Studies of Z $\to$ 4$\mathrm{\ell }$ decays in proton-proton collisions at $\sqrt{s}$ = 8 and 13 TeV

Decays of Z bosons to four charged leptons (electrons and muons) are studied in proton-proton collisions at $\sqrt{s}$ = 8 and 13 TeV. The analysis is based on data collected with the CMS detector at the LHC corresponding to an integrated luminosity of 19.7 fb${}^{-1}$ at 8 TeV and 138 fb${}^{-1}$ at 13 TeV. The measured value of the inclusive branching fraction for all four-lepton decay modes, $\mathcal{B}$(Z $\to$ 4$\mathrm{\ell }$), is [4.67 $\pm$ 0.11 (stat) $\pm$ 0.10 (syst)] $\times$ 10${}^{-6}$, which has a precision of about 3% limited by both statistical and systematic uncertainties. Measurements of the individual branching fractions for the decays Z $\to$ 4$\mu$, Z $\to$ 4e, and Z $\to$ 2$\mu$2e are also reported. Differential decay rates are presented as functions of kinematic and angular quantities in the Z boson rest frame. Measurements of triple-product asymmetries, which are sensitive to possible violations of charge conjugation and parity invariance, are performed for Z $\to$ 4$\mathrm{\ell }$ decays. The results are compared with standard model predictions and used to set limits on the production of new gauge bosons.