CP violation in D0-(D)over-bar0 oscillations: general considerations and applications to the Littlest Higgs model with T-parity

The observed D-0 - (D) over bar (0) oscillations provide a new stage in our search for New Physics in heavy flavour dynamics. The theoretical verdict on the observed values of x(D) and y(D) remains ambiguous: while they could be totally generated by Standard Model dynamics, they could also contain a sizable or even leading contribution from New Physics. Those oscillations are likely to enhance the observability of CP violation as clear manifestations of New Physics. We present general formulae for D-0 - (D) over bar (0) oscillations, concentrating on the case of negligible direct CP violation. In particular we derive a general formula for the time-dependent mixing-induced CP asymmetry in decays to a CP eigenstate and its correlation with the semileptonic CP asymmetry a(SL)(D-0) in D-0(t) -> lvK. We apply our formalism to the Littlest Higgs model with T-parity, using the time-dependent CP asymmetry in D-0 -> K-S phi as an example. We find observable effects at a level well beyond anything possible with CKM dynamics. Comparisons with CP violation in the K and B systems offer an excellent test of this scenario and reveal the specific pattern of flavour and CP violation in the D-0 - (D) over bar (0) system predicted by this model. We discuss a number of charm decays that could potentially offer an insight in the dynamics of CP violation in D decays. We also apply our formalism to B-s - (B) over bar (s) mixing.