On the Minimal Flavor Violating Leptoquark Explanation of the $R_{D^{(*)}}$ Anomaly

There has been persistent disagreement between the Standard Model (SM) prediction and experimental measurements of $R_{D^{(*)}}=\mathcal{B}(\bar B \rightarrow D^{(*)} \tau \bar\nu_\tau)/\mathcal{B}(\bar B \rightarrow D^{(*)} l \bar\nu_l)$ $(l=e,\mu)$. This anomaly may be addressed by introducing interactions beyond the Standard Model involving new states, such as leptoquarks. Since the processes involved are quark flavor changing, any new states would need to couple to at least two different generations of quarks, requiring a non-trivial flavor structure in the quark sector while avoiding stringent constraints from flavor-changing neutral current processes. In this work, we look at scalar leptoquarks as a possible solution for the $R_{D^{(*)}}$ anomaly under the assumption of $\it{minimal~flavor~violation}$ (MFV). We investigate all possible representations for the leptoquarks under the SM quark flavor symmetry group, consistent with asymptotic freedom. We consider constraints on their parameter space from self-consistency of the MFV scenario, perturbativity, the FCNC decay $b\to s\bar\nu\nu$ and precision electroweak observables. We find that none of the scalar leptoquarks can explain the $R_{D^{(*)}}$ anomaly while simultaneously avoiding all constraints within this scenario. Thus scalar leptoquarks with MFV-generated quark couplings do not work as a solution to the $R_{D^{(*)}}$ anomaly.