On CP asymmetries in two-, three- and four-body D decays

Abstract

Indirect and direct CP violations have been established in K _L and B _d decays. They have been found in two-body decay channels — with the exception of K _L → π ⁺ π ⁻ e ⁺ e ⁻ transitions. Evidence for direct CP asymmetry has just appeared in LHCb data on A _CP(D ⁰ → K ⁺ K ⁻) − A _CP(D ⁰ → π ⁺ π ⁻) with 3.5σ significance. Manifestations of New Dynamics (ND) can appear in CP asymmetries just below experimental bounds. We discuss $D_{{(s)}}^{\pm }$, ${D^0}/{\overline D^0}$ and D _L /D _S transitions to 2-, 3- and 4-body final states with a comment on predictions for inclusive vs. exclusive CP asymmetries. In particular we discuss T asymmetries in D → h ₁ h ₂ l ⁺ l ⁻ in analogy with K _L → π ⁺ π ⁻ e ⁺ e ⁻ transitions due to interference between M1, internal bremsstrahlung and possible E1 amplitudes. Such an effect depends on the strength of CP violation originating from the ND — as discussed here for Little Higgs Models with T parity and non-minimal Higgs sectors — but also in the interferences between these amplitudes even in the Standard Model. More general lessons can be learnt for T asymmetries in non-leptonic D decays like D → h ₁ h ₂ h ₃ h ₄. Such manifestations of ND can be tested at LHCb and other Super-Flavour Factories like the projects at KEK near Tokyo and at Tor Vergata/Frascati near Rome.