Search for CP Violation in the Phase Space of $$ {d}^0\to {k}_s^0{k}^{\pm }{\pi}^{\mp } $$ Decays with the Energy Test

A bstract A search for CP violation in $$ {D}^0\to {K}_S^0{K}^{+}{\pi}^{-} $$ D 0 → K S 0 K + π − and $$ {D}^0\to {K}_S^0{K}^{-}{\pi}^{+} $$ D 0 → K S 0 K − π + decays is reported. The search is performed using an unbinned model-independent method known as the energy test that probes local CP violation in the phase space of the decays. The data analysed correspond to an integrated luminosity of 5 . 4 fb − 1 collected in proton-proton collisions by the LHCb experiment at a centre-of-mass energy of $$ \sqrt{s} $$ s = 13 TeV, amounting to approximately 950 thousand and 620 thousand signal candidates for the $$ {D}^0\to {K}_S^0{K}^{-}{\pi}^{+} $$ D 0 → K S 0 K − π + and $$ {D}^0\to {K}_S^0{K}^{+}{\pi}^{-} $$ D 0 → K S 0 K + π − modes, respectively. The method is validated using D 0 → K − π + π − π + and $$ {D}^0\to {K}_S^0{\pi}^{+}{\pi}^{-} $$ D 0 → K S 0 π + π − decays, where CP -violating effects are expected to be negligible, and using background-enhanced regions of the signal decays. The results are consistent with CP symmetry in both the $$ {D}^0\to {K}_S^0{K}^{-}{\pi}^{+} $$ D 0 → K S 0 K − π + and the $$ {D}^0\to {K}_S^0{K}^{+}{\pi}^{-} $$ D 0 → K S 0 K + π − decays, with p -values for the hypothesis of no CP violation of 70% and 66%, respectively.