Possible triple-charm molecular pentaquarks from ${\mathrm{\Xi }}_{cc}{D}_1/{\mathrm{\Xi }}_{cc}{D}_2^{*}$ interactions

In this work, we explore a systematic investigation on $S$-wave interactions between a doubly charmed baryon ${\mathrm{\Xi }}_{cc}(3621)$ and a charmed meson in a $T$ doublet $(D_1,D_2^{*})$. We first analyze the possibility for forming ${\mathrm{\Xi }}_{cc}{D}_1/{\mathrm{\Xi }}_{cc}{D}_2^{*}$ bound states with the heavy quark spin symmetry. Then, we further perform a dynamical study on the ${\mathrm{\Xi }}_{cc}{D}_1/{\mathrm{\Xi }}_{cc}{D}_2^{*}$ interactions within a one-boson-exchange model by considering both the $S-D$ wave mixing and coupled channel effect. Finally, our numerical results conform the proposals from the heavy quark spin symmetry analysis: the ${\mathrm{\Xi }}_{cc}{D}_1$ systems with $I(J^P)=0(1/2^{+},3/2^{+})$ and the ${\mathrm{\Xi }}_{cc}{D}_2^{*}$ systems with $I(J^P)=0(3/2^{+},5/2^{+})$ can possibly be loose triple-charm molecular pentaquarks. Meanwhile, we also extend our model to the ${\mathrm{\Xi }}_{cc}{\overline{D}}_1$ and ${\mathrm{\Xi }}_{cc}{\overline{D}}_2^{*}$ systems, and our results indicate the isoscalars of ${\mathrm{\Xi }}_{cc}{\overline{D}}_1$ and ${\mathrm{\Xi }}_{cc}{\overline{D}}_2^{*}$ can be possible molecular candidates.

Figure 1

Diagram for $9-j$ coefficients in a heavy quark basis. Here, $j_1$ and $j_2$ are the spins for the doubly-charmed baryon and charmed meson, respectively. Inside the hadrons, $s_1$ and $s_2$ stand for the spins of the heavy quarks, while $l_1$ and $l_2$ are the total angular momentum for the light quarks. $l_2=3/2$ for $D_1/D_2^{*}$ mesons, and $l_2=1/2$ for $D/D^{*}$ mesons.

Figure 2

The effective potential for the ${\mathrm{\Xi }}_{cc}{D}_1$ system with $I(J^P)=0(1/2^{+})$, and cutoff $\mathrm{\Lambda }$ is fixed as 1.00 GeV. Here, $V_{11}(\mathbf{r})=⟨{{}^2\mathbb{S}}_{\frac{1}{2}}|{\mathcal{V}}^{{\mathrm{\Xi }}_{cc}{D}_1\to {\mathrm{\Xi }}_{cc}{D}_1}(\mathbf{r})|{{}^2\mathbb{S}}_{\frac{1}{2}}⟩$, $V_{12}(\mathbf{r})=⟨{{}^4\mathbb{D}}_{\frac{1}{2}}|{\mathcal{V}}^{{\mathrm{\Xi }}_{cc}{D}_1\to {\mathrm{\Xi }}_{cc}{D}_1}(\mathbf{r})|{{}^2\mathbb{S}}_{\frac{1}{2}}⟩$, and $V_{22}(\mathbf{r})=⟨{{}^4\mathbb{D}}_{\frac{1}{2}}|{\mathcal{V}}^{{\mathrm{\Xi }}_{cc}{D}_1\to {\mathrm{\Xi }}_{cc}{D}_1}(\mathbf{r})|{{}^4\mathbb{D}}_{\frac{1}{2}}⟩$.

Figure 3

$\mathrm{\Lambda }$ dependence of bound state solutions (the binding energy $E$ and root-mean-square radius $r_{\mathrm{rms}}$) for the single ${\mathrm{\Xi }}_{cc}{D}_1$ and ${\mathrm{\Xi }}_{cc}{D}_2^{*}$ systems with all the possible configurations.