Extraction of multiple exponential signals from lattice correlation functions

Abstract

We present a fast and simple algorithm that allows the extraction of multiple exponential signals from the temporal dependence of correlation functions evaluated on the lattice including the statistical fluctuations of each signal and treating properly backward signals. The basic steps of the method are the inversion of appropriate matrices and the determination of the roots of an appropriate polynomial, constructed using discretized derivatives of the correlation function. The method is tested strictly using fake data generated assuming a fixed number of exponential signals included in the correlation function with a controlled numerical precision and within given statistical fluctuations. All the exponential signals together with their statistical uncertainties are determined exactly by the algorithm. The only limiting factor is the numerical rounding off. In the case of correlation functions evaluated by large-scale QCD simulations on the lattice various sources of noise, other than the numerical rounding, can affect the correlation function and they represent the crucial factor limiting the number of exponential signals, related to the hadronic spectral decomposition of the correlation function, that can be properly extracted. The algorithm can be applied to a large variety of correlation functions typically encountered in QCD or QCD+QED simulations on the lattice, including the case of exponential signals corresponding to poles with arbitrary multiplicity and/or the case of oscillating signals. The method is able to to detect the specific structure of the multiple exponential signals without any a priori assumption and it determines accurately the ground-state signal without the need that the lattice temporal extension is large enough to allow the ground-state signal to be isolated.

arXiv comment45 pages, 9 figures, 13 tables; few references added and few minor points addressed; version to appear in PRD

References in corpus (14)

• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• Constrained Curve Fitting
• Decay width of light quark hybrid meson from the lattice
• Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD
• Leading isospin breaking effects on the lattice
• Electromagnetic and strong isospin-breaking corrections to the muon $g-2$ from Lattice QCD+QED
• First lattice calculation of the QED corrections to leptonic decay rates
• Light-meson leptonic decay rates in lattice QCD+QED
• Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions
• Isospin breaking effects due to the up-down mass difference in Lattice QCD
• High Statistics Analysis using Anisotropic Clover Lattices: (I) Single Hadron Correlation Functions
• The light-quark contribution to the leading HVP term of the muon $g-2$ from twisted-mass fermions
• Strange and charm HVP contributions to the muon ($g-2)$ including QED corrections with twisted-mass fermions
• Excited-State Effective Masses in Lattice QCD

Cited by in corpus (6)

• Ratio of kaon and pion leptonic decay constants with $N_f=2+1+1$ Wilson-clover twisted-mass fermions
• On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods
• On the equivalence of Prony and Lanczos methods for Euclidean correlation functions
• Automated label flows for excited states of correlation functions in lattice gauge theory
• Di-nucleons do not form bound states at heavy pion mass
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo