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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.17316 |
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| _version_ | 1866918380481544192 |
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| author | Bernard, Véronique Descotes-Genon, Sébastien Knecht, Marc Moussallam, Bachir |
| author_facet | Bernard, Véronique Descotes-Genon, Sébastien Knecht, Marc Moussallam, Bachir |
| contents | We reconsider the constraints on the form factors $W_+ (s)$ and $W_S (s)$, describing the radiative decay modes $K^+\toπ^+ \ell^+\ell^-$ and $K_S\toπ^0 \ell^+\ell^-$, associated with the general properties of analyticity and unitarity. Starting from the simple consideration of the asymptotic behaviours of the two combinations $2 W_+ (s) - W_S (s)$ and $W_+ (s) + W_S (s)$, we derive a minimal pair of dispersive representations which involves only two free parameters. An important input for these representations consists of the $K\to3π$ decay amplitudes, for which we use a set of solutions of the Khuri-Treiman equations obtained recently. These solutions provide an extrapolation from the physical $K\to3π$ decay region up to the resonant $Kπ\toππ$ scattering regions. We show that the experimental energy dependence of $|W_+|^2$ can be well reproduced and that the sign of $W_+$ is unambiguously determined. We also show that the yet unknown $Δ{I}=1/2$ part of the $K_S\to π^+ π^- π^0$ amplitude can be determined from the value of $W_+(0) + W_S(0)$. The possibility of fixing the sign of $W_S(0)$ using experimental data on both $|W_+|^2$ and $|W_S|^2$ is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A dispersive approach to the CP conserving $K\toπ\ell^+\ell^-$ radiative decays Bernard, Véronique Descotes-Genon, Sébastien Knecht, Marc Moussallam, Bachir High Energy Physics - Phenomenology We reconsider the constraints on the form factors $W_+ (s)$ and $W_S (s)$, describing the radiative decay modes $K^+\toπ^+ \ell^+\ell^-$ and $K_S\toπ^0 \ell^+\ell^-$, associated with the general properties of analyticity and unitarity. Starting from the simple consideration of the asymptotic behaviours of the two combinations $2 W_+ (s) - W_S (s)$ and $W_+ (s) + W_S (s)$, we derive a minimal pair of dispersive representations which involves only two free parameters. An important input for these representations consists of the $K\to3π$ decay amplitudes, for which we use a set of solutions of the Khuri-Treiman equations obtained recently. These solutions provide an extrapolation from the physical $K\to3π$ decay region up to the resonant $Kπ\toππ$ scattering regions. We show that the experimental energy dependence of $|W_+|^2$ can be well reproduced and that the sign of $W_+$ is unambiguously determined. We also show that the yet unknown $Δ{I}=1/2$ part of the $K_S\to π^+ π^- π^0$ amplitude can be determined from the value of $W_+(0) + W_S(0)$. The possibility of fixing the sign of $W_S(0)$ using experimental data on both $|W_+|^2$ and $|W_S|^2$ is discussed. |
| title | A dispersive approach to the CP conserving $K\toπ\ell^+\ell^-$ radiative decays |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2510.17316 |