Measurement of direct photon emission in theKL→π+π−γdecay mode

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Abstract

In this paper the KTeV collaboration reports the analysis of $112.1\ifmmode\times\else\texttimes\fi{}{10}^{3}$ candidate ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ decays including a background of $671\ifmmode\pm\else\textpm\fi{}41$ events with the objective of determining the photon production mechanisms intrinsic to the decay process. These decays have been analyzed to extract the relative contributions of the $CP$ violating bremsstrahlung process and the $CP$ conserving M1 and $CP$ violating E1 direct photon emission processes. The M1 direct photon emission amplitude and its associated vector form factor parameterized as $|{\stackrel{\texttildelow{}}{g}}_{M1}|(1+\frac{{a}_{1}/{a}_{2}}{({M}_{\ensuremath{\rho}}^{2}\ensuremath{-}{M}_{K}^{2})+2{M}_{K}{E}_{\ensuremath{\gamma}}})$ have been measured to be $|{\stackrel{\texttildelow{}}{g}}_{M1}|=1.198\ifmmode\pm\else\textpm\fi{}0.035(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.086(\mathrm{syst})$ and ${a}_{1}/{a}_{2}=\ensuremath{-}0.738\ifmmode\pm\else\textpm\fi{}0.007(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.018(\mathrm{syst})\text{ }\text{ }{\mathrm{GeV}}^{2}/{c}^{2}$ respectively. An upper limit for the $CP$ violating E1 direct emission amplitude $|{g}_{E1}|\ensuremath{\le}0.21$ (90%CL) has been found. The overall ratio of direct photon emission (DE) to total photon emission including the bremsstrahlung process (IB) has been determined to be $\mathrm{DE}/(\mathrm{DE}+\mathrm{IB})=0.689\ifmmode\pm\else\textpm\fi{}0.021$ for ${E}_{\ensuremath{\gamma}}\ensuremath{\ge}20\text{ }\text{ }\mathrm{MeV}$.

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