Search for exotic decays of the Higgs boson to a pair of pseudoscalars in the and final states

A search for exotic decays of the Higgs boson ($$) with a mass of 125$$ to a pair of light pseudoscalars $$ is performed in final states where one pseudoscalar decays to two $$ quarks and the other to a pair of muons or $$ leptons. A data sample of proton-proton collisions at $$ corresponding to an integrated luminosity of 138$$ recorded with the CMS detector is analyzed. No statistically significant excess is observed over the standard model backgrounds. Upper limits are set at 95% confidence level ($$) on the Higgs boson branching fraction to $$ and to $$ via a pair of $$s. The limits depend on the pseudoscalar mass $$ and are observed to be in the range (0.17-3.3) $$ and (1.7-7.7) $$ in the $$ and $$ final states, respectively. In the framework of models with two Higgs doublets and a complex scalar singlet (2HDM+S), the results of the two final states are combined to determine upper limits on the branching fraction $$ at 95% $$, with $$ being a muon or a $$ lepton. For different types of 2HDM+S, upper bounds on the branching fraction $$ are extracted from the combination of the two channels. In most of the Type II 2HDM+S parameter space, $$ values above 0.23 are excluded at 95% $$ for $$ values between 15 and 60$$.