arXiv2021
We consider effects of coloured scalar mediators in decays $c\to u \, {\it invisibles}$. In particular, in these processes, as invisibles, we consider massive right-handed fermions. The coloured scalar $\bar S_1\equiv (\bar 3, 1, -2/3)$, due to its coupling to weak singlets up-quarks and invisible right-handed fermions ($χ$), is particularly interesting. Then, we consider $\tilde R_2 \equiv (\bar 3, 2, 1/6)$, which as a weak doublet is a subject of severe low-energy constraints. The $χ$ mass is considered in the range $(m_K - m_π)/2\leq m_χ\leq (m_D - m_π)/2$. We determine branching ratios for $D\to χ\bar χ$, $D\to χ\bar χγ$ and $D\to πχχ$ for several $χ$ masses, using most constraining bounds. For $\bar S_1$, the most constraining is $D^0 -\bar D^0$ mixing, while in the case of $\tilde R_2$ the strongest constraint comes from $B\to K {\it missing\, energy}$ . We find in decays mediated by $\bar S_1$ that branching ratios can be $\mathcal B(D\to χ\bar χ)< 10^{-8}$ for $m_χ=0.8$ GeV, $\mathcal B(D\to χ\bar χγ) \sim 10^{-8}$ for $m_χ=0.18$ GeV, while $\mathcal B(D^+ \to π^+ χ\bar χ)$ can reach $ \sim 10^{-8}$ for $m_χ=0.18$ GeV. In the case of $\tilde R_2$ these decay rates are very suppressed. We find that future tau-charm factories and Belle II experiments offer good opportunities to search for such processes. Both $\bar S_1$ and $\tilde R_2$ might have masses within LHC reach.