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New Measurement of the Properties of the Rare Decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>→</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:mrow><mml:…
A low-background sample of 10 300 events has been collected for the decay mode ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{e}^{+}{e}^{\ensuremath{-}}$ by experiment E865 at the Brookhaven Alternating Gradient Synchrotron. The branching ratio is measured to be $[2.94\ifmmode\pm\else\textpm\fi{}0.05(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.13(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.05(\mathrm{model})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$, the vector nature of this decay is firmly established, and the decay form factor $f(z){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}f}_{0}(1+\ensuremath{\delta}z)({z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}M}_{\mathrm{ee}}^{2}{/m}_{K}^{2})$ is determined to …