Conclusions from CDF results on CP violation in D 0 → π + π −, K + K − and future tasks

Abstract

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 \( \mathcal{O}\left( {{{10}^{ - 4}}} \right) \), probably even \( \mathcal{O}\left( {{{10}^{ - 5}}} \right) \); direct effects are estimated at not larger than 10−4. At B factories direct and indirect asymmetries have been studied with \( {{{\left\langle t \right\rangle }} \left/ {{{\tau_{{D^0}}}}} \right.} \simeq 1 \); 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 \( {{{\left\langle t \right\rangle }} \left/ {{{\tau_{{D^0}}}}} \right.} \simeq 2.4 \) [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 \( a_{\text{CP}}^{\text{ind}} = \left( { - 0.01\pm {{0.06}_{\text{stat}}}\pm {{0.05}_{\text{syst}}}} \right)\% \) 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.