$X(3872)$ as a four-quark state in a Dyson-Schwinger/Bethe-Salpeter approach

Abstract

We generalise the framework of Dyson-Schwinger and Bethe-Salpeter equations for four-quark states to accommodate the case of unequal quark masses. As a first application, we consider the quantum numbers $I(J^{PC})=0(1^{++})$ of the $X(3872)$ and study the four-quark states with quark contents $cq\bar{q}\bar{c}$ and $cs\bar{s}\bar{c}$. Their Bethe-Salpeter amplitudes are represented by a basis of heavy-light meson-meson, hadro-charmonium and diquark-antidiquark operators, which allows for a dynamical distinction between different internal configurations. In both cases we find the heavy-light meson-meson component to be dominant. For the putative $X(3872)$ we obtain a mass of $3916(74)$ MeV; the corresponding $cs\bar{s}\bar{c}$ state is predicted at $4068(61)$ MeV.

arXiv comment8 pages, 2 figures; v2: minor typos corrected

References in corpus (31)

• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• Multiquark Resonances
• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• Heavy-Quark QCD Exotica
• Observation of the Narrow State $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ in $\bar{p}p$ Collisions at $\sqrt{s}=1.96 \TeV$
• Exotics: Heavy Pentaquarks and Tetraquarks
• Observation and Properties of the X(3872) Decaying to J/psi pi+ pi- in p-p(bar) Collisions at sqrt(s) = 1.96 TeV
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Study of the B- --> J/psi K- pi+ pi- Decay and Measurement of the B- --> X(3872) K- Branching Fraction
• Charmonium
• Baryons as relativistic three-quark bound states
• Determination of the X(3872) meson quantum numbers
• Lattice Prediction for Deeply Bound Doubly Heavy Tetraquarks
• Observation of X(3872) production in pp collisions at sqrt(s)= 7 TeV
• Evidence for X(3872) from DD* scattering on the lattice
• Nucleon electromagnetic form factors from the covariant Faddeev equation
• Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD
• Tetraquark bound states in a Bethe-Salpeter approach
• X(3872) and Y(4140) using diquark-antidiquark operators with lattice QCD
• Study of the $Z_c^{+}$ channel using lattice QCD
• Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: are sigma and kappa tetraquarks?
• Remarks on pole trajectories for resonances
• The light scalar mesons as tetraquarks
• $ud\bar{b}\bar{b}$ tetraquark resonances with lattice QCD potentials and the Born-Oppenheimer approximation
• Four-point functions and the permutation group S4
• Recent developments in bound-state calculations using the Dyson-Schwinger and Bethe-Salpeter equations
• Charmed mesons with a symmetry-preserving contact interaction
• Aspects of open-flavour mesons in a comprehensive DSBSE study

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• The light scalars: four- vs. two-quark states in the complex energy plane from Bethe-Salpeter equations
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