A dispersive study of final-state interactions in amplitudes

Véronique Bernard; Sébastien Descotes-Genon; Marc Knecht; Bachir Moussallam

doi:10.1140/epjc/s10052-024-13084-y

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 744
https://doi.org/10.1140/epjc/s10052-024-13084-y

Regular Article - Theoretical Physics

A dispersive study of final-state interactions in $K \to π π π$ $K\rightarrow \pi \pi \pi$ amplitudes

Véronique Bernard¹, Sébastien Descotes-Genon¹, Marc Knecht²^c and Bachir Moussallam¹

¹ Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405, Orsay, France
² Centre de Physique Théorique, CNRS/Aix-Marseille Univ./Univ. de Toulon (UMR7332), CNRS-Luminy Case 907, 13288, Marseille Cedex 9, France

^c knecht@cpt.univ-mrs.fr

Received: 4 April 2024
Accepted: 21 June 2024
Published online: 26 July 2024

Abstract

A system of dispersive representations of the Omnès–Khuri–Treiman–Sawyer–Wali type for the final-state interactions in the amplitudes of the $K \to π π π$ $K\rightarrow \pi \pi \pi$ weak transitions is constructed, under the assumptions that CP and isospin symmetries are conserved. Both the $Δ I = 1 / 2$ $\Delta I = 1/2$ and $Δ I = 3 / 2$ $\Delta I = 3/2$ transition channels are considered. The set of single-variable functions involved in these representations is identified, and the polynomial ambiguities in their definitions are discussed. Numerical solutions for the system of coupled integral relations satisfied by these functions are provided, and the determination of the subtraction constants in terms of the experimental information on the amplitudes in the decay region is addressed.

© The Author(s) 2024

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