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

Abstract

Motivated by the deviations between experimental data and SM predictions for the branching fractions of $\bar{B}_{(s)}^{0} \to D_{(s)}^{(*)+}L^-$ decays with $L=\pi,K^{(*)},\rho$, 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 $\Delta_{d(s)}^{LL}$ can reconcile the discrepancies at $1\sigma$, while the mixed right-left coupling $\Delta_{d(s)}^{RL}$ remains compatible with data only at about $2\sigma$. Extending to the two-coupling case, we find viable parameter regions as long as $\Delta_{d(s)}^{LL}\neq 0$. Incorporating the LHCb measurement of the ratio $R_{\pi/\mu\nu_{\mu}}$ further reduces the allowed range of $\Delta_{d}^{LL}$, but does not yield meaningful extra restriction on $\Delta_{d}^{RL}$. Hence, while either $\Delta_{d(s)}^{LL}$ or $\Delta_{d(s)}^{RL}$ 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 $R_{(s)L}^{(*)}$, which can be probed by forthcoming LHCb and Belle II measurements.