B anomalies and dark matter: a complex connection

We study an extension of the Standard Model that addresses the hints of lepton flavour universality violation observed in $B\to K^{(*)} l^+l^-$ decays at LHCb, while providing a viable candidate for dark matter. The model incorporates two new scalar fields and a Majorana fermion that induce one-loop contributions to $B$ meson decays. We show that agreement with observational data requires the new couplings to be complex and that the Majorana fermion can reproduce the observed dark matter relic density. This combination of cosmological and flavour constraints sets an upper limit on the dark matter and mediator masses. We have studied LHC dijet and dilepton searches, finding that they rule out large regions of parameter space by setting lower bounds on the dark matter and mediator masses. In particular, dilepton bounds are much more constraining in a future high-luminosity phase. Finally, we have computed the scattering cross section of dark matter off nuclei and compared it to the sensitivity of current and future direct detection experiments, showing that parts of the parameter space could be accessible in the future to multi-ton experiments. Future collider and direct DM searches complement each other to probe large areas of the parameter space of this model.