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arXiv · 2505.02878

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

Wren Yamada·Osamu Morimatsu·Toru Sato·Koichi Yazaki
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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.

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Wren Yamada, Osamu Morimatsu, Toru Sato, Koichi Yazaki. 2025-05-05. Pole-Expansion of Two-Hadron Imaginary-Time Correlation Function -a new method of analysis for unstable states in lattice QCD-. https://arxiv.org/abs/2505.02878

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