Linking $R_{K^{(\ast)}}$ anomalies to $H_0$ tension via Dirac neutrino

The recently updated measurement from LHCb has strengthened the deviation of $R_{K}$, implying a stronger hint of new physics beyond the Standard Model. We show in this paper that, the long-standing $R_{K^{(*)}}$ anomalies can be explained by Dirac neutrinos embedded in a two-Higgs-doublet model. The explanation induces a thermalized right-handed Dirac neutrino in the early Universe, which contributes as extra radiation to the Hubble expansion and prompts a shift of the effective neutrino number, $N_{eff}$. In mimicking the favored scenarios for resolving the Hubble ($H_0$) tension, we show that the simultaneous explanation of $R_{K^{(*)}}$ anomalies and $H_0$ tension via one flavor right-handed Dirac neutrino can be readily tested or ruled out by the upcoming $H_0$ confirmation.