Exotic triple-charm deuteronlike hexaquarks

Adopting the one-boson-exchange model, we perform a systematic investigation of interactions between a doubly charmed baryon $({\mathrm{\Xi }}_{cc})$ and an $S$-wave charmed baryon (${\mathrm{\Lambda }}_c$, ${\mathrm{\Sigma }}_c^{(*)}$, and ${\mathrm{\Xi }}_c^{(\prime ,*)}$). Both the $S-D$ mixing effect and coupled-channel effect are considered in this work. Our results suggest that there may exist several possible triple-charm deuteronlike hexaquarks. Meanwhile, we further study the interactions between a doubly charmed baryon and an $S$-wave anticharmed baryon. We find that a doubly charmed baryon and an $S$-wave anticharmed baryon can be easily bound together to form shallow molecular hexaquarks. These heavy flavor hexaquarks predicted here can be accessible at future experiment like LHCb.

Figure 1

Charmed baryons in ${\overline{3}}_F$ and $6_F$ representations and doubly charmed baryons. Here, we define $[q_1{q}_2]=\frac{1}{\sqrt{2}}(q_1{q}_2-q_2{q}_1)$ and $\{q_1{q}_2\}=\frac{1}{\sqrt{2}}(q_1{q}_2+q_2{q}_1)$.

Figure 2

The $r$ dependence of the deduced effective potentials for the ${\mathrm{\Xi }}_{cc}{\mathrm{\Lambda }}_c$ system with $I(J^P)=1/2(0^{+})$ and the ${\mathrm{\Xi }}_{cc}{\mathrm{\Xi }}_c$ system with $I(J^P)=0(0^{+})$. Here, we take the cutoff $\mathrm{\Lambda }=1.00\mathrm{GeV}$.

Figure 3

Bound state solutions (binding energy $E$ and RMS radius $r_{\mathrm{RMS}}$) for the ${\mathrm{\Xi }}_{cc}{\mathrm{\Xi }}_c$ system with $I(J^P)=0(0^{+}/1^{+})$.

Figure 4

$\mathrm{\Lambda }$ dependence of binding energy $E$ for the ${\mathrm{\Xi }}_{cc}{\mathrm{\Sigma }}_c^{(*)}$ and ${\mathrm{\Xi }}_{cc}{\mathrm{\Xi }}_c^{(\prime ,*)}$ systems.

Figure 5

Left: Bound state properties (binding energy $E$ and root-mean-square radius $r_{\mathrm{RMS}}$) for all of the ${\mathrm{\Xi }}_{cc}{\mathrm{\Lambda }}_c/{\mathrm{\Xi }}_{cc}{\mathrm{\Sigma }}_c/{\mathrm{\Xi }}_{cc}{\mathrm{\Sigma }}_c^{*}$ systems when the coupled channel effect is included in our calculation. Right: Probability for the different channels.

Figure 6

Left: Bound state properties (binding energy $E$ and root-mean-square radius $r_{\mathrm{RMS}}$) for all of the ${\mathrm{\Xi }}_{cc}{\mathrm{\Xi }}_c/{\mathrm{\Xi }}_{cc}{\mathrm{\Xi }}_c^{\prime }/{\mathrm{\Xi }}_{cc}{\mathrm{\Xi }}_c^{*}$ systems when the coupled channel effect is included in our calculation. Right: Probability for the different channels.