Search for <i>CP</i> violation in the phase space of D<SUP>0</SUP><i>→</i> π<i><SUP>-</SUP></i>π<SUP>+</SUP>π<SUP>0</SUP> decays with the energy test

A search for CP violation in D ⁰ → π ⁻ π ⁺ π ⁰ decays is reported, using pp collision data collected by the LHCb experiment from 2015 to 2018 corresponding to an integrated luminosity of 6 fb ⁻¹. An unbinned model-independent approach provides sensitivity to local CP violation within the two-dimensional phase space of the decay. The method is validated using the Cabibbo-favoured channel D ⁰ → K ⁻ π ⁺ π ⁰ and background regions of the signal mode. The results are consistent with CP symmetry in this decay. [Figure not available: see fulltext.].