Machine Learning Unveils Finite-volume Energy Shifts in Three-body System
Abstract
Finite-volume extrapolation (FVE) is essential for extracting physical observables in the lattice calculation. While rigorous FVE formulations are well established for short-range potentials in both two- and three-body systems, long-range interactions with force ranges comparable to the lattice size L remain challenging. Extending a previous data-driven scheme for two-body systems, we apply symbolic regression (PySR) to uncover universal three-body FVE formulae. For short-range potentials, we reproduce the two limiting cases, i.e. κ3≫κ2 and κ3∼κ2. For pure long-range potentials, we obtain a dedicated analytic expression, and after incorporating short-range contributions, we uncover a unified formula consistent with the original PySR solution, which performs excellently in the intermediate force range around 1 fm. This work demonstrates that combining machine learning with physical constraints can yield novel analytical results inaccessible to conventional theoretical tools, advancing data-driven methodologies in hadron physics.
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BibTeX
@misc{zhang2026machine,
title = {{Machine Learning Unveils Finite-volume Energy Shifts in Three-body System}},
author = {Wei-Jie Zhang and Zhenyu Zhang and Jifeng Hu and Bing-Nan Lu and Jin-Yi Pang and Qian Wang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28700},
eprint = {2608.28700},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28700},
}
RIS
TY - UNPB
TI - Machine Learning Unveils Finite-volume Energy Shifts in Three-body System
AU - Wei-Jie Zhang
AU - Zhenyu Zhang
AU - Jifeng Hu
AU - Bing-Nan Lu
AU - Jin-Yi Pang
AU - Qian Wang
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.28700
UR - https://arxiv.org/abs/2608.28700
AB - Finite-volume extrapolation (FVE) is essential for extracting physical observables in the lattice calculation. While rigorous FVE formulations are well established for short-range potentials in both two- and three-body systems, long-range interactions with force ranges comparable to the lattice size L remain challenging. Extending a previous data-driven scheme for two-body systems, we apply symbolic regression (PySR) to uncover universal three-body FVE formulae. For short-range potentials, we reproduce the two limiting cases, i.e. κ_3≫κ_2 and κ_3∼κ_2. For pure long-range potentials, we obtain a dedicated analytic expression, and after incorporating short-range contributions, we uncover a unified formula consistent with the original PySR solution, which performs excellently in the intermediate force range around 1 fm. This work demonstrates that combining machine learning with physical constraints can yield novel analytical results inaccessible to conventional theoretical tools, advancing data-driven methodologies in hadron physics.
ER -