Coloured Scalars Mediated Rare Charm Meson Decays to Invisible Fermions

Abstract

We consider effects of coloured scalar mediators in decays $c\to uinvisibles$. 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 $(m_K-m_{\pi })/2\le m_{\chi }\le (m_D-m_{\pi })/2$. 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 $B\to Kmissingenergy$ . 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 $\mathcal{B}(D^{+}\to {\pi }^{+}\chi \bar{\chi })$ 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.

arXiv comment8 pages, 4 figures

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