Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules

Abstract

We discuss the possible power counting schemes that can be applied in the effective field theory description of heavy meson molecules, such as the X(3872) or the recently discovered Zb(10610) and Zb(10650) states. We argue that the effect of coupled channels is suppressed by at least two orders in the effective field theory expansion, meaning that they can be safely ignored at lowest order. The role of the one pion exchange potential between the heavy mesons, and in particular the tensor force, is also analyzed. By using techniques developed in atomic physics for handling power-law singular potentials, which have been also successfully employed in nuclear physics, we determine the range of center-of-mass momenta for which the tensor piece of the one pion exchange potential is perturbative. In this momentum range, the one pion exchange potential can be considered a subleading order correction, leaving at lowest order a very simple effective field theory consisting only on contact-range interactions.

21 pages, 1 figure

References in corpus (17)

• Chiral effective field theory and nuclear forces
• Observation of two charged bottomonium-like resonances in Y(5S) decays
• Pion Interactions in the X(3872)
• Isospin breaking effects in the X(3872) resonance
• Heavy Quark Symmetry Predictions for Weakly Bound B-Meson Molecules
• Renormalizing Chiral Nuclear Forces: Triplet Channels
• Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Three-body $D\bar{D}\pi$ dynamics for the X(3872)
• Renormalizing Chiral Nuclear Forces: A Case Study of 3P0
• BB Potentials in Quenched Lattice QCD
• Strong D* -> D+pi and B* -> B+pi couplings
• Renormalization Group Analysis of Boundary Conditions in Potential Scattering
• Axial couplings and strong decay widths of heavy hadrons
• Coupled-channel effective field theory and proton-${}^7$Li scattering
• Precision study of B^* Bπcoupling for the static heavy-light meson
• Determination of the strong coupling $g_{B^{\ast }B\pi }$ from semi-leptonic $B\to \pi \ell \nu$ decay

Cited by in corpus (87)

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• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules
• Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• Heavy-quark spin and flavour symmetry partners of the X(3872) revisited: what can we learn from the one boson exchange model?
• The hidden charm pentaquark states and ${\Sigma }_c{\bar{D}}^{(\ast )}$ interaction in chiral perturbation theory
• Exploring the threshold behavior and implications on the nature of Y(4260) and $Z_c(3900)$
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• Employing spin symmetry to disentangle different models for the XYZ states
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• Strange molecular partners of the $Z_c(3900)$ and $Z_c(4020)$
• Hidden-charm and bottom tetra- and pentaquarks with strangeness in the hadro-quarkonium and compact tetraquark models
• One pion exchange and the quantum numbers of the Pc(4440) and Pc(4457) pentaquarks
• Decays of $P_c$ into $J/\psi N$ and ${\eta }_{c}N$ with heavy quark spin symmetry
• $D{D}^{\ast }$ potentials in chiral perturbation theory and possible molecular states
• Decay widths of the spin-2 partners of the X(3872)
• Quarkonium Contribution to Meson Molecules
• X(3872) in the molecular model
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• The line shapes of the $Z_b(10610)$ and $Z_b(10650)$ in the elastic and inelastic channels revisited
• Can discovery of hidden charm strange pentaquark states help determine the spins of $P_c(4440)$ and $P_c(4457)$?
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• 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
• Structure of the $\mathbf{\Lambda }(1405)$ from Hamiltonian effective field theory
• General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions
• Detecting the long-distance structure of the X(3872)
• Heavy Antiquark--Diquark Symmetry and Heavy Hadron Molecules: Are There Triply Heavy Pentaquarks?
• New Ideas in Constraining Nuclear Forces
• Heavy-Quark Symmetry Partners of the Pc(4450) Pentaquark
• ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ interactions in chiral effective field theory
• Heavy Baryon-Antibaryon Molecules in Effective Field Theory
• How to understand the $X(2900)$?
• Threshold corrections of ${\chi }_{\mathrm{c}}(2P)$ and ${\chi }_{\mathrm{b}}(3P)$ states and $J/\psi \rho$ and $J/\psi \omega$ transitions of the $X(3872)$ in a coupled-channel model
• Hadronic molecular assignment for the newly observed ${\Omega }^{\ast }$ state
• $Z_c(3900)$ as a $D{\bar{D}}^{\ast }$ molecule from the pole counting rule
• Heavy-hadron molecules from light-meson-exchange saturation
• Tetraquarks in large-$N_c$ QCD
• Model independent determination of the spins of the $P_c$(4440) and $P_c$(4457) from the spectroscopy of the triply charmed dibaryons
• Axial meson exchange and the $Z_c(3900)$ and $Z_{cs}(3985)$ resonances as heavy hadron molecules
• Hidden charm molecules in finite volume
• A unified description of the hidden-charm tetraquark states $Z_{cs}(3985)$, $Z_c(3900)$ and $X(4020)$
• Decay behavior of the strange and beauty partners of $P_c$ hadronic molecules
• Spin-parities of the $P_c(4440)$ and $P_c(4457)$ in the One-Boson-Exchange Model
• Interpretations of the new LHCb $P_c(4337{)}^{+}$ pentaquark state
• Binding energy of the $X(3872)$ at unphysical pion masses
• Heavy-hadron molecular spectrum from light-meson exchange saturation
• Heavy- and light-flavor symmetry partners of the $T_{cc}^{+}(3875)$, the $X(3872)$ and the $X(3960)$ from light-meson exchange saturation
• Photoproduction of strange hidden-charm and hidden-bottom states
• Is $X(7200)$ the heavy anti-quark diquark symmetry partner of $X(3872)$?
• Revisiting $X(3872)\to D^0{\bar{D}}^0{\pi }^0$ in XEFT
• Hunting for the $X_b$ via hidden bottomonium decays
• ${\eta }_{\mathrm{c}}$- and $J/\psi$-isoscalar meson bound states in the hadro-charmonium picture
• Are there narrow flavor-exotic tetraquarks in large-$N_c$ QCD?
• Quark structure of the ${\chi }_{\mathrm{c}}(3P)$ and $X(4274)$ resonances and their strong and radiative decays
• The $D^{\ast }{D}^{\ast }\bar{D}$ and $D^{\ast }{D}^{\ast }{\bar{D}}^{\ast }$ Three-Body Systems
• Distinguishing cusp effects and near-threshold-pole effects
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• Cluster reducibility of multiquark operators
• The $Z_b$ structures in a constituent quark model coupled-channels calculation
• Hadronic states with both open charm and bottom in effective field theory
• Search for $J^{PC}=1^{-+}$ exotic state in $e^{+}{e}^{-}$ annihilation
• Mass spectra of meson molecular states for heavy and light sectors
• An effective field theory approach to monopolium
• What hath Weinberg wrought? Reflections on what Weinberg's papers on 'Nuclear Forces from Chiral Lagrangians' did and did not accomplish
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• Charmoniumlike Channels $1^{+}$ with Isospin $1$ from Lattice and Effective Field Theory
• The ${\bar{D}}^{\ast }{\bar{D}}^{\ast }{\Sigma }_c$ Three-Body System
• Spin Partners of the $B^{(\ast )}{\bar{B}}^{(\ast )}$ resonances with a different approach than the Breit-Wigner parameterization
• Modification by pion exchange of near threshold resonance line shape in open heavy flavor channel
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• Hidden charm and bottom molecular states
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• Hadronic molecules and multiquark states
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
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• Decoding the near-threshold $X_{0,1}(4140)$ and $X_1(4685)$ states via OZI-suppressed coupled-channel scattering