Old and new anomalies in charm

Abstract

The recent LHCb determination of the direct CP asymmetries in the decays $D^0 \to K^+ K^-, \pi^+ \pi^-$ hints at a sizeable breaking of two approximate symmetries of the SM: CP and U-spin. We aim at explaining the data with BSM physics and use the framework of flavorful $Z^\prime$ models. Interestingly, experimental and theoretical constraints very much narrow down the shape of viable models: Viable, anomaly-free models are electron- and muon-phobic and feature a light $Z^\prime$ of 10-20 GeV coupling only to right-handed fermions. The $Z^\prime$ can be searched for in low mass dijets or at the LHC as well as dark photon searches. A light $Z^\prime$ of $\sim$ 3 GeV or $\sim$ 5-7 GeV can moreover resolve the longstanding discrepancy in the $J/\psi, \psi^\prime$ branching ratios with pion form factors from fits to $e^+ e^- \to \pi^+ \pi^-$ data, and simultaneously explain the charm CP asymmetries. Smoking gun signatures for this scenario are $\Upsilon$ and charmonium decays into pions, taus or invisbles.