Linking the $R_{K^{(\ast )}}$ anomalies to the Hubble tension via a single right-handed neutrino

Abstract

The updated measurements from the LHCb and SH0ES collaborations have respectively strengthened the deviations of the ratio $R_K$ in rare semi-leptonic $B$-meson decays and the present-day Hubble parameter $H_0$ in the Universe, implying tantalizing hints of new physics beyond the Standard Model. In this paper, we consider a simple flavor-specific two-Higgs-doublet model, where the long-standing $R_{K^{(\ast )}}$ anomalies can be addressed by a one-flavor right-handed neutrino. One of the intriguing predictions resulting from the parameter space for the $R_{K^{(\ast )}}$ resolution under flavor- and collider-physics constraints points toward a shift of the effective neutrino number, $\Delta N_{\mathrm{eff}}=N_{\mathrm{eff}}-N_{\mathrm{eff}}^{\mathrm{SM}}$, as favored to ease the $H_0$ tension. Depending on whether the neutrino is of Dirac or of Majorana type, we show that the resulting shift is $\Delta N_{\mathrm{eff}}\simeq 1.0$ for the former and $\Delta N_{\mathrm{eff}}\simeq 0.5$ for the latter case, respectively. While the Dirac case is disfavored by the CMB polarization measurements, the Majorana solution is consistent with the recent studies via a combined data set from various sources. Consequently, such a simple flavor-specific two-Higgs-doublet model provides a link between the $R_{K^{(\ast )}}$ anomalies and the $H_0$ tension, which in turn can be readily verified or falsified by the upcoming measurements.

Comments: 31 pages, 6 figures; more discussions and references added, final version published in the journal