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In light of the current discrepancies between the recent predictions based onQCD factorisation (QCDF) and the experimental data for several non-leptoniccolour-allowed two-body $B$-meson decays, we obtain new determinations of thenon-factorisable soft-gluon contribution to the decays $\bar B_{s}^0 \toD_{s}^+ \pi^-$ and $\bar B^0 \to D^+ K^-$, using the framework of light-conesum rule (LCSR), with a suitable three-point correlation function and $B$-mesonlight-cone distribution amplitudes. In particular, we discuss the problemassociated with a double light-cone (LC) expansion of the correlator, andmotivate future determinations of the three-particle $B$-meson matrix elementwith the gluon and the spectator quark aligned along different light-conedirections. Performing a LC-local operator product expansion of the correlationfunction, we find, for both modes considered, the non-factorisable part of theamplitude to be sizeable and positive, however, with very large systematicuncertainties. Furthermore, we also determine for the first time, using LCSR,the factorisable amplitudes at LO-QCD, and thus the corresponding branchingfractions. Our predictions are in agreement with the experimental data andconsistent with the results based on QCDF, although again within very largeuncertainties. In this respect, we provide a rich outlook for futureimprovements and investigations.

Non-factorisable effects in the decays $\bar B_{s}^0 \to D_{s}^+ \pi^-$ and $\bar B^0 \to D^+ K^-$ from LCSR