φ → 3π and φπ⁰ transition form factor from Khuri-Treiman equations

This work studies the φ → 3π decay and the φ → π⁰ γ^ transition form factor, utilizing the Khuri-Treiman formalism to account for analyticity, crossing, and unitarity. Using once-subtracted dispersion relations, we perform a simultaneous fit to the φ → 3π Dalitz plot distribution and the φ → π⁰ γ^ measurements from the KLOE collaboration, finding good agreement with these experimental data. These results reaffirm the applicability of the Khuri-Treiman approach in the analysis of three-body decays. An interesting result is that the subtraction constant appearing in the equations is similar to a sum rule expectation, in contrast to analogous studies of ω → 3π decays and ω → π⁰ γ^, which shows significant deviations. Our results also provide a reasonable description of the trend of the transition form factor data from BaBar in the e⁺e⁻→φπ⁰ scattering region. These intriguing theoretical differences between the decays of φ and ω could encourage further experimental measurements to assess the discrepancies and refine the theoretical predictions.