S-matrix informed neural networks

Wyatt A. Smith (LBNL, U. California Berkeley, William & Mary, Messina U., ExoHad postdoc), Arkaitz Rodas (ODU & JLab, co-PI), Marius D. Thomas (U. California Berkeley), César Fernández-Ramírez (UNED, co-PI), Giorgio Foti (Messina U., ExoHad PhD student), Lin Qiu (ODU, ExoHad postdoc), Adam P. Szczepaniak (Indiana U. & JLab, co-PI), and Alessandro Pilloni (Messina U. & INFN Catania, co-PI) from the Joint Physics Analysis Center studied low-energy pion scattering by replacing fixed parametrizations with S-matrix informed neural networks. By evaluating how these constrained networks respond to different experiments, they isolated a subset of data that agrees with first principles and extracted the properties of three light-meson resonances.

Physicists rely on scattering data to map the spectrum of hadrons and isolate the background for precision measurements. Analyzing that data usually requires guessing a mathematical shape for the amplitude. That guess biases the final result, especially for broad, short-lived states like the $\sigma/f_0(500)$. The bias compounds when the underlying measurements contradict each other, a frequent issue in historical pion scattering data. The neural-network approach breaks this dependence by letting the data determine the shape of the amplitude, while strictly enforcing unitarity, analyticity, and crossing symmetry.

The resulting model-independent amplitudes pin down the pole positions of the $\sigma/f_0(500)$, $\rho(770)$, and $f_0(980)$ resonances. They also predict the locations of the Adler zeros and determine the scattering lengths without chiral input. Because pions dominate the final states of many particle collisions, these clean amplitudes immediately improve the hadronic corrections needed for muon $g-2$ calculations and heavy-meson decay analyses. The same neural approach can now be applied to kaon and nucleon scattering.