Hint of a new scalar interaction in LHCb data?

Abstract

We explain recent LHCb measurements of the lepton universality ratios, $R_{D^{(*)}}^{\tau/\ell}\equiv \frac{\mathcal{B}(\bar B \to D^{(*)+} \tau^- \bar\nu_\tau)} {\mathcal{B}(\bar B \to D^{(*)+}\ell^- \bar\nu_\ell)}$ and ${R(\Lambda_c^+)}^{\tau/\ell} \equiv \frac{\mathcal{B}(\Lambda_b \to \Lambda_c^+ \tau^- \bar{\nu}_{\tau})}{\mathcal{B}(\Lambda_b \to \Lambda_c^+ \ell^- \bar{\nu}_{\ell})}$ with $\ell=\mu$, via new physics that affects $R_D^{\tau/\ell}$ and $R(\Lambda_c^+)^{\tau/\ell}$ but not $R_{D^*}^{\tau/\ell}$. The scalar operator in the effective theory for new physics is indicated. We find that the forward-backward asymmetry and $\tau$ polarization in $\bar{B} \to D^+ \tau^{-} \bar{\nu}_{\tau}$ and $\Lambda_b \to \Lambda_c^+ \tau^- \bar{\nu}_{\tau}$ decays are significantly affected by the scalar interaction. We construct a simple two Higgs doublet model as a realization of our scenario and consider lepton universality in semileptonic charm and top decays, radiative $B$ decay, $B$-mixing, and $Z \to b \bar b$.