Abstract
In light of the current discrepancies between the recent predictions based on QCD factorisation (QCDF) and the experimental data for several non-leptonic colour-allowed two-body B-meson decays, we obtain new determinations of the non-factorisable soft-gluon contribution to the decays \( {\overline{B}}_s^0\to {D}_s^{+}{\pi}^{-} \) and \( {\overline{B}}^0\to {D}^{+}{K}^{-} \), using the framework of light-cone sum rule (LCSR), with a suitable three-point correlation function and B-meson light-cone distribution amplitudes. In particular, we discuss the problem associated with a double light-cone (LC) expansion of the correlator, and motivate future determinations of the three-particle B-meson matrix element with the gluon and the spectator quark aligned along different light-cone directions. Performing a LC-local operator product expansion of the correlation function, we find, for both modes considered, the non-factorisable part of the amplitude to be sizeable and positive, however, with very large systematic uncertainties. Furthermore, we also determine for the first time, using LCSR, the factorisable amplitudes at LO-QCD, and thus the corresponding branching fractions. Our predictions are in agreement with the experimental data and consistent with the results based on QCDF, although again within very large uncertainties. In this respect, we provide a rich outlook for future improvements and investigations.
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Acknowledgments
We are really grateful to Alexander Khodjamirian for many insightful discussions and valuable comments. We also thank Nico Gubernari, Thorsten Feldmann, Alexander Lenz, and Danny van Dyk, for helpful discussions. In addition, we would like to thank Alexander Khodjamirian, and Alexander Lenz, for their constant support throughout this work and for carefully proofreading the manuscript. We also acknowledge the TP1 group in Siegen for the useful feedback provided during the journal club, where this work has been informally presented. MLP wishes to thank Thorsten Feldmann, Peter Stangl, Javier Virto, and Roman Zwicky, for interesting discussions. The work of MLP was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — project number 500314741.
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Piscopo, M.L., Rusov, A.V. Non-factorisable effects in the decays \( {\overline{B}}_s^0\to {D}_s^{+}{\pi}^{-} \) and \( {\overline{B}}^0\to {D}^{+}{K}^{-} \) from LCSR. J. High Energ. Phys. 2023, 180 (2023). https://doi.org/10.1007/JHEP10(2023)180
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DOI: https://doi.org/10.1007/JHEP10(2023)180