Semileptonic decays $B/B_s \to (D^{(*)},D_s^{(*)}) l \nu_l$ in the PQCD approach with the lattice QCD input

In this paper, we studied the semileptonic $B/B_s \to (D^{(*)},D_s^{(*)}) l\nu_l$ decays in the framework of the standard model (SM) , by employing the perturbative QCD (PQCD) factorization formalism combining with the lattice QCD inputs of the relevant transition form factors. We calculated the branching ratios ${\cal B}(B_{(s)} \to D_{(s)}^{(*)} l \nu_l )$ with $l=(e,\mu.\tau)$ , the ratios of the branching ratios $R(D^{(*)})$ and $R(D_s^{(*)} )$ and other physical observables $P_\tau(D_{(s)}^{(*)})$, $F_L(D^*_{(s)})$ and $A_{FB}(\tau)$. The "PQCD+Lattice" predictions for ${\cal B}(B \to D^{(*)} l\nu_l)$ and $R(D^{(*)})$ do agree well with those currently available experimental measurements within the errors. For the ratios $R(D_s)$ and $R(D_s^*)$, the "PQCD+Lattice" predictions agree well with other known predictions. For both $P_\tau(D^*)$ and $F_L(D^*)$, our theoretical predictions agree well with the measured values within errors. Our theoretical predictions about the considered semileptonic $B/B_s$ decays could be tested in the near future LHCb and the Belle II experiments.