On the equivalence of left-hand-cut and three-body formalisms
Abstract
The "left-hand cut problem" in lattice QCD arises when exchange singularities invalidate standard relations used to extract scattering amplitudes from the finite-volume spectrum. In recent years, several approaches were proposed to resolve this problem. We establish analytically and verify numerically the equivalence between the three-body approach proposed in [JHEP 06 (2024) 051] and the two-body left-hand cut formalism developed in [JHEP 08 (2024) 075]. We test the equivalence in a scalar model describing a particle scattering from an S-wave two-particle bound state through one-particle exchange. Both approaches reproduce the same infinite-volume particle--bound-state amplitude and correctly encode the associated left-hand cut in the finite-volume spectrum. Crucially, we identify that the exponentially suppressed finite-volume effects neglected in both formalisms can be numerically large, compromising amplitude extraction at small lattice volumes.
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BibTeX
@misc{baiaoraposo2026equivalence,
title = {{On the equivalence of left-hand-cut and three-body formalisms}},
author = {André Baião-Raposo and Raul Briceño and Sebastian M. Dawid},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02840},
eprint = {2609.02840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02840},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the equivalence of left-hand-cut and three-body formalisms
AU - André Baião-Raposo
AU - Raul Briceño
AU - Sebastian M. Dawid
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02840
UR - https://arxiv.org/abs/2609.02840
AB - The "left-hand cut problem" in lattice QCD arises when exchange singularities invalidate standard relations used to extract scattering amplitudes from the finite-volume spectrum. In recent years, several approaches were proposed to resolve this problem. We establish analytically and verify numerically the equivalence between the three-body approach proposed in [JHEP 06 (2024) 051] and the two-body left-hand cut formalism developed in [JHEP 08 (2024) 075]. We test the equivalence in a scalar model describing a particle scattering from an S-wave two-particle bound state through one-particle exchange. Both approaches reproduce the same infinite-volume particle--bound-state amplitude and correctly encode the associated left-hand cut in the finite-volume spectrum. Crucially, we identify that the exponentially suppressed finite-volume effects neglected in both formalisms can be numerically large, compromising amplitude extraction at small lattice volumes.
ER -