K_L to \pi^+ \pi^- e^+ e^-

Abstract

We calculate all of the form factors for the one-photon, $K_L\to {\pi }^{+}{\pi }^{-}{\gamma }^{\ast }\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ contribution to the $K_L\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ decay amplitude at leading order in chiral perturbation theory. These form factors depend on one unknown constant that is a linear combination of coefficients of local $\mathcal{O}(p^4)$ operators in the chiral lagrangian for weak radiative kaon decay. We determine the differential rate for $\text{K}$ and also the magnitude of two CP violating observables.

Comments: 20 pages, 11 uuencoded figures included, uses harvmac, epsf and tables