et al. Here we extend their method by exploring the propagation of the statistical and systematic errors that accompany a lattice QCD calculation through this interpolation process. A simplified example of a multiparticle spectral function is studied with a focus on the possible applications of these methods to the calculation of inclusive heavy-particle decays.

42 pages, 10 figures, updated to match PRD version

References in corpus (14)

• Nevanlinna Analytical Continuation
• From deep inelastic scattering to heavy-flavor semi-leptonic decays: Total rates into multi-hadron final states from lattice QCD
• Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
• On the extraction of spectral densities from lattice correlators
• Reconstructing QCD Spectral Functions with Gaussian Processes
• Scattering amplitudes from finite-volume spectral functions
• Reconstruction of smeared spectral function from Euclidean correlation functions
• Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics
• Approaches to inclusive semileptonic $B_{(s)}$-meson decays from Lattice QCD
• Inverse problems, real-time dynamics and lattice simulations
• Bayesian inference of real-time dynamics from lattice QCD
• Minimal pole representation and analytic continuation of matrix-valued correlation functions
• Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation
• TRIQS/Nevanlinna: Implementation of the Nevanlinna Analytic Continuation method for noise-free data