Coloured Scalars Mediated Rare Charm Meson Decays to Invisible Fermions

TL;DR

This paper investigates how coloured scalar mediators could induce rare charm meson decays into invisible fermions, providing predictions for branching ratios and discussing experimental constraints and detection prospects.

Contribution

It introduces new decay channels mediated by coloured scalars involving invisible fermions, with detailed analysis of constraints and potential experimental signatures.

Findings

Branching ratios for $D$ decays to invisible fermions can reach $10^{-8}$.

Constraints from $D^0-ar D^0$ mixing and $B o K$ missing energy are significant.

Future experiments like Belle II and tau-charm factories can probe these decay modes.

Abstract

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 $\tilde R_2 \equiv (\bar 3, 2, 1/6)$, which as a weak doublet is a subject of severe low-energy constraints. The $\chi$ mass is considered in the range $(m_K - m_\pi)/2\leq m_\chi \leq (m_D - m_\pi)/2$. We determine branching ratios for $D\to \chi \bar \chi$, $D\to \chi \bar \chi \gamma$ and $D\to \pi \chi \chi$ for several $\chi$ 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 $\mathcal B(D\to \chi \bar \chi)< 10^{-8}$ for $m_\chi=0.8$ GeV, $\mathcal B(D\to \chi \bar \chi \gamma) \sim 10^{-8}$ for $m_\chi=0.18$ GeV, while $\mathcal B(D^+ \to \pi^+ \chi \bar \chi )$ can reach $ \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.