Coloured Scalars Mediated Rare Charm Meson Decays to Invisible Fermions

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 ($\chi$), is particularly interesting. Then, we consider ${\tilde{R}}_2\equiv (\bar{3},2,1\mathrm{/}6)$, which as a weak doublet is a subject of severe low-energy constraints. The $\chi$ mass is considered in the range $(m_K

• m_\pi)/2\leq m_\chi \leq (m_D - m_\pi)/2$\mathrm{.}Wedeterminebranchingratiosfor$D\to \chi \bar \chi$,$D\to \chi \bar \chi \gamma$and$D\to \pi \chi \chi$forseveral$\chi$masses,usingmostconstrainingbounds\mathrm{.}For$\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 $B\to Kmissingenergy$ . We find in decays mediated by ${\bar{S}}_1$ that branching ratios can be $\mathcal B(D\to \chi \bar \chi)< 10^{-8}$for$m_\chi=0.8$GeV,$\mathcal B(D\to \chi \bar \chi \gamma) \sim 10^{-8}$for$m_\chi=0.18$GeV,while$\mathcal B(D^+ \to \pi^+ \chi \bar \chi )$canreach$ \sim 10^{-8}$for$m_\chi=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.