A puzzle in $\bar{B}_{(s)}^0 \to D_{(s)}^{(*)+} \lbrace \pi^-, K^-\rbrace$ decays and extraction of the $f_s/f_d$ fragmentation fraction

Abstract

We provide updated predictions for the hadronic decays $\bar{B}_s^0\to D_s^{(*)+} \pi^-$ and $\bar{B}^0\to D^{(*)+} K^-$. They are based on $\mathcal{O}(\alpha_s^2)$ results for the QCD factorization amplitudes at leading power and on recent results for the $\bar{B}_{(s)} \to D_{(s)}^{(*)}$ form factors up to order ${\cal O}(\Lambda_{\rm QCD}^2/m_c^2)$ in the heavy-quark expansion. We give quantitative estimates of the matrix elements entering the hadronic decay amplitudes at order ${\cal O}(\Lambda_{\rm QCD}/m_b)$ for the first time. Our results are very precise, and uncover a substantial discrepancy between the theory predictions and the experimental measurements. We explore two possibilities for this discrepancy: non-factorizable contributions larger than predicted by the QCD factorization power counting, and contributions beyond the Standard Model. We determine the $f_s/f_d$ fragmentation fraction for the CDF, D0 and LHCb experiments for both scenarios.