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

Abstract

We provide updated predictions for the hadronic decays bar{B}_s^0rightarrow D_s^{(*)+} pi ^- and bar{B}^0rightarrow 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)} rightarrow D_{(s)}^{(*)} 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.