Pole-Expansion of Two-Hadron Imaginary-Time Correlation Function -a new method of analysis for unstable states in lattice QCD-

TL;DR

This paper introduces a novel pole expansion method for analyzing two-hadron imaginary-time correlation functions in lattice QCD, enabling extraction of unstable state properties like masses and widths.

Contribution

The paper develops and validates a pole expansion technique using the Mittag-Leffler expansion and uniformization variables for analyzing unstable states in lattice QCD.

Findings

Pole expansion accurately describes the correlation functions for $ ho$ meson and $ ext{Lambda}(1405)$.

Explicit formulas for pole expansion are derived for single- and two-channel cases.

Method effectively extracts unstable state parameters from lattice QCD data.

Abstract

We analyze the pole expansion of the two-hadron imaginary-time correlation function. We first explain the general idea that the imaginary-time correlation function is expressed as a sum of the pole terms, the Mittag-Leffler expansion, in terms of the uniformization variable, which makes the S-matrix single-valued. We then derive explicit expressions of the pole expansion for the single-channel ($\rho$ meson) and two-channel ($\Lambda(1405)$) examples and demonstrate that the pole expansion actually holds employing phenomenological models, the vector-dominance model for the $\rho$ meson and the chiral unitary model for $\Lambda(1405)$. From this observation we propose the pole expansion as a method to extract information of unstable states such as masses and widths from the two-hadron imaginary-time correlation functions obtained by lattice QCD simulations.