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.
Highlights
We consider the hadronic decays in this ratio very advantageous from the theory point of view
We update the values of the Bq → Dq(∗) form factors based on a recent analysis within the heavy-quark expansion (HQE) [3]
We explore the possibility that the discrepancy between data and the Standard Model (SM) calculation is caused by beyond the Standard Model (BSM) physics
Summary
For the first time, conservative numerical estimates for the necessary hadronic matrix elements that enter at next-to-leading-power in QCD/mb. Based on these improvements we predict the branching fractions of the four decays and, for the first time, use their theoretical correlation to reduce the uncertainty on their ratios RsP/(dV ). We discuss the numerical input parameters that enter our expressions, and give results for the non-leptonic branching fractions and the ratios RsP/(dV ) at leading power. 3 we compare the theoretical predictions to experimental data, explain in detail our extraction of the fs/ fd fragmentation fraction for various hadron colliders and uncover the puzzling pattern in non-leptonic B(0s) → D(+s){π −, K −} decays.
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