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 D 0 → π + π − , K + K − transitions, although the effects are tiny: Indirect CP asymmetry cannot exceed , probably even ; direct effects are estimated at not larger than 10 −4 . At B factories direct and indirect asymmetries have been studied with ; no CP asymmetry was found with an upper bound of about 1%. CDF has shown intriguing data on CP violation in D 0 → π + π − [ K + K − ] with [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 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.