Exploiting CP-asymmetries in rare charm decays

Abstract

We analyze patterns from CP-violating new physics (NP) in hadronic and semileptonic rare charm $|\Delta c|=|\Delta u|=1$ transitions. Observation of direct CP-violation in hadronic decays, as in $\Delta A_{\text{CP}}$, provides opportunities for $c\to u{\ell }^{+}{\ell }^{-}$, $\ell =e,\mu$ transitions, and vice versa. For the concrete case of flavorful, anomaly-free $Z^{\prime }$-models a NP-interpretation of $\Delta A_{\text{CP}}$ 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 $\Delta A_{\text{CP}}$. 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 $D^0\to {\pi }^{+}{\pi }^{-}$, $D^0\to K^{+}{K}^{-}$ 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.

13 pages, 5 figures