Heavy-quark spin and flavour symmetry partners of the X(3872) revisited: what can we learn from the one boson exchange model?

Abstract

Heavy-quark symmetry as applied to heavy hadron systems implies that their interactions are independent of their heavy-quark spin (heavy-quark spin symmetry) and heavy flavour contents (heavy flavour symmetry). In the molecular hypothesis the $X(3872)$ resonance is a $1^{++}$ $D^{\ast }\bar{D}$ bound state. If this is the case, the application of heavy-quark symmetry to a molecular $X(3872)$ suggests the existence of a series of partner states, the most obvious of which is a possible $2^{++}$ $D^{\ast }{\bar{D}}^{\ast }$ bound state for which the two-body potential is identical to that of the $1^{++}$ $D^{\ast }\bar{D}$ system, the reason being that these two heavy hadron-antihadron states have identical light-spin content. As already discussed in the literature this leads to the prediction of a partner state at $4012\mathrm{MeV}$, at least in the absence of other dynamical effects which might affect the location of this molecule. However the prediction of further heavy-quark symmetry partners cannot be done solely on the basis of symmetry and requires additional information. We propose to use the one boson exchange model to fill this gap, in which case we will be able to predict or discard the existence of other partner states. Besides the isoscalar $2^{++}$ $D^{\ast }{\bar{D}}^{\ast }$ bound state, we correctly reproduce the location and quantum numbers of the isovector hidden-bottom $Z_b(10610)$ and $Z_b(10650)$ molecular candidates. We also predict the hidden-bottom $1^{++}$ $B^{\ast }{\bar{B}}^{\ast }$ and $2^{++}$ $B^{\ast }{\bar{B}}^{\ast }$ partners of the $X(3872)$, in agreement with previous theoretical speculations, plus a series of other states. The isoscalar, doubly charmed $1^{+}$ $D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ molecules and their doubly bottomed counterparts are likely to bind, providing a few instances of explicitly exotic systems.

16 pages, 10 tables, corresponds to published version

References in corpus (20)

• Dynamically Generated Open and Hidden Charm Meson Systems
• Discovery of doubly-charmed Xi_{cc} baryon implies a stable (b b ubar dbar) tetraquark
• Heavy-quark symmetry implies stable heavy tetraquark mesons $Q_i{Q}_j{\bar{q}}_k{\bar{q}}_l$
• X(3872) and Other Possible Heavy Molecular States
• Pion Interactions in the X(3872)
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Isospin breaking effects in the X(3872) resonance
• Exotic meson-meson molecules and compact four--quark states
• Implications of Heavy Quark-Diquark Symmetry for Excited Doubly Heavy Baryons and Tetraquarks
• What can radiative decays of the X(3872) teach us about its nature?
• Calculation of the heavy-hadron axial couplings g_1, g_2, and g_3 using lattice QCD
• Amplitude analysis of e+e- => Y(nS)pi+pi- at sqrt(s)=10.865 GeV
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• Detecting the long-distance structure of the X(3872)
• Heavy-Quark Symmetry Partners of the Pc(4450) Pentaquark
• ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ interactions in chiral effective field theory
• Exotic $bc\bar{q}\bar{q}$ four-quark states
• A Model Study of Discrete Scale Invariance and Long-Range Interactions
• $X(3872)$, $X_b$, and the ${\chi }_{b1}(3P)$ state
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Cited by in corpus (23)

• Pentaquark and Tetraquark states
• Emergence of a complete heavy-quark spin symmetry multiplet: seven molecular pentaquarks in light of the latest LHCb analysis
• A survey of heavy-heavy hadronic molecules
• Lattice QCD investigation of a doubly-bottom $\bar{b}\bar{b}ud$ tetraquark with quantum numbers $I(J^P)=0(1^{+})$
• Probing the long-range structure of the $T_{cc}^{+}$ with the strong and electromagnetic decays
• Can discovery of hidden charm strange pentaquark states help determine the spins of $P_c(4440)$ and $P_c(4457)$?
• Excited $K$ meson, $K_c(4180)$, with hidden charm as a $D\bar{D}K$ bound state
• Investigation of the possible $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ molecule states
• The quasi-fission phenomeonon of double charm $T_{cc}^{+}$ induced by nucleon
• Is $X(7200)$ the heavy anti-quark diquark symmetry partner of $X(3872)$?
• Photoproduction of strange hidden-charm and hidden-bottom states
• Double-charm heptaquark states composed of two charmed mesons and one nucleon
• New type of doubly charmed molecular pentaquarks containing most strange quarks: Mass spectra, radiative decays, and magnetic moments
• Searching for doubly charmed tetraquark candidates $T_{cc}$ and $T_{cc\bar{s}}$ in $B_c$ decays
• One way to verify the molecular picture of exotic hadrons --from $DK$ to $DDK/D{\bar{D}}^{(\ast )}K$
• Study of charmonium and charmonium-like contributions in $B^{+}\to J/\psi \eta K^{+}$ decays
• $\sigma$ exchange in the one-boson exchange model involving the ground state octet baryons
• hidden charm decays of $X(4014)$ in a $D^{\ast }{\bar{D}}^{\ast }$ molecule scenario
• Study on triple-hadron bound states with Gaussian expansion method
• Study of the hidden charm $D{\bar{D}}^{\ast }$ interactions in chiral effective field theory
• Possible ${\Sigma }_c^{\ast }\bar{\Sigma }$ molecular states
• Strong coupling constants of charmed and bottom mesons with light vector mesons in QCD sum rules
• Investigation of Doubly Heavy Tetraquark Systems using Lattice QCD