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

Abstract

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 $\ddot{I}{‡}_1$ and $\ddot{I}{‡}_2$, with $m(\ddot{I}{‡}_2)>m(\ddot{I}{‡}_1)$, is induced by a dark Higgs field and a corresponding dark Higgs boson $h^{\prime }$. 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 $365\,\mbox{fb}^{-1}$ 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 $\ddot{I}ƒ\left(e^{+}{e}^{-}\to h^{\prime }\ddot{I}{‡}_1\ddot{I}{‡}_2\right)$, and the product of branching fractions $\mathcal{B}\left(\ddot{I}{‡}_2\to \ddot{I}{‡}_1{e}^{+}{e}^{-}\right)\times \mathcal{B}\left(h^{\prime }\to x^{+}{x}^{-}\right)$, where $x^{+}{x}^{-}$ indicates $\hat{I}{¼}^{+}\hat{I}{¼}^{-},\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, or $K^{+}{K}^{-}$, as functions of $h^{\prime }$ mass and lifetime at the level of $10^{-1}\,\mbox{fb}$. 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.