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 to pi^+ pi^- e^+ e^- transitions. Evidence for direct CP asymmetry has
just appeared in LHCb data on A_{CP}(D^0 to K^+ K^-) - A_{CP}(D^0 to pi^+ pi^-)
with 3.5 sigma significance. Manifestations of New Dynamics (ND) can appear in
CP asymmetries just below experimental bounds. We discuss D^{\pm}_{(s)},
D^0/\bar 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 to h_1 h_2 l^+ l^- in analogy with K_L
to pi^+ pi^- 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 (SM).
More general lessons can be learnt for T asymmetries in non-leptonic D decays
like D to h_1h_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.Comment: 27 pages, 6 figures. Revised with current results from LHCb and HFAG
and further interpretation
