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

TL;DR

This paper uses a dispersive approach to analyze rare kaon decays involving photons and leptons, improving upon chiral perturbation theory by including final-state interactions and avoiding off-shell ambiguities.

Contribution

It extends previous predictions by incorporating dispersive methods to account for final-state interactions in rare kaon decays, providing more accurate rate predictions.

Findings

Significant corrections to chiral perturbation theory predictions for leptonic decay rates.

Numerical solutions of dispersion relations yield decay rate predictions.

Analysis is free from off-shell extrapolation ambiguities.

Abstract

We analyse the rare kaon decays $K_S \to \gamma\gamma$ and $K_S \to \gamma\ell^+\ell^-$ $(\ell = e \mbox{ or } \mu)$ 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 $K_S \to \pi\pi$ and $\gamma\gamma^{(*)}\to\pi\pi$, we solve the once-subtracted dispersion relations numerically to predict the rates for $K_S \to \gamma\gamma$ and $K_S \to \gamma\ell^+\ell^-$. In the leptonic modes, we find sizeable corrections to the $\chi$PT$_3$ predictions for the integrated rates.