Possible $\bar{D}^{(*)} Ξ_{cc}^{(*)}$ and $Ξ_{cc}^{(*)}Ξ_{cc}^{(*)}$ molecules as superflavor partners of $T_{cc}$

Abstract

The doubly charmed tetraquark $T_{cc}$ has been reported by the LHCb experiment in 2022, and a lot of theoretical studies has been conducted. The small binding energy measured from $D^{\ast + }D^0$ threshold indicates that $T_{cc}$ is a $DD^\ast$ molecule. On the other hand, the superflavor symmetry, which relates heavy antiquarks to heavy diquarks, provides a useful framework for predicting the existence of partner exotic hadrons associated with $T_{cc}$. By replacing $\bar{D}^{(*)}$ with $Ξ_{cc}^{(*)}$ within this symmetry, $\bar{D}^{(*)} Ξ_{cc}^{(*)}$ and $Ξ_{cc}^{(*)}Ξ_{cc}^{(*)}$ are expected to form partner structures of $T_{cc}$. In this paper, we investigate bound and resonant states of $\bar{D}^{(*)} Ξ_{cc}^{(*)}$ and $Ξ_{cc}^{(*)}Ξ_{cc}^{(*)}$ based on the one boson exchange potential, where $π$, $ρ$, $ω$ and $σ$ are considered as bosons. The cutoff parameter and the coupling constants for $\bar{D}^{(*)} Ξ_{cc}^{(*)}$ and $Ξ_{cc}^{(*)}Ξ_{cc}^{(*)}$ are taken to be the same as those for $T_{cc}$ due to superflavor symmetry. We also discuss the $σ$ coupling constant, which is uncertain, dependence of these mass spectra. A lot of bound and resonant states with some quantum numbers are obtained for each $σ$ coupling constant, but these mass spectra depend on the $σ$ coupling constant significantly.

Figures (6)

• Figure 1: Masses of the isoscalar $\bar{D}^{(\ast)}\Xi^{(\ast)}_{cc}$ with $\frac{1}{2}^-$, $\frac{3}{2}^-$ and $\frac{5}{2}^-$. The black dotted line shows the thresholds. The red circle and magenta cross show the masses of the bound states with $g_\sigma^L$ and $g_\sigma^S$, respectively. The blue upward triangles and green downward triangles show the masses of the resonances with $g_\sigma^L$ and $g_\sigma^S$, respectively. Numerical values displayed in the figure correspond to the eigenvalues $-B$ for bound states and $E_r - i\frac{\Gamma}{2}$ for resonances. The values are given in units of MeV.
• Figure 2: Wavefunctions of $\bar{D}^{(\ast)}\Xi^{(\ast)}_{cc}$ with $I(J^P) = 0(\frac{1}{2}^-)$. The left panel shows the wavefunction of $\bar{D}^{(\ast)}\Xi^{(\ast)}_{cc}$ with $g_\sigma^L$, while right one shows the wavefunction of $\bar{D}^{(\ast)}\Xi^{(\ast)}_{cc}$ with $g_\sigma^S$. The red, magenta, blue and green lines show the wavefunctions for $\bar{D}\Xi_{cc}$, $\bar{D}\Xi_{cc}^\ast$, $\bar{D}^\ast\Xi_{cc}$ and $\bar{D}^\ast\Xi_{cc}^\ast$.
• Figure 3: $g_\sigma$ dependence of the expectation values of the Hamiltonian and OBEP for $\bar{D}^{(\ast)}\Xi^{(\ast)}_{cc}$ with $0(\frac{1}{2}^-)$. The solid line shows the expectation value of the Hamiltonian $\braket{H}$, which is equivalent to the binding energy of $\bar{D}^{(\ast)}\Xi^{(\ast)}_{cc}$, while the other lines show the expectation values of the one boson exchange potentials denoted by $\braket{V^\pi}$, $\braket{V^\rho}$, $\braket{V^\omega}$ and $\braket{V^\sigma}$. The cutoff parameter is determined to reproduce the binding energy of $T_{cc}$ for each $g_\sigma$.
• Figure 4: Masses of $\Xi^{(\ast)}_{cc}\Xi^{(\ast)}_{cc}$ with $0(1^+)$, $0(2^+)$, $1(0^+)$, $1(1^+)$ and $1(2^+)$. The same notation as Fig. \ref{['fig;mass_DXi']} is used.
• Figure 5: Wavefunctions of $\Xi^{(\ast)}_{cc}\Xi^{(\ast)}_{cc}$ with $I(J^P) = 0(1^+)$. The left panel shows the wavefunction of $\Xi^{(\ast)}_{cc}\Xi^{(\ast)}_{cc}$ with $g_\sigma^L$, while right one shows the wavefunction of $\Xi^{(\ast)}_{cc}\Xi^{(\ast)}_{cc}$ with $g_\sigma^S$. The red, blue and green lines show the wavefunctions for $\Xi_{cc}\Xi_{cc}$, $[\Xi_{cc}\Xi_{cc}^\ast]_\pm$ and $\Xi_{cc}^\ast\Xi^\ast_{cc}$, respectively.