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 χ₁ and χ₂, with m(χ₂) > m(χ₁), 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^ χ₁ χ₂), and the product of branching fractions B(χ₂→χ₁ e⁺ e⁻)(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.