$K\rightarrow \pi\pi e^+e^-$ decays and chiral low-energy constants

Abstract.

The branching ratios of the measured decay $K_{\mathrm{L}}\rightarrow \pi^+\pi^-e^+e^-$ and of the still unmeasured decay $K^+\rightarrow\pi^+\pi^0e^+e^-$ are calculated to next-to-leading order in chiral perturbation theory (CHPT). Recent experimental results are used to determine two possible values of the combination $(N^{\mathrm{r}}_{16}-N_{17})$ of weak low-energy couplings (LECs) from the $\cal{O}(p^4)$ chiral Lagrangian. The values obtained are compared to the predictions of theoretical approaches to weak counterterm couplings to distinguish between the two values. Using the favoured value of the combination $(N^{\mathrm{r}}_{16}-N_{17})$ and taking into account additional assumptions suggested by the considered models, one obtains the branching ratio of the second decay as a function of the unknown combination $(N^{\mathrm{r}}_{14}+2N^{\mathrm{r}}_{15})$ of weak low-energy couplings. Finally, using values of the individual LECs derived from a particular model, one predicts the branching ratio of the $K^+$ decay.