Coupled-channel approach to $T_{cc}^{+}$ including three-body effects

Abstract

A coupled-channel approach is applied to the charged tetraquark state $T_{cc}^{+}$ recently discovered by the LHCb Collaboration. The parameters of the interaction are fixed by a fit to the observed line shape in the three-body $D^0{D}^0{\pi }^{+}$ channel. Special attention is paid to the three-body dynamics in the $T_{cc}^{+}$ due to the finite life time of the $D^{\ast }$. An approach to the $T_{cc}^{+}$ is argued to be self-consistent only if both manifestations of the three-body dynamics, the pion exchange between the $D$ and $D^{\ast }$ mesons and the finite $D^{\ast }$ width, are taken into account simultaneously to ensure that three-body unitarity is preserved. This is especially important to precisely extract the pole position in the complex energy plane whose imaginary part is very sensitive to the details of the coupled-channel scheme employed. The $D^0{D}^0$ and $D^0{D}^{+}$ invariant mass distributions, predicted based on this analysis, are in good agreement with the LHCb data. The low-energy expansion of the $D^{\ast }D$ scattering amplitude is performed and the low-energy constants (the scattering length and effective range) are extracted. The compositeness parameter of the $T_{cc}^{+}$ is found to be close to unity, which implies that the $T_{cc}^{+}$ is a hadronic molecule generated by the interactions in the $D^{\ast +}{D}^0$ and $D^{\ast 0}{D}^{+}$ channels. Employing heavy-quark spin symmetry, an isoscalar $D^{\ast }{D}^{\ast }$ molecular partner of the $T_{cc}^{+}$ with $J^P=1^{+}$ is predicted under the assumption that the $D{D}^{\ast }$-$D^{\ast }{D}^{\ast }$ coupled-channel effects can be neglected.

28 pages, 8 figures. Version published in Phys. Rev. D

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• Doubly Charmed Tetraquark $T_{cc}^{+}$ from Lattice QCD near Physical Point
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• Triangle Singularity in the Production of $T_{cc}^{+}$(3875) and a Soft Pion
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• Heavy Flavour Physics and CP Violation at LHCb: a Ten-Year Review
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• Masses and widths of the exotic molecular $B_{(s)}^{(\ast )}{B}_{(s)}^{(\ast )}$ states
• The quasi-fission phenomeonon of double charm $T_{cc}^{+}$ induced by nucleon
• Heavy- and light-flavor symmetry partners of the $T_{cc}^{+}(3875)$, the $X(3872)$ and the $X(3960)$ from light-meson exchange saturation
• New insight into the exotic states strongly coupled with the $D{\bar{D}}^{\ast }$ from the $T_{cc}^{+}$
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• Near-threshold states in coupled $D{D}^{\ast }-D^{\ast }{D}^{\ast }$ scattering from lattice QCD
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• 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
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• Doubly heavy tetraquark bound and resonant states
• Hadronic decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$
• Three-body molecules $\bar{D}{\bar{D}}^{\ast }{\Sigma }_c$- understanding the nature of $T_{cc}$, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• The role of the pion in the lineshape of the $X(3872)$
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• Doubly heavy tetraquark states in a mass splitting model
• Searching for doubly charmed tetraquark candidates $T_{cc}$ and $T_{cc\bar{s}}$ in $B_c$ decays
• Photo- and electro-production of narrow exotic states: from light quarks to charm and up to bottom
• Molecular states of $D^{\ast }{D}^{\ast }{\bar{K}}^{\ast }$ nature
• Flavor Physics at the CEPC: a General Perspective
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• Doubly-Charged $T_{cc}^{++}$ States in the Dynamical Diquark Model
• Semi-inclusive electroproduction of hidden-charm and double-charm hadronic molecules
• Magnetic dipole moments of $B_{(s)}^{(\ast )}{B}_{(s)}^{(\ast )}$ states
• Entanglement suppression and low-energy scattering of heavy mesons
• hidden charm decays of $X(4014)$ in a $D^{\ast }{\bar{D}}^{\ast }$ molecule scenario
• Study of exotic hadrons with machine learning
• Substructure of Multiquark Hadrons (Snowmass 2021 White Paper)
• Lattice study of $cc\bar{u}\bar{s}$ tetraquark channel in $D^{(\ast )}{D}_s^{(\ast )}$ scattering
• The study of possible molecular states of $D_s^{(\ast )}{D}_s^{(\ast )}$ and $B_s^{(\ast )}{B}_s^{(\ast )}$
• Isospin violation effect and three-body decays of the $T_{cc}^{+}$ state
• Binding of the three-hadron $D{D}^{\ast }K$ system from the lattice effective field theory
• Molecular states in $D_s^{(\ast )+}{\Xi }_c^{{(}^{\prime },\ast )}$ systems
• Radiative decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$
• Investigating the Isospin Property of $T_{cc}^{+}$ from its Dalitz Plot Distribution
• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Predictions of super-exotic heavy mesons from $K^{\ast }{B}^{\ast }{B}^{\ast }$ interactions
• Classification of Coupled-Channel Near-Threshold Structures
• Hunting for the prospective $T_{cc}$ family based on the diquark-antidiquark configuration
• Investigation on the bottom analogs of the $T_{cc}^{+}$
• Model-independent predictions for decays of double-heavy hadrons into pairs of heavy hadrons
• Strong decays of $P_{\psi }^N(4440{)}^{+}$ and $P_{\psi }^N(4457{)}^{+}$ within the Bethe-Salpeter framework
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• Low-energy $DD$ scattering in lattice QCD
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