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.