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 $χ_{1}$ and $χ_{2}$, with $m(χ_{2}) > m(χ_{1})$, is induced by a dark Higgs field and a corresponding dark Higgs boson $h^{\prime}$. 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 $σ\left(e^+e^- \to h^\prime χ_1 χ_2\right)$, and the product of branching fractions $\mathcal{B}\left(χ_2\toχ_1 e^+ e^-\right)\times\mathcal{B}\left(h^\prime\to x^+x^-\right)$, where $x^+x^-$ indicates $μ^+μ^-, π^+π^-$, 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.

Figures (4)

• Figure 1: Feynman diagram depicting the search channel for $A^{\prime\xspace}$ production in association with a $h^{\prime}\xspace$ with subsequent decays into both visible and dark sector states. Here $x^+x^-$ indicates $\mu^+\mu^-$, $\pi^+\pi^-$, or $K^+K^-$. Mixing between dark sector and visible states is indicated by black dots.
• Figure 2: Distribution of $M(\pi^+\pi^-)$ together with the stacked contributions from the various simulated SM background samples for $h^{\prime}\xspace\to\pi^+\pi^-$ candidates. Simulation is normalized to a luminosity of 365 $\hbox{,fb}^{-1}$.
• Figure 3: Exclusion regions at 95 % credibility level in the plane of the sine of the mixing angle $\theta$ and dark Higgs mass $m(h^{\prime}\xspace)\xspace$ from this work (teal) together with existing constraints at 90 % confidence level from PS191 Gorbunov:2021ccu, E949 BNL-E949:2009dza, NA62 NA62:2020pwiNA62:2021zjw, KOTO KOTO:2020prkFerber:2023iso, KTeV KTEV:2000ngj, and BABAR BaBar:2015jvuWinkler:2018qyg, and at 95 % confidence level from MicroBooNE MicroBooNE:2021uswMicroBooNE:2022ctmFerber:2023iso, L3 L3:1996omeFerber:2023iso, CHARM CHARM:1985anbWinkler:2018qyg, LHCb LHCb:2015nkvLHCb:2016awgWinkler:2018qyg, Belle II Belle-II:2023ueh, and CMS CMS:2021sch for $\alpha_D = 0.1$, $m(A^{\prime\xspace})\xspace = 3\,m(\chi_{1})\xspace$, $\Delta m=0.4\,m(\chi_{1})\xspace$, $\epsilon = 1.5\times 10^{-3}$, and $m(\chi_{1})\xspace = 2.5\,{\mathrm{\,Ge V\!/}c^2}\xspace$. Constraints colored in gray with dashed outline are reinterpretations not performed by the experimental collaborations. All constraints except for the one from this work do not require the presence of a dark photon or iDM.
• Figure 4: Exclusion regions at 95 % credibility level in the plane of the dimensionless variable $y = \epsilon^2\alpha_D(m(\chi_1)/m(A'))^4$ and DM mass $m(\chi_{1})\xspace$ from this work (teal) together with existing constraints at 90 % confidence level from CHARM Gninenko:2012eqTsai:2019buq, NuCal Blumlein:2011mvBlumlein:2013cuaTsai:2019buq, and BABAR BaBar:2017tizDuerr:2019dmv) for $\alpha_D = 0.1$, $m(A^{\prime\xspace})\xspace = 3\,m(\chi_{1})\xspace$, $\Delta m=0.4\,m(\chi_{1})\xspace$, $\sin \theta = 2.6\times 10^{-4}$, and $m(h^{\prime}\xspace)\xspace = 0.4\,{\mathrm{\,Ge V\!/}c^2}\xspace$. Constraints colored in gray with dashed outline are reinterpretations not performed by the experimental collaborations. All constraints except for the one from this work do not require the presence of a dark Higgs boson or iDM.