A puzzle in $$\varvec{\bar{B}_{(s)}^0 \rightarrow D_{(s)}^{(*)+} \lbrace \pi ^-, K^-\rbrace }$$
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Regular Article - Theoretical Physics
0 → D (∗)+ {π − , K − } decays and extraction of the A puzzle in B¯ (s) (s) f s / f d fragmentation fraction Marzia Bordone1,a , Nico Gubernari2,b , Tobias Huber1,c , Martin Jung3,d , Danny van Dyk2,e 1
Theoretische Physik 1, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany Technische Universität München, James-Franck-Straße 1, 85748 Garching, Germany 3 Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino, 10125 Turin, Italy
2
Received: 29 July 2020 / Accepted: 2 October 2020 © The Author(s) 2020
Abstract We provide updated predictions for the hadronic (∗)+ decays B¯ s0 → Ds π − and B¯ 0 → D (∗)+ K − . They are based on O(αs2 ) results for the QCD factorization amplitudes (∗) at leading power and on recent results for the B¯ (s) → D(s) form factors up to order O(2QCD /m 2c ) in the heavy-quark expansion. We give quantitative estimates of the matrix elements entering the hadronic decay amplitudes at order O(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.
1 Introduction The physics programs of the Large Hadron Collider experiments promise data sets of unprecedented sizes for a variety of Bs decays. Consequently, analyses that emerge from these programs now dominate determinations of absolute branching fractions of Bs decays. The biggest source of uncertainties in these analyses is the poorly known fraction of the b quark fragmentation into B¯ s0 versus B¯ 0 mesons, denoted as f s / f d . A promising approach to determine this ratio [1] from data is the measurement of a ratio of branching fractions for
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0123456789().: V,-vol
hadronic B decays: σ ( pp → B¯ s0 X ) × B( B¯ s0 → Ds(∗)+ π − ) σ ( pp → B¯ 0 X ) × B( B¯ 0 → D (∗)+ K − ) σ ( pp → B¯ s0 X ) P(V ) ≡ × Rs/d . σ ( pp → B¯ 0 X )
(1)
We consider the hadronic decays in this ratio very advantageous from the theory point of view. Since in these decays all valence quarks are distinguishable, we do not have to account for decay topologies involving penguin operators. For the same reason weak annihilation is not an issue either. Moreover, these decays are dominated by the color-allowed tree topology, and the color-suppressed operator enters only through perturbative or power corrections. In Ref. [2] the P is given with a relative uncerratio that we here call Rs/d tainty of ∼ 9%. The purpose of the present article is threefold. First, we re
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