D⁰ → γγ and D⁰ → μ⁺μ^- rates on an unlikely impact of the littlest Higgs model with T parity

The decays D⁰ → γγ, μ⁺μ ^- are highly suppressed in the standard model (SM) with the lion's share of the rate coming from long distance dynamics; D⁰ → μ⁺μ^- is driven predominantly by D⁰ → γγ → μ⁺μ^-. 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 D⁰ transitions. One would guess that LHT has a "fighting chance" to affect these D⁰ → γγ, μ⁺μ^- 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 D⁰ → γγ, μ⁺μ ^- modes are observed at greatly enhanced rates, LHT scenarios will not be candidates for generating such signals. LHT-like frameworks will not yield larger D⁰ → γγ / μ⁺μ ^- rates as they are constrained by B and K rare decays.