Exotic $h \to Z a$ Higgs decays into $\tau$ leptons

Exotic Higgs decays are among the most promising areas to be explored at the High-Luminosity LHC, given the unprecedentedly large amount $(\sim 3 \times 10^8)$ of 125 GeV Higgs bosons that will be produced. In this context, we propose a new search channel for which the Higgs boson decays to a (leptonically decaying) $Z$ boson and a light BSM pseudoscalar $a$, which subsequently decays to a pair of $\tau$-leptons ($h \to Z a \to \ell\ell \tau\tau $). After performing a validation of existing ATLAS and CMS exotic Higgs decay searches in related channels, we analyze the HL-LHC projected sensitivity of our $a\to \tau\tau$ search, targeting the kinematic region where the exotic Higgs decay is two-body. We are able to probe pseudoscalar masses $m_a \in [5,\, 33]$ GeV by leveraging both leptonic and hadronic $\tau$ decays, and establish model-independent 95\% C.L. sensitivity projections on the branching fraction ${\rm BR}(h \to Z a) \times {\rm BR}(a \to \tau\tau)$. These $a\to \tau\tau$ projections yield a competitive probe of light pseudoscalars, which depending on the model can become significantly more sensitive than projections from existing experimental searches in $a \to \mu\mu$ and $a \to \gamma\gamma$ final states. Finally, we explore the potential of our search to probe an Axion-Like-Particle (ALP) solution to the muon $(g-2)$ anomaly (when taken face-value), finding that our proposed $h\to Z a$, $a\to\tau\tau$ search can provide valuable constraints on such ALP scenario, in complementarity with existing $h\to Z a$, $a \to \gamma\gamma$ experimental searches.