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Search for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>violation and a measurement of the relative branching fraction in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</…
We report on a search for the $CP$ asymmetry in the singly Cabibbo-suppressed decays ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{\ensuremath{\pi}}^{+}$ and in the resonant decays ${D}^{+}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}$ and ${D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{*0}{K}^{+}$ based on a data sample of $79.9\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ recorded by the BABAR detector. We use the Cabibbo-favored ${D}_{s}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{\ensuremath{\pi}}^{+}$ branching fraction as normalization in the measurements to …