Excesses of muon $g-2$, $R_{D^{(\ast )}}$, and $R_K$ in a leptoquark model

In this study, we investigate muon $g-2$, $R_{K^{(\ast )}}$, and $R_{D^{(\ast )}}$ anomalies in a specific model with one doublet, one triplet, and one singlet scalar leptoquark (LQ). When the strict limits from the $\ell’ \to \ell \gamma$,$\Delta B=2$,$B_{s}\to \mu^+ \mu^-$,and$B^+ \to K^+ \nu \bar\nu$ processes are considered, it is difficult to use one scalar LQ to explain all of the anomalies due to the strong correlations among the constraints and observables. After ignoring the constraints and small couplings, the muon $g-2$ can be explained by the doublet LQ alone due to the $m_t$ enhancement, whereas the measured and unexpected smaller $R_{K^{(\ast )}}$ requires the combined effects of the doublet and triplet LQs, and the $R_D$ and $R_{D^{\ast }}$ excesses depend on the singlet LQ through scalar- and tensor-type interactions.