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Exploiting CP-asymmetries in rare charm decays

We analyze patterns from CP-violating new physics (NP) in hadronic and semileptonic rare charm $\vert Δc \vert=\vert Δu\vert=1$ transitions. Observation of direct CP-violation in hadronic decays, as in $ΔA_{\text{CP}}$, provides opportunities for $c \to u \,\ell^+ \ell^-$, $\ell=e,μ$ transitions, and vice versa. For the concrete case of flavorful, anomaly-free $Z^\prime$-models a NP-interpretation of $ΔA_{\text{CP}}$ suggests measurable CP-asymmetries in semileptonic decays such as $D \to π\, \ell^+ \ell^-$ or $D \to ππ\, \ell^+ \ell^-$. Conversely, an observation of CP-violation in $c \to u\, e^+ e^-$ or $c \to u\, μ^+ μ^-$ decays supports a NP--interpretation of $ΔA_{\text{CP}}$. Flavorful $U(1)^\prime$-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 $D^0 \to π^+ π^-$, $D^0 \to K^+ K^-$ and $D^0 \to π^0 π^0$, $D^+ \to π^+ π^0$ decays, which can be probed in the future at LHCb and Belle II and provide further informative cross checks.