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Pole-expansion of two-hadron imaginary-time correlation function: A new analysis method for unstable states in lattice QCD

Wren Yamada1,*, Osamu Morimatsu2,†, Toru Sato3,‡, and Koichi Yazaki1,§

  • *Contact author: rento.yamada@riken.jp
  • †Contact author: osamu@post.kek.jp
  • ‡Contact author: tsato@rcnp.osaka-u.ac.jp
  • §Contact author: koichiyzk@yahoo.co.jp
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Phys. Rev. D 112, 034040 – Published 29 August, 2025

DOI: https://doi.org/10.1103/yjz9-9d8y

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 (ρ meson) and two-channel [Λ(1405)] examples and demonstrate that the pole expansion actually holds employing phenomenological models, the vector-dominance model for the ρ meson and the chiral unitary model for Λ(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 quantum chromodynamics (QCD) simulations.

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Phys. Rev. D 112, 034040– Published 29 August, 2025
  • Received 13 May 2025
  • Accepted 28 July 2025
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