Neuro-dispersive extractions of light-meson resonances
We present the first dispersive extraction of resonant poles from analytically continued neural networks. We use S-matrix informed neural networks (SINNs) trained to respect unitarity, analyticity, and crossing symmetry, without fixing a specific amplitude parametrization. The SINN framework controls representation dependence, enables constrained data selection, and enforces first principles. A large ensemble of networks trained on $\pi\pi$ scattering data propagates correlated uncertainties to all derived observables. We obtain robust determinations of the $\sigma/f_0(500)$, $\rho(770)$, and $f_0(980)$ poles of $\pi\pi$ scattering. Scattering lengths are determined alongside the amplitudes, while Adler zeroes emerge as predictions of the analytic structure. The results are stable against variations of the network architecture, and our approach can easily be adjusted for analysis of other reactions relevant to New Physics searches.