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In this study, we investigate muon $g-2$, $R_{K^{(*)}}$, and $R_{D^{(*)}}$anomalies in a specific model with one doublet, one triplet, and one singletscalar 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 allof the anomalies due to the strong correlations among the constraints andobservables. 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, whereasthe measured and unexpected smaller $R_{K^{(*)}}$ requires the combined effectsof the doublet and triplet LQs, and the $R_D$ and $R_{D^*}$ excesses depend onthe singlet LQ through scalar- and tensor-type interactions.

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