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arXiv · 2608.28700

Machine Learning Unveils Finite-volume Energy Shifts in Three-body System

Wei-Jie Zhang·Zhenyu Zhang·Jifeng Hu·Bing-Nan Lu·Jin-Yi Pang·Qian Wang
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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. $\kappa_3\gg\kappa_2$ and $\kappa_3\sim\kappa_2$. 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.

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Wei-Jie Zhang, Zhenyu Zhang, Jifeng Hu, Bing-Nan Lu, Jin-Yi Pang, Qian Wang. 2026-08-27. Machine Learning Unveils Finite-volume Energy Shifts in Three-body System. https://arxiv.org/abs/2608.28700

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