Revisiting the $D{D}^{\ast }$ chiral interactions with the local momentum-space regularization up to the third order and the nature of $T_{cc}^{+}$

Abstract

We revisit the $D{D}^{\ast }$ interactions in chiral effective field theory up to the third order for the first time. We deal with the pion-exchanged interactions via local momentum-space regularization, in which we focus on their long-range behaviors through demanding their contributions vanish at the origin in the coordinate space. The short-range contact interactions and subleading pion-charmed meson couplings are estimated with the phenomenological resonance saturation model. The subleading pion-charmed meson couplings are much weaker than those in the pion-nucleon system, thus the $D{D}^{\ast }$ binding mechanism is very different with that of the $NN$ system. We also obtain the analytic structure of the two-pion exchange interactions in the coordinate space, and we find that its asymptotic behavior at long distance is similar to but slightly different with the $NN$ interactions. We get the same asymptotic behavior of the two-pion exchange interaction with that from HAL QCD method but appearing in the longer distance rather than $1<r<2\text{ fm}$. The binding solution only exists in the isoscalar channel. Our calculation supports the molecular interpretation of $T_{cc}^{+}$.

15 pages, 6 figures, and 2 tables

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Cited by in corpus (21)

• Tetraquark bound states in constituent quark models: benchmark test calculations
• Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ from finite volume energy levels
• New insight into the exotic states strongly coupled with the $D{\bar{D}}^{\ast }$ from the $T_{cc}^{+}$
• Doubly heavy tetraquark states in the constituent quark model using diffusion Monte Carlo method
• Spectrum of the molecular tetraquarks: Unraveling the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$
• 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
• Doubly heavy tetraquark bound and resonant states
• Virtual states in the coupled-channel problems with an improved complex scaling method
• Doubly heavy tetraquark states in a mass splitting model
• Doubly-Charged $T_{cc}^{++}$ States in the Dynamical Diquark Model
• Isospin violation effect and three-body decays of the $T_{cc}^{+}$ state
• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Mass and decay width of $T_{ccs}$ from symmetries
• 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
• Investigation on the bottom analogs of the $T_{cc}^{+}$
• Electromagnetic characteristics as probes into the inner structures of the predicted ${\Xi }_c^{{(}^{\prime },\ast )}{D}_s^{(\ast )}$ molecular states
• An alternative way to decipher the nature of the doubly charmed tetraquark $T_{cc}(3875{)}^{+}$: its antiparticle $T_{\bar{c}\bar{c}}(3875{)}^{-}$ photoproduction off nuclei near threshold
• $D^{(\ast )}{\bar{B}}^{(\ast )}$ dynamics in chiral effective field theory
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$