Phenomenological study of diquark effects in ${\bar{B}}_{(s)}^0\to D_{(s)}^{(\ast )+}{L}^{-}$ decays

Motivated by the deviations between experimental data and SM predictions for the branching fractions of ${\bar{B}}_{(s)}^0\to D_{(s)}^{(\ast )+}{L}^{-}$ decays with $L=\pi ,K^{(\ast )},\rho$, we investigate whether the type-IV scalar diquark can offer a plausible explanation for them. By matching the renormalized amplitudes in the full theory onto those in the low-energy effective theory formulated in the diquark operator basis, we extract the corresponding Wilson coefficients up to NLO in ${\alpha }_s$ at the NP scale ${\mu }_{\phi }=M_{\phi }$. We then rewrite the obtained operators in the SM basis and apply the renormalization-group running to evolve the Wilson coefficients down to the hadronic scale ${\mu }_b=m_b$. For the hadronic matrix elements of the relevant NP operators, we employ the QCD factorization approach to evaluate the non-factorizable one-loop vertex corrections, and confront our theoretical predictions to the latest data to constrain the diquark parameter space. In the single-coupling case, we find that the purely left-handed coupling ${\mathrm{\Delta }}_{d(s)}^{LL}$ can reconcile the discrepancies at $1\sigma$, while the mixed right-left coupling ${\mathrm{\Delta }}_{d(s)}^{RL}$ remains compatible with data only at about $2\sigma$. Extending to the two-coupling case, we find viable parameter regions as long as ${\mathrm{\Delta }}_{d(s)}^{LL}\mathrm{\ne }0$. Incorporating the LHCb measurement of the ratio $R_{\pi \mathrm{/}\mu {\nu }_{\mu }}$ further reduces the allowed range of ${\mathrm{\Delta }}_d^{LL}$, but does not yield meaningful extra restriction on ${\mathrm{\Delta }}_d^{RL}$. Hence, while either ${\mathrm{\Delta }}_{d(s)}^{LL}$ or ${\mathrm{\Delta }}_{d(s)}^{RL}$ can separately provide an acceptable NP interpretation, our phenomenological results favor a scenario dominated by purely left-handed diquark-quark couplings. Finally, we present updated predictions for the branching fractions and the ratios $R_{(s)L}^{(\ast )}$, which can be probed by forthcoming LHCb and Belle II measurements.