Exploiting CP-asymmetries in rare charm decays

We analyze patterns from CP-violating new physics (NP) in hadronic and semileptonic rare charm $\mathrm{\mid }\mathrm{\Delta }c\mathrm{\mid }=\mathrm{\mid }\mathrm{\Delta }u\mathrm{\mid }=1$ transitions. Observation of direct CP-violation in hadronic decays, as in $\mathrm{\Delta }{A}_{\text{CP}}$, provides opportunities for $c\to u{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$, $\mathrm{\ell }=e,\mu$ transitions, and vice versa. For the concrete case of flavorful, anomaly-free $Z^{\mathrm{\prime }}$-models a NP-interpretation of $\mathrm{\Delta }{A}_{\text{CP}}$ suggests measurable CP-asymmetries in semileptonic decays such as $D \to \pi, \ell^+ \ell^-$or$D \to \pi \pi, \ell^+ \ell^-$. Conversely, an observation of CP-violation in $c\to u{e}^{+}{e}^{-}$ or $c\to u{\mu }^{+}{\mu }^{-}$ decays supports a NP–interpretation of $\mathrm{\Delta }{A}_{\text{CP}}$. Flavorful $U(1{)}^{\mathrm{\prime }}$-extensions provide explicit U–spin and isospin breaking which can be probed in patterns of hadronic decays of charm mesons. We work out signatures for CP-asymmetries in $D^0\to {\pi }^{+}{\pi }^{-}$, $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^0{\pi }^0$, $D^{+}\to {\pi }^{+}{\pi }^0$ decays, which can be probed in the future at LHCb and Belle II and provide further informative cross checks.