Search for a Dark Higgs Boson Produced in Association with Inelastic Dark Matter at the Belle II Experiment

Inelastic dark matter models that have two dark matter particles and a massive dark photon can reproduce the observed relic dark matter density without violating cosmological limits. The mass splitting between the two dark matter particles χ_{1} and χ_{2}, with m(χ_{2})>m(χ_{1}), is induced by a dark Higgs field and a corresponding dark Higgs boson h^{'}. We present a search for dark matter in events with two vertices, at least one of which must be displaced from the interaction region, and missing energy. Using a 365  fb^{-1} data sample collected at Belle II, which operates at the SuperKEKB e^{+}e^{-} collider, we observe no evidence for a signal. We set upper limits on the product of the production cross section σ(e^{+}e^{-}→h^{'}χ_{1}χ_{2}), and the product of branching fractions B(χ_{2}→χ_{1}e^{+}e^{-})×B(h^{'}→x^{+}x^{-}), where x^{+}x^{-} indicates μ^{+}μ^{-},π^{+}π^{-}, or K^{+}K^{-}, as functions of h^{'} mass and lifetime at the level of 10^{-1}  fb. We set model-dependent upper limits on the dark Higgs mixing angle at the level of 10^{-5} and on the dark photon kinetic mixing parameter at the level of 10^{-3}. This is the first search for dark Higgs bosons in association with inelastic dark matter.