Exploiting CP asymmetries in rare charm decays

Abstract

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