Speaker
Description
A description of the two form factor $W_+$, $W_S$, associated with the radiative decays of the $K^+$ and the $K_S$, based on general properties of analyticity and unitarity is proposed. Starting from the simple consideration of the asymptotic behaviour of the two combinations $2W_+ - W_S$ and $W_+ + W_S$ we derive a dispersive representation involving only two parameters. Using the rich experimental information of the $K \to 3\pi$ amplitudes, extended beyond the low energy region using the Khuri-Treiman formalism, we show that the sign of the the $W_+$ form factor is unambiguously determined and its energy dependence is well reproduced. We also show that the yet unknown $\Delta{I}=1/2$ part of the $K_S \to \pi^+ \pi^- \pi^0$ can be determined from the value of $W_+(0)+W_S(0)$. The possibility of fixing the sign of $W_S$ from experiment is discussed.
