Exotic decays of the 125 GeV Higgs boson at future $e^+e^-$ lepton colliders

Discovery of unexpected properties of the Higgs boson offers an intriguing opportunity of shedding light on some of the most profound puzzles in particle physics. The Beyond Standard Model (BSM) decays of the Higgs boson could reveal new physics in a direct manner. Future electron-positron lepton colliders operating as Higgs factories, including CEPC, FCC-ee and ILC, with the advantages of a clean collider environment and large statistics, could greatly enhance the sensitivity in searching for these BSM decays. In this work, we perform a general study of Higgs exotic decays at future $e^+e^-$ lepton colliders, focusing on the Higgs decays with hadronic final states and/or missing energy, which are very challenging for the High-Luminosity program of the Large Hadron Collider (HL-LHC). We show that with simple selection cuts, $O(10^{-3}\sim10^{-5})$ limits on the Higgs exotic decay branching fractions can be achieved using the leptonic decaying spectator $Z$ boson in the associated production mode $e^+e^-\rightarrow Z H$. We further discuss the interplay between the detector performance and Higgs exotic decay, and other possibilities of exotic decays. Our work is a first step in a comprehensive study of Higgs exotic decays at future lepton colliders, which is a key ingredient of Higgs physics that deserves further investigation.