Search for the $Z$ Boson Decay to $\tau \tau \mu \mu $ in Proton-Proton Collisions at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$

The first search for the $Z$ boson decay to $\tau \tau \mu \mu $ at the CERN LHC is presented, based on data collected by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of $138\text{}\text{}{\mathrm{fb}}^{-1}$. The data are compatible with the predicted background. For the first time, an upper limit at the 95% confidence level of 6.9 times the standard model expectation is placed on the ratio of the $Z\to \tau \tau \mu \mu $ to $Z\to 4\mu $ branching fractions. Limits are also placed on the six flavor-conserving four-lepton effective-field-theory operators involving two muons and two tau leptons, for the first time testing all such operators.