PINNing the pion: conformal deep learning for $F_π(s)$ and the $(g-2)_μ$ hadronic contribution
Extracting the pion electromagnetic form factor $F_π(s)$ 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 $F_π(s)$ directly from first principles across spacelike and timelike domains: charge normalisation and Schwarz reflection are enforced by construction, while Cauchy-Riemann analyticity, dispersion relations, Watson's theorem, and perturbative QCD asymptotics enter through the loss functional. Thus, the fundamental S-matrix principles dictate the form factor's behaviour while data act as constraints. Mapp...
| Authors | Mayank Goel, Subhadip Mitra, Monalisa Patra |
|---|---|
| Primary category | hep-ph |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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