Simultaneous Explanation of the $R_K$ and $R(D^{(\ast )})$ Puzzles

Abstract

At present, there are several hints of lepton flavor non-universality. The LHCb Collaboration has measured $R_K\equiv \mathcal{B}(B^{+}\to K^{+}{\mu }^{+}{\mu }^{-})/\mathcal{B}(B^{+}\to K^{+}{e}^{+}{e}^{-})$, and the BaBar Collaboration has measured $R(D^{(\ast )})\equiv \mathcal{B}(\bar{B}\to D^{(\ast )+}{\tau }^{-}{\bar{\nu }}_{\tau })/\mathcal{B}(\bar{B}\to D^{(\ast )+}{\ell }^{-}{\bar{\nu }}_{\ell })$ ($\ell =e,\mu$). In all cases, the experimental results differ from the standard model predictions by 2-3$\sigma$. Recently, an explanation of the $R_K$ puzzle was proposed in which new physics (NP) generates a neutral-current operator involving only third-generation particles. Now, assuming the scale of NP is much larger than the weak scale, this NP operator must be made invariant under the full $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y$ gauge group. In this Letter, we note that, when this is done, a new charged-current operator can appear, and this can explain the $R(D^{(\ast )})$ puzzle. A more precise measurement of the double ratio $R(D)/R(D^{\ast })$ can rule out this model.

Comments: 11 pages, text and citations added, version published in Phys. Lett. B