Three-pion Decay \(V→ π ⁺π ⁻π ⁰\) and \(V→ π ⁰γ *\) Transition Form Factors (\(V=ω ,φ ,J/ψ \)) with Khuri–Treiman Equations

We study the three-pion decays of vector mesons, \(V→ π ⁺π ⁻π ⁰\) (\(V=ω ,φ ,J/ψ \)), within the framework of Khuri–Treiman to account for analyticity, unitarity, and crossing symmetry. Using once-subtracted dispersion relations, we perform a simultaneous analysis of the \(ω ,φ → 3π \) Dalitz plot and of the \(ω /φ → π ⁰γ *\) transition form factor measurements finding good agreement with these experimental data. We also analyze the di-pion invariant mass distributions of the vector charmonium decay \(J/ψ → 3π \) experimental data, and predict the \(J/ψ → π ⁰γ *\) form factor. Abstract Published by the Jagiellonian University 2026 authors