Quark mixing in the discrete dark matter model

We consider a model in which dark matter is stable as it is charged under a Z2 symmetry that is residual after an A4 flavour symmetry is broken. We consider the possibility to generate the quark masses by charging the quarks appropriately under A4. We find that it is possible to generate the CKM mixing matrix by an interplay of renormalisable and dimension-six operators. In this set-up, we predict the third neutrino mixing angle to be large and the dark matter relic density to be in the correct range. Low energy observables - in particular meson-antimeson oscillations - are hard to facilitate. We find that only in a situation where there is a strong cancellation between the Standard Model contribution and the contribution of the new Higgs fields, B meson oscillations are under control.