Scalar dark matter explanation of the excess in the Belle II $B^{+}\to K^{+}+$ invisible measurement

Abstract

Recently Belle II reported the first measurement of $B^{+}\to K^{+}+\mathrm{invisible}(\mathrm{inv})$, which is $2.7\sigma$ above the standard model (SM) prediction. If confirmed, this calls for new physics beyond SM. In the SM, the invisible particles are neutrino-anti-neutrino pairs. There are more possibilities when going beyond the SM. In this work, we focus on decays to dark matter (DM) and show that the $B\to K+\mathrm{inv}$ excess from Belle II and DM relic density can be simultaneously explained in a simple extension of the SM. The model introduces a real scalar singlet $\varphi$ acting as a DM candidate, and two heavy vector-like quarks $Q,D$ with the same quantum numbers as the SM left-handed quark doublet and right-handed down-type quark singlet, respectively. All these new particles are odd under a ${\mathbb{Z}}_2$ symmetry while the SM particles are even. The model can successfully explain the Belle II anomaly and DM relic density for TeV-scale heavy quarks with hierarchical Yukawa couplings involving $b$ and $s$ quarks. At the same time, it can easily satisfy other flavour physics constraints. Direct detection searches utilizing the Migdal effect constrain some of the parameter space.

Comments: v2: add the dark matter direct detection constraints due to the Migdal effect. To appear in JHEP