PINNing the pion: conformal deep learning for $F_\pi(s)$ and the $(g-2)_\mu$ hadronic contribution

Excerpt

arXiv:2609.40008v1 Announce Type: cross Abstract: Extracting the pion electromagnetic form factor $F_{\pi}(s)$ through phenomenological curve-fitting models introduces model dependence, unphysical artefacts, and kinematic inconsistencies. We introduce a Physics-Informed Neural Network (PINN) embedded in a conformal $z$-plane that constructs $F_{\pi}(s)$ directly from first principles across spacelike and timelike domains: charge normalisation and Schwarz reflection are enforced by construction,