Machine Learning Unveils the Power Law of Finite-Volume Energy Shifts

Abstract

Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations. However, it is a significant challenge for the system with long-range interactions. We employ symbolic regression to regress finite-volume extrapolation formula for both short-range and long-range interactions. The regressed formula still holds the exponential form with a factor $L^n$ in front of it. The power decreases with the decreasing range of the force. When the range of the force becomes sufficiently small, the power converges to $-1$, recovering the short-range formula as expected. Our work represents a significant advancement in leveraging machine learning to probe uncharted territories within particle physics.

13 pages, 6 figures

References in corpus (19)

• Structure and rotations of the Hoyle state
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Signature of a doubly charm tetraquark pole in $D{D}^{\ast }$ scattering on the lattice
• Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws
• Doubly Charmed Tetraquark $T_{cc}^{+}$ from Lattice QCD near Physical Point
• $T_{cc}^{+}(3875)$ relevant $D{D}^{\ast }$ scattering from $N_f=2$ lattice QCD
• Emergent geometry and duality in the carbon nucleus
• Wavefunction matching for solving quantum many-body problems
• Benchmark calculations for elastic fermion-dimer scattering
• Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ from finite volume energy levels
• Relativistic $N$-particle energy shift in finite volume
• Perturbative quantum Monte Carlo method for nuclear physics
• Properties of Nucleon Resonances by means of a Genetic Algorithm
• Two-particle scattering from finite-volume quantization conditions using the plane wave basis
• Structure Factors for Hot Neutron Matter from Ab Initio Lattice Simulations with High-Fidelity Chiral Interactions
• Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression
• Binding of the three-hadron $D{D}^{\ast }K$ system from the lattice effective field theory
• Rediscovery of Numerical Lüscher's Formula from the Neural Network