Search for CP violation in the phase space of D⁰ → K⁰_SK^±π^∓ decays with the energy test

A search for CP violation in D⁰ → K⁰_SK⁺π⁻ and D⁰ → K⁰_SK⁻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 √s = 13 TeV, amounting to approximately 950 thousand and 620 thousand signal candidates for the D⁰ → K⁰_SK⁻π⁺ and D⁰ → K⁰_SK⁺π⁻ modes, respectively. The method is validated using D⁰ → K⁻π⁺π⁻π⁺ and D⁰ → K⁰_Sπ⁺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 D⁰ → K⁰_SK⁻π⁺ and the D⁰ → K⁰_SK⁺π⁻ decays, with p-values for the hypothesis of no CP violation of 70% and 66%, respectively.