Search for dark matter produced in association with a Higgs boson decaying to a $\tau$ lepton pair in proton-proton collisions at $\sqrt{s}$ = 13 TeV

A search for dark matter particles produced in association with a Higgs boson decaying into a pair of $\tau$ leptons is performed using data collected in proton-proton collisions at a center-of-mass energy of 13 TeV with the CMS detector. The analysis is based on a data set corresponding to an integrated luminosity of 101 fb$^{-1}$ collected in 2017$-$2018. No significant excess over the expected standard model background is observed. This result is interpreted within the frameworks of the 2HDM+a and baryonic Z$'$ benchmark simplified models. The 2HDM+a model is a type-II two-Higgs-doublet model featuring a heavy pseudoscalar with an additional light pseudoscalar. Upper limits at 95% confidence level are set on the product of the production cross section and the branching fraction for each of these two simplified models. Heavy pseudoscalar boson masses between 400 and 700 GeV are excluded for a light pseudoscalar mass of 100 GeV. For the baryonic Z$'$ model, a statistical combination is made with an earlier search based on a data set of 36 fb$^{-1}$ collected in 2016. In this model, Z$'$ boson masses up to 1050 GeV are excluded for a dark matter particle mass of 1 GeV.