Two-pion exchange for coupled-channel scattering of two heavy mesons

Abstract

To improve the theoretical understanding of multiquark states like $Z_b(10610)$ and $Z_b(10650)$, we calculate the heavy-meson heavy-(anti)meson scattering potential up to next-to-leading order, $O(Q^2)$, within chiral effective field theory ($\chi$EFT) employing a power counting scheme that explicitly keeps track with the large momentum scale $Q\sim \sqrt{2\mu \delta }$ (where $\delta =m_V-m_P$ is the vector-pseudoscalar mass difference and $\mu$ their reduced mass) introduced by the coupled channel dynamics. We provide expressions for the two-pion exchange (TPE) terms up to $O(Q^2)$ and their partial-wave decomposition. We show that these potentials are well-approximated by contact terms at $O(Q^2)$, with minor residual non-analytic TPE contributions, supporting $\chi$EFT convergence in the theoretical predictions for $Z_b(10610)$ and $Z_b(10650)$, as well as their spin partners. These findings are also relevant for $D^{(\ast )}{D}^{(\ast )}$ scattering, especially for the $T_{cc}$ state, for both physical and lattice QCD data with moderately larger pion masses. We further demonstrate that the differences between isovector and isoscalar potentials for heavy mesons are naturally explained by the TPE contributions.

41 pages, 18 figures

References in corpus (32)

• Chiral effective field theory and nuclear forces
• Multiquark Resonances
• Pentaquark and Tetraquark states
• Exotics: Heavy Pentaquarks and Tetraquarks
• An updated review of the new hadron states
• Observation of a resonance-like structure in the pi^+- psi' mass distribution in exclusive B-->K pi^+- psi' decays
• Observation of the resonant character of the $Z(4430{)}^{-}$ state
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Pion Interactions in the X(3872)
• Coupled-channel approach to $T_{cc}^{+}$ including three-body effects
• Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• Signature of a doubly charm tetraquark pole in $D{D}^{\ast }$ scattering on the lattice
• Doubly Charmed Tetraquark $T_{cc}^{+}$ from Lattice QCD near Physical Point
• On the nature of near-threshold bound and virtual states
• Interplay of quark and meson degrees of freedom in a near-threshold resonance
• Effective range expansion for narrow near-threshold resonances
• Study of $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ interactions in $I=1$ and relationship to the $Z_b(10610)$, $Z_b(10650)$ states
• Is the existence of a $J/\psi J/\psi$ bound state plausible?
• Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction
• ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ interactions in chiral effective field theory
• Revisiting the $D{D}^{\ast }$ chiral interactions with the local momentum-space regularization up to the third order and the nature of $T_{cc}^{+}$
• Precision lattice QCD computation of the $B^{\ast }B\pi$ coupling
• Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ from finite volume energy levels
• Towards the quark mass dependence of $T_{cc}^{+}$ from lattice QCD
• Generalized weak-binding relations of compositeness in effective field theory
• Spin partners $W_{bJ}$ from the line shapes of the $Z_b(10610)$ and $Z_b(10650)$
• Two-body wave functions and compositeness from scattering amplitudes. I. General properties with schematic models
• Deciphering the charged heavy quarkoniumlike states in chiral effective field theory
• Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from ${\rm Y}(10860)$
• How does the $X(3872)$ show up in $e^{+}{e}^{-}$ collisions: dip versus peak
• On the emergence of heavy quark spin symmetry breaking in heavy quarkonium decays

Cited by in corpus (5)

• $bb\bar{u}\bar{d}$ and $bs\bar{u}\bar{d}$ tetraquarks from lattice QCD using two-meson and diquark-antidiquark variational basis
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
• Scattering Theory
• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints