Simultaneous Explanation of $R(D^{(*)})$ and $b\to sμ^+μ^-$: The Last Scalar Leptoquarks Standing

Abstract: Over the past years, experiments accumulated intriguing hints for new physics (NP) in flavor observables, namely in the anomalous magnetic moment of the muon ($a_\mu$), in $R(D^{(*)})={\rm Br}(B\to D^{(*)}\tau\nu)/{\rm Br}(B\to D^{(*)}\ell\nu)$ and in $b\to s\mu^+\mu^-$ transitions, which are all at the $3-4\,\sigma$ level. In this article we point out that one can explain the $R(D^{(*)})$ anomaly using two scalar leptoquarks (LQs) with the same mass and coupling to fermions related via a discrete symmetry: an $SU(2)$ singlet and an $SU(2)$ triplet, both with hypercharge $Y=-2/3$. In this way, potentially dangerous contributions to $b\to s\nu\nu$ are avoided and non-CKM suppressed effects in $R(D^{(*)})$ can be generated. This allows for smaller overall couplings to fermions weakening the direct LHC bounds. In our model, $R(D^{(*)})$ is directly correlated to $b\to s\tau^+\tau^-$ transitions where an enhancement by orders of magnitude compared to the standard model (SM) is predicted, such that these decay modes are in the reach of LHCb and BELLE II. Furthermore, one can also naturally explain the $b\to s\mu^+\mu^-$ anomalies (including $R(K)$) by a $C_9=-C_{10}$ like contribution without spoiling $\mu-e$ universality in charged current decays. In this case sizable effects in $b\to s\tau\mu$ transitions are predicted which are again well within the experimental reach. One can even address the longstanding anomaly in $a_\mu$, generating a sizable decay rate for $\tau\to\mu\gamma$. However, we find that out of the three anomalies $R(D^{(*)})$, $b\to s\mu^+\mu^-$ and $a_{\mu}$ only two (but any two) can be explained simultaneously.