Dispersive analysis of the $\boldsymbol{ϕ\to γπ^0 π^0}$ process
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arXiv
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| Format: | Preprint |
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2026
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| author | Hoid, Bai-Long Danilkin, Igor Vanderhaeghen, Marc |
| author_facet | Hoid, Bai-Long Danilkin, Igor Vanderhaeghen, Marc |
| contents | We present an analysis of the radiative decay $ϕ\to γπ^0 π^0$ in a dispersive framework, where the two-pion subsystem undergoes strong final-state interactions that cover the $f_0(500)$ and $f_0(980)$ regions. We employ a coupled-channel Muskhelishvili-Omnès framework that allows for a consistent treatment of two scalar resonances and crossed-channel singularities induced by the Born and vector-meson exchanges. We explicitly verify the equivalence between the modified and standard Muskhelishvili-Omnès representations for vector-meson pole contributions when the isoscalar Omnès matrix is chosen asymptotically bounded, and we adopt the standard representation in decay kinematics. This yields, for the first time, a parameter-free dispersive prediction for the kaon Born rescattering, which provides a dominant contribution. To obtain a good fit to the KLOE and SND data, we employ a once-subtracted coupled-channel dispersion relation with heavier left-hand cut contributions and two unknown subtraction constants. The results demonstrate the consistency among the data for $ππ$ scattering, $γγ$ fusion, and $ϕ$ radiative decay, thereby validating the underlying dispersive formalism and the input used for the hadronic Omnès matrix and left-hand cuts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_15100 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dispersive analysis of the $\boldsymbol{ϕ\to γπ^0 π^0}$ process Hoid, Bai-Long Danilkin, Igor Vanderhaeghen, Marc High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Theory We present an analysis of the radiative decay $ϕ\to γπ^0 π^0$ in a dispersive framework, where the two-pion subsystem undergoes strong final-state interactions that cover the $f_0(500)$ and $f_0(980)$ regions. We employ a coupled-channel Muskhelishvili-Omnès framework that allows for a consistent treatment of two scalar resonances and crossed-channel singularities induced by the Born and vector-meson exchanges. We explicitly verify the equivalence between the modified and standard Muskhelishvili-Omnès representations for vector-meson pole contributions when the isoscalar Omnès matrix is chosen asymptotically bounded, and we adopt the standard representation in decay kinematics. This yields, for the first time, a parameter-free dispersive prediction for the kaon Born rescattering, which provides a dominant contribution. To obtain a good fit to the KLOE and SND data, we employ a once-subtracted coupled-channel dispersion relation with heavier left-hand cut contributions and two unknown subtraction constants. The results demonstrate the consistency among the data for $ππ$ scattering, $γγ$ fusion, and $ϕ$ radiative decay, thereby validating the underlying dispersive formalism and the input used for the hadronic Omnès matrix and left-hand cuts. |
| title | Dispersive analysis of the $\boldsymbol{ϕ\to γπ^0 π^0}$ process |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2602.15100 |