Study of theKL0→π+π−γDirect Emission Vertex

We have perfomed studies of the $K_L^0\to {\pi }^{+}{\pi }^{-}\gamma$ direct emission ( $\mathrm{DE}$) and inner Bremsstrahlung ( $\mathrm{IB}$) vertices, based on data collected by KTeV during the 1996 Fermilab fixed target run. We find $a_1/a_2=-0.737\mathrm{}\pm 0.034{\mathrm{GeV}}^2$ for the $\mathrm{DE}$ form-factor parameter in the $\rho$-propagator parametrization, and report on fits of the form factor to linear and quadratic functions as well. We concurrently measure $\Gamma (K_L^0\to {\pi }^{+}{\pi }^{-}\gamma {,E}_{\gamma }^{*}>20\mathrm{}\mathrm{MeV})/\Gamma (K_L^0\to {\pi }^{+}{\pi }^{-})=(20.8\pm 0.3)\times {10}^{-3\mathrm{}}$, and a $K_L^0\to {\pi }^{+}{\pi }^{-}\gamma$ $\mathrm{DE}/(\mathrm{DE}+\mathrm{IB})$ branching ratio of $0.683\pm 0.011$.