New insights into the $b\rightarrow c \bar{u}q$ puzzle through Top-Bottom synergies

Anomalies in the non-leptonic $\bar{B}^0\rightarrow D^{(*)+}K^{(*)-}$ and $\bar{B}^0_s\rightarrow D^{(*)+}_s\pi^-$ decays may be an indication of physics beyond the Standard Model, but the large deviations require strongly coupled new physics that should be visible at colliders. We explore three new directions that could lead to viable new physics models, performing a detailed collider study to examine the possible weakening of previously known constraints on additional $SU(2)_L$ doublets. Our results show that, despite the difficulty of probing $t\bar{t}$ final states, increasing the branching ratio to this decay mode does not significantly weaken the bounds on weak doublet scalars, as additionally existing charged Higgs searches are equally strong. Beyond this, we analyse a potentially large breakdown of QCD factorisation by including large-power corrections to $B$ decays, and the effect of diluting collider searches with multi-scalar extensions. We find that these typical model-building routes for constructing a viable scenario remain constrained by collider measurements, indicating that these non-leptonic anomalies remain among the most puzzling discrepancies from the SM.