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 in neutral<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>meson Cabibbo-suppressed three-body decays

Using $385\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ collision data collected at center-of-mass energies around 10.6 GeV, we search for time-integrated $CP$ violation in the Cabibbo-suppressed decays ${D}^{0}/{\overline{D}}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ and ${D}^{0}/{\overline{D}}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{\ensuremath{\pi}}^{0}$ with both model-independent and model-dependent methods. Measurements of the asymmetries in amplitudes of flavor states and $CP$ eigenstates provide constraints on theories beyond the standard model, some of which predict $CP$ violation in amplitudes at the 1% level or higher. We find no evidence of $CP$ violation and hence no conflict with the standard model.

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