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A sample of $4.687\times 10^6$ fully reconstructed $K^\pm\to\pi^\pm\pi^0_D$, $\pi^0_D\to\gamma e^+e^-$ decay candidates in the kinematic range $m_{ee}>10~{\rm MeV}/c^2$ with a negligible background contamination collected by the NA48/2 experiment at CERN in 2003-04 is analysed to search for the dark photon ($A'$) via the decay chain $K^\pm\to\pi^\pm\pi^0$, $\pi^0\to\gamma A'$, $A'\to e^+e^-$.
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