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

Abstract

We calculate all of the form factors for the one-photon, $K_L \rightarrow \pi^+ \pi^- \gamma^* \rightarrow \pi^+ \pi^- e^+e^-$ contribution to the $K_L \rightarrow \pi^+ \pi^- e^+e^-$ 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 ${\cal O}(p^4)$ operators in the chiral lagrangian for weak radiative kaon decay. We determine the differential rate for $\K$ and also the magnitude of two CP violating observables.