Dispersive treatment of and

Gilberto Colangelo; Ramon Stucki; Lewis C. Tunstall

doi:10.1140/epjc/s10052-016-4449-2

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2016) 76: 604
https://doi.org/10.1140/epjc/s10052-016-4449-2

Regular Article - Theoretical Physics

Dispersive treatment of $K_S\rightarrow \gamma \gamma$ and $K_S\rightarrow \gamma \ell ^+\ell ^-$

Gilberto Colangelo, Ramon Stucki and Lewis C. Tunstall^*

Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

^* e-mail: tunstall@itp.unibe.ch

Received: 19 September 2016
Accepted: 19 October 2016
Published online: 5 November 2016

Abstract

We analyse the rare kaon decays $K_S \rightarrow \gamma \gamma$ and $K_S \rightarrow \gamma \ell ^+\ell ^-$ $(\ell = e \text{ or } \mu )$ in a dispersive framework in which the weak Hamiltonian carries momentum. Our analysis extends predictions from lowest order $SU(3)_L\times SU(3)_R$ chiral perturbation theory ( $\chi$ PT $$_3$$ ) to fully account for effects from final-state interactions, and is free from ambiguities associated with extrapolating the kaon off-shell. Given input from $K_S \rightarrow \pi \pi$ and $\gamma \gamma ^{(*)}\rightarrow \pi \pi$ , we solve the once-subtracted dispersion relations numerically to predict the rates for $K_S \rightarrow \gamma \gamma$ and $K_S \rightarrow \gamma \ell ^+\ell ^-$ . In the leptonic modes, we find sizeable corrections to the $\chi$ PT $$_3$$ predictions for the integrated rates.