K_L to π^+ π^- e^+ e^-

We calculate all of the form factors for the one-photon, $K_L \rightarrow π^+ π^- γ^* \rightarrow π^+ π^- e^+e^-$ contribution to the $K_L \rightarrow π^+ π^- e^+e^-$ 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.

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