Explaining Belle Data on $B\to K^{(*)}\nu\bar{\nu}$ Decays via Dark $Z$ Resonances

The Belle II Collaboration reported the first measurement on ${\rm Br}(B^+\rightarrow K^+\nu\bar{\nu})$, which lies 2.7$\sigma$ away from the Standard Model expectation. This result may be manifestation of new physics beyond the Standard Model. In present work, motivated by the Belle II measurement, we investigate the effect of a dark photon/dark $Z$ on the rare $B$ meson decay $B^+\rightarrow K^+\nu\bar{\nu}$ and show that the ${\rm Br}(B^+\rightarrow K^+\nu\bar{\nu})$ excess from Belle II over the Standard Model expectation explained by the appearance of the dark $Z$ especially in resonances. We also derive constraints on various parameters of the two-Higgs-doublet model extended with a dark Abelian gauge group, in light of the measurement of the ${\rm Br}(B^+\rightarrow K^+\nu\bar{\nu})$ by the Belle-II Collaboration as well as the upper bound on ${\rm Br}(B^0\rightarrow K^{*0}\nu\bar{\nu})$ decay, set by the Belle data. Our results indicate that there exists a common region where both experimental results are satisfied for a dark $Z$ mass around 4.5 GeV with suitable values of the other parameters.