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During the past few years, hints of Lepton Flavour Universality (LFU)violation have been observed in $b \to c \tau \bar\nu$ and $b \to s \ell^+\ell^-$ transitions. Recently, the $D^*$ and $\tau$ polarization fractions$P_L^{D^*}$ and $P_L^\tau$ in $B \to D^* \tau \bar\nu$ decay have also beenmeasured by the Belle collaboration. Motivated by these intriguing results, werevisit the $R_{D^{(*)}}$ and $R_{K^{(*)}}$ anomalies in a scalar leptoquark(LQ) model, in which two scalar LQs, one being $SU(2)_L$ singlet and the other$SU(2)_L$ triplet, are introduced simultaneously. We consider five $b \to c\tau \bar\nu$ mediated decays, $B \to D^{(*)}\tau \bar\nu$, $B_c \to \eta_c\tau \bar\nu$, $B_c \to J/\psi \tau \bar\nu$, and $\Lambda_b \to \Lambda_c \tau\bar\nu$, and focus on the LQ effects on the $q^2$ distributions of thebranching fractions, the LFU ratios, and the various angular observables inthese decays. Under the combined constraints by the available data on$R_{D^{(*)}}$, $R_{J/\psi}$, $P_L^\tau(D^*)$, and $P_L^{D^*}$, we perform scansfor the LQ couplings and make predictions for a number of observables. It isfound numerically that both the differential branching fractions and the LFUratios are largely enhanced by the LQ effects, with the latter being expectedto provide testable signatures at the SuperKEKB and High-Luminosity LHCexperiments.

Phenomenology of $b\to c\tau\bar\nu$ decays in a scalar leptoquark model