The charm of 331

Abstract: We perform a detailed analysis of flavour changing neutral current processes in the charm sector in the context of 331 models. As pointed out recently, in the case of $Z^\prime$ contributions in these models there are no new free parameters beyond those already present in the $B_{d,s}$ and $K$ meson systems analyzed in the past. As a result, definite ranges for new Physics (NP) effects in various charm observables could be obtained. While generally NP effects turn out to be small, in a number of observables they are much larger than the tiny effects predicted within the Standard Model. In particular we find that the branching ratio of the mode $D^0 \to \mu^+ \mu^-$, despite remaining tiny, can be enhanced by 6 orders of magnitude with respect to the SM. We work out correlations between this mode and rare $B_{d,s}$ and $K$ decays. We also discuss neutral charm meson oscillations and CP violation in the charm system. In particular, we point out that 331 models provide new weak phases that are a necessary condition to have non-vanishing CP asymmetries. In the case of $\Delta A_{CP}$, the difference between the CP asymmetries in $D^0 \to K^+ K^-$ and $D^0 \to \pi^+ \pi^-$, we find that agreement with experiment can be obtained provided that two conditions are verified: the phases in the ranges predicted in 331 models and large hadronic matrix elements.