Search for $\text{CP}$ violation in the phase space of $D^0\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp }$ decays with the energy test

Abstract

A search for $\text{CP}$ violation in $D^0\to K_S^0{K}^{+}\ddot{I}{€}^{-}$ and $D^0\to K_S^0{K}^{-}\ddot{I}{€}^{+}$ decays is reported. The search is performed using an unbinned model-independent method known as the energy test that probes local $\text{CP}$ 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 $\sqrt{s}=13$~TeV, amounting to approximately 950 thousand and 620 thousand signal candidates for the $D^0\to K_S^0{K}^{-}\ddot{I}{€}^{+}$ and $D^0\to K_S^0{K}^{+}\ddot{I}{€}^{-}$ modes, respectively. The method is validated using $D^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}$ and $D^0\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays, where $\text{CP}$-violating effects are expected to be negligible, and using background-enhanced regions of the signal decays. The results are consistent with $\text{CP}$ symmetry in both the $D^0\to K_S^0{K}^{-}\ddot{I}{€}^{+}$ and the $D^0\to K_S^0{K}^{+}\ddot{I}{€}^{-}$ decays, with $p$-values for the hypothesis of no $\text{CP}$ violation of 70% and 66%, respectively.

All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2023-019.html (LHCb public pages)