This work studies the $\varphi \to 3\pi$ decay and the $\varphi \to {\pi }^0{\gamma }^{*}$ 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 $\varphi \to 3\pi$ Dalitz plot distribution and the $\varphi \to {\pi }^0{\gamma }^{*}$ 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 $\omega \to 3\pi$ decays and $\omega \to {\pi }^0{\gamma }^{*}$, which shows significant deviations. Our results also provide a reasonable description of the trend of the transition form factor data from BABAR in the $e^{+}{e}^{-}\to \varphi {\pi }^0$ scattering region. These intriguing theoretical differences between the decays of $\varphi$ and $\omega$ could encourage further experimental measurements to assess the discrepancies and refine the theoretical predictions.

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• Chiral perturbation theory
• Form factors
• Particle interactions
• Phase shift
• QCD phenomenology
• Quantum chromodynamics