Conclusions from CDF results on CP violation in D⁰ → π⁺π^-,K⁺K^- and future tasks

Within the Standard Model (SM) one predicts both direct and indirect CP violation in D⁰ → π⁺π^-,K ⁺K^- transitions, although the effects are tiny: Indirect CP asymmetry cannot exceed O(10-4), probably even O(10^-5); direct effects are estimated at not larger than 10-4.At B factories direct and indirect asymmetries have been studied with (t)/τD⁰ ≈ 1; no CP asymmetry was found with an upper bound of about 1%.CDF has shown intriguing data on CP violation in D⁰ → π⁺π^-, K⁺K^- with (t)/τD⁰ ≈ 2.4[2.65].Also,CDF has not seen any CP violation.For direct CP asymmetry,CDF has a sensitivity similar to the combination of the B factories,yet for indirect CP violation it yields a significantly smaller sensitivity of aind CP = (-0.01 ± 0.06stat ± 0.05syst)% due to it being based on longer decay times.New Physics models (NP) like Little Higgs Models with T-Parity (LHT) can produce an indirect CP asymmetry up to 1%; CDF's findings thus cover the upper range of realistic NP predictions ̃ 0.1-1%. One hopes that LHCb and a Super-Flavour Factory will probe the lower range down to ̃ 0.01%.Such non-ad-hoc NP like LHT cannot enhance direct CP violation significantly over the SM level in D ⁰ → π⁺π^-,K⁺K^- and D^± → π^±K⁺K ^- transitions,but others might well do so.