$CP$-violating effects of the neutral triple gauge couplings in $Z(\mathrm{\ell }\mathrm{\ell })\gamma$ production at the LHC

The main goal of modern experiments in high-energy physics area is to find deviations from the Standard Model, the theoretical framework which describes data well but is expected to be extended to a more general theory. The anomalous coupling approach provides an opportunity to look for a wide range of new physics effects in different experimental signatures thanks to its model independence. In this work, the neutral triple gauge couplings are considered in $Z(\mathrm{\ell }\mathrm{\ell })\gamma$ channel, and an effective field theory is used to parameterize these couplings in the Lagrangian. Neutral triple gauge couplings are triple interactions between $Z$ bosons and photons, and some of them violate $CP$ symmetry. This work presents a study of $CP$-sensitive variables in the aforementioned channel using special angular variables and matrix-element-based optimal observables. Based on these variables, expected limits on the coupling parameters are set for the conditions of Run II and Run III at LHC experiments, demonstrating the possibility of studying the $CP$-violation using a neutral triple gauge coupling approach and special $CP$-sensitive variables.