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

Abstract

We analyse the rare kaon decays $K_S\to \gamma \gamma$ and $K_S\to \gamma {\ell }^{+}{\ell }^{-}$ $(\ell = e \mbox{ or } μ)$ 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 $\gamma {\gamma }^{(\ast )}\to \pi \pi$, 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.

arXiv comment12 pages, 9 figures. v2: Improved assessment of systematic uncertainties, some typos corrected, matches published version

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• $K\to {\mu }^{+}{\mu }^{-}$ as a clean probe of short-distance physics
• Beyond the Standard Model prospects for kaon physics at future experiments
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$