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We study the $\bar{B}\to D(D^*) \ell^-\bar{\nu}_{\ell}$ decays based on theup-to-date available inputs from experiments and the lattice. First, we reviewthe standard model (SM) predictions of the different observables associatedwith these decay channels. In the analyses, we consider new physics (NP)effects in the channels with the heavy ($\tau$), as well as the light leptons($\mu, e$). We have extracted $|V_{cb}|$ along with the new physics Wilsoncoefficients (WCs) from the available data on light leptons; the extractedvalue of $|V_{cb}|$ is $(40.3 \pm 0.5)\times 10^{-3}$. The extracted WCs arezero consistent, but some could be of order $10^{-2}$. Also, we have done thesimultaneous analysis of the data in $\bar{B} \to D^{(*)}(\mu^-,e^-)\bar{\nu}$alongside the inputs on $R(D^{(*)}) = \frac{\Gamma(\bar{B}\toD^{(*)}\tau^-\bar{\nu}_{\tau})}{\Gamma(\bar{B}\toD^{(*)}\ell^-\bar{\nu}_{\ell})}$ and the $D^*$ longitudinal polarisationfraction $F_L^{D^*}$ in different NP scenarios and extracted $|V_{cb}|$ whichis consistent with the number mentioned above. Also, the simultaneousexplanation of $R(D^{(*)})$ and $F_L^{D^*}$ is not possible in the one-operatorscenarios. However, the two operator scenarios with $\mathcal{O}_{S_2}^{\tau} =(\bar{q}_R b_L)(\bar{\tau}_R\nu_{\tau L})$ as one of the operators couldexplain all these three measurements. Finally, we have given predictions of allthe related observables in $\bar{B} \to D^{(*)}(\tau^-,\mu^-,e^-)\bar{\nu}$decays in the NP scenarios, which could be tested in future experiments. Wehave repeated this exercise for $\bar{B} \to \pi\ell^-\bar{\nu}_{\ell}$ decayswith the light lepton and extracted $|V_{ub}|$ and the new WCs. Finally, usingall these available data for the light and heavy leptons, we have given boundson the couplings of the relevant SM effective field theory (SMEFT) operatorsand the probable NP scale $\Lambda$.

Test of new physics effects in $\bar{B} \to (D^{(*)}, \pi) \ell^-\bar{\nu}_{\ell}$ decays with heavy and light leptons