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

Abstract

We provide updated predictions for the hadronic decays ${\bar{B}}_s^0\to D_s^{(\ast )+}{\pi }^{-}$ and ${\bar{B}}^0\to D^{(\ast )+}{K}^{-}$. They are based on $\mathcal{O}({\alpha }_s^2)$ results for the QCD factorization amplitudes at leading power and on recent results for the ${\bar{B}}_{(s)}\to D_{(s)}^{(\ast )}$ form factors up to order $\mathcal{O}({\Lambda }_{\mathrm{QCD}}^2/m_c^2)$ in the heavy-quark expansion. We give quantitative estimates of the matrix elements entering the hadronic decay amplitudes at order $\mathcal{O}({\Lambda }_{\mathrm{QCD}}/m_b)$ 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.

Comments: 13 pages, 4 tables: v2: minor modifications, accepted for publication in EPJC