Weakly-bound Hadronic Molecule near a 3-body Threshold

Abstract

The X(3872) seems to be a loosely-bound hadronic molecule whose constituents are two charm mesons. A novel feature of this molecule is that the mass difference of the constituents is close to the mass of a lighter meson that can be exchanged between them, namely the pion. We analyze this feature in a simple model with spin-0 mesons only. Various observables are calculated to next-to-leading order in the interaction strength of the exchanged meson. Renormalization requires summing a geometric series of next-to-leading order corrections. The dependence of observables on the ultraviolet cutoff can be removed by renormalizations of the mass of the heaviest meson, the coupling constant for the contact interaction between the heavy mesons, and short-distance coefficients in the operator product expansion. The next-to-leading order correction has an unphysical infrared divergence at the threshold of the two heavier mesons that can be eliminated by a further resummation that takes into account the nonzero width of the heaviest meson.

37 pages, 13 figures, submitted to Phys.Rev.D

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• Line Shapes of the X(3872)
• Interpretation of the X(3872) as a charmonium state plus an extra component due to the coupling to the meson-meson continuum
• X(3872) as a hadronic molecule and its decays to charmonium states and pions
• X(3872) as a molecular DD* state in a potential model
• Quark structure of the $X(3872)$ and ${\chi }_b(3P)$ resonances
• J/psi gamma and psi(2S) gamma decay modes of the X(3872)
• Three-body $D\bar{D}\pi$ dynamics for the X(3872)
• Nature of X(3872) from data
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• Quark model description of the tetraquark state X(3872) in a relativistic constituent quark model with infrared confinement
• The $X(3872)\to J/\psi \gamma$ decay in the $D{\bar{D}}^{\ast }$ molecular picture
• The Spin-orbit force, recoil corrections and possible $B{\bar{B}}^{\ast }$ and $D{\bar{D}}^{\ast }$ molecular states
• Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction
• Interpretations for the X(4160) observed in the double charm production at B factories
• A Phenomenological analysis on isospin-violating decay of $X(3872)$
• X(3872) and the bound state problem of $D^0{\bar{D}}^{\ast 0}$ (${\bar{D}}^0{D}^{\ast 0}$) in a chiral quark model
• $P$-wave coupled channel effects in electron-positron annihilation
• Dimesonic states with the heavy-light flavour mesons
• One-pion exchange in the X(3872) revisited
• Dynamical study of the possible molecular state X(3872) with the s-channel one gluon exchange interaction
• A Study of Degenerate Two-Body and Three-Body Coupled-Channel Systems -Renormalized Effective AGS Equations and Near-Threshold Resonances-
• $Z_c(3900)$ in a hadronic molecule and a triangle singularity approach at finite temperature
• ${\bar{D}}^0{D}^{0\ast }$ $(D^0{\bar{D}}^{0\ast })$ System in QCD-Improved Many Body Potential
• Recent issues in open and hidden charm spectroscopy
• Newly observed charmed states: the case of X(3872)