D^0 -> gamma gamma and D^0 -> mu^+ mu^- Rates on an Unlikely Impact of the Littlest Higgs Model with T-Parity

The decays D^0 -> gamma gamma, $mu^+ mu^- are highly suppressed in the Standard Model (SM) with the lion's share of the rate coming from long distance dynamics; D^0 -> mu^+ mu^- is driven predominantly by D^0 -> gamma gamma -> mu^+ mu^-. Their present experimental bounds are small, yet much larger than SM predictions. New Physics models like the Littlest Higgs models with T parity (LHT) can induce even large indirect CP violation in D^0 transitions. One would guess that LHT has a `fighting chance' to affect these D^0 -> gamma gamma, mu^+ mu^- rates in an observable way. We have found LHT contributions can be much larger than short distance SM amplitude by orders of magnitude. Yet those can barely compete with the long distance SM effects. If D^0 -> gamma gamma, mu^+ mu^- modes are observed at greatly enhanced rates, LHT scenarios will not be candidates for generating such signals. LHT-like frameworks will not yield larger D^0 rightarrow gamma gamma/mu^+ mu^- rates as they are constrained by B and K rare decays.