S-matrix informed neural networks for amplitude analysis
hep-ph, cs.LG, nucl-th
Submitted: 2026-08-24
Updated: 2026-08-24
Comments: 29 pages, 23 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: Reconstructing scattering amplitudes from finite, noisy, and mutually inconsistent measurements is an ill-posed inverse problem common to many reactions relevant to particle physics.
Terminology
Abstract
Reconstructing scattering amplitudes from finite, noisy, and mutually inconsistent measurements is an ill-posed inverse problem common to many reactions relevant to particle physics. We introduce S-matrix informed neural networks (SINNs), and demonstrate their ability to learn scattering amplitudes directly from data while respecting first principles. We further develop a novel data selection procedure, which uses the response of constrained neural network ensembles to identify a set of experiments compatible with first principles, and with each other. We apply this framework to ππ scattering, producing reusable amplitudes and correlated uncertainties without relying on a fixed functional form. We validate our results against residual model dependencies and training biases through closure tests and ablations. We find negligible impact of model architecture on our results. Our workflow unifies physics-constrained representation learning, data selection, and uncertainty quantification. Our strategy is transferable to other scattering processes, and other constrained physics problems limited by inconsistent data.
Sources
- Precise Measurement of the e+ e- --> pi+ pi- (gamma) Cross Section with the Initial-State Radiation Method at BABAR
- Combination of KLOE $\sigma\big(e^+e^-\rightarrow\pi^+\pi^-\gamma(\gamma)\big)$ measurements and determination of $a_{\mu}^{\pi^+\pi^-}$ in the energy range $0.10 < s < 0.95$ GeV$^2$
- Two-pion contribution to hadronic vacuum polarization
- The anomalous magnetic moment of the muon in the Standard Model
- Dispersion relation for hadronic light-by-light scattering: two-pion contributions
- Observation of several sources of $CP$ violation in $B^+ \to \pi^+ \pi^+ \pi^-$ decays
- Dispersive $\pi\pi\rightarrow K\bar K$ amplitude and giant CP violation in B to three light-meson decays at LHCb
- The inverse amplitude method in Chiral Perturbation Theory
- Bethe-Salpeter Approach for Unitarized Chiral Perturbation Theory
- Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the \sigma, f_0(980), a_0(980) Scalar Mesons
- Meson-Meson interaction in a non-perturbative chiral approach
- N/D Description of Two Meson Amplitudes and Chiral Symmetry
- Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
- Light scalars as tetraquarks or two-meson states from large Nc and unitarized Chiral Perturbation Theory
- Elimination of ambiguities in pion-pion phase shifts using crossing symmetry
- Experimental status of the $\pi\pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
- Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
- Study for a model-independent pole determination of overlapping resonances
- Novel approaches in Hadron Spectroscopy
- Scattering Theory
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