Nature of the doubly-charmed tetraquark $T_{cc}^{+}$ in a constituent quark model

Abstract

The recently discovered $T_{cc}^{+}$ is evaluated as a $D{D}^{\ast }$ molecular structure in the $J^P=1^{+}$ sector. A coupled-channels calculation in charged basis, considering the $D^0{D}^{\ast +}$, $D^{+}{D}^{\ast 0}$ and $D^{\ast 0}{D}^{\ast +}$ channels, is done in the framework of a constituent quark model that successfully described other molecular candidates in the charmonium spectrum such as the $X(3872)$. The $T_{cc}^{+}$ is found as a $D^0{D}^{\ast +}$ molecule ($87\%$) with a binding energy of $387$ keV/c${}^2$ and a width of $81$ keV, in agreement with the experimental measurements. The quark content of the state forces the inclusion of exchange diagrams to treat indistinguishable quarks between the $D$ mesons, which are found to be essential to bind the molecule. The $D^0{D}^0{\pi }^{+}$ line shape, scattering lengths and effective ranges of the molecule are also analyzed, which are found to be in agreement with the LHCb analysis. We search for further partners of the $T_{cc}^{+}$ in other charm and bottom sectors, finding different candidates. In particular, in the charm sector we find a shallow $J^P=1^{+}$ $D^{+}{D}^{\ast 0}$ molecule ($83\%$), dubbed $T_{cc}^{\prime }$, just $1.8$ MeV above the $T_{cc}^{+}$ state. In the bottom sector, we find an isoscalar and an isovector $J^P=1^{+}$ bottom partners, as $B{B}^{\ast }$ molecules lying $21.9$ MeV/c${}^2$ ($I=0$) and $10.5$ MeV/c${}^2$ ($I=1$), respectively, below the $B^0{B}^{\ast +}$ threshold.

arXiv comment11 pages, 3 figures, 7 tables

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• Near-threshold states in coupled $D{D}^{\ast }-D^{\ast }{D}^{\ast }$ scattering from lattice QCD
• Doubly heavy tetraquark states in the constituent quark model using diffusion Monte Carlo method
• Masses and Magnetic Moments of Doubly Heavy Tetraquarks via Diffusion Monte Carlo Method
• Higher molecular $P_{\psi s}^{\Lambda /\Sigma }$ pentaquarks arising from the ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}_1/{\Xi }_c^{(\prime ,\ast )}{\bar{D}}_2^{\ast }$ interactions
• Virtual states in the coupled-channel problems with an improved complex scaling method
• Doubly heavy tetraquark states in a mass splitting model
• Electromagnetic properties of the $T_{cc}^{+}$ molecular states
• Molecular states in $D_s^{(\ast )+}{\Xi }_c^{{(}^{\prime },\ast )}$ systems
• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Hunting for the prospective $T_{cc}$ family based on the diquark-antidiquark configuration
• Structure of open-flavour four-quark states in the charm and bottom region
• Investigation of Mass and Decay Characteristics of the Light-Strange Tetraquark
• Coupled-channel scattering of $DD,D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ in isospin-$1$ from lattice QCD
• Lattice study of scattering phase shifts for $D{D}^{\ast }$ and $B{B}^{\ast }$ systems using twisted boundary conditions: Search for bound state formation
• The impact of quark many-body effects on exotic hadrons