The possible $K{\bar{K}}^{\ast }$ and $D{\bar{D}}^{\ast }$ bound and resonance states by solving Schrodinger equation

Abstract

The Schrodinger equation with a Yukawa type of potential is solved analytically. When different boundary conditions are taken into account, a series of solutions are indicated as Bessel function, the first kind of Hankel function and the second kind of Hankel function, respectively. Subsequently, the scattering processes of $K{\bar{K}}^{\ast }$ and $D{\bar{D}}^{\ast }$ are investigated. In the $K{\bar{K}}^{\ast }$ sector, the $f_1(1285)$ particle is treated as a $K{\bar{K}}^{\ast }$ bound state, therefore, the coupling constant in the $K{\bar{K}}^{\ast }$ Yukawa potential can be fixed according to the binding energy of the $f_1(1285)$ particle. Consequently, a $K{\bar{K}}^{\ast }$ resonance state is generated by solving the Schrodinger equation with the outgoing wave condition, which lie at $1417-i18$MeV on the complex energy plane. It is reasonable to assume that the $K{\bar{K}}^{\ast }$ resonance state at $1417-i18$MeV might correspond to the $f_1(1420)$ particle in the review of Particle Data Group(PDG).In the $D{\bar{D}}^{\ast }$ sector, since the $X(3872)$ particle is almost located at the $D{\bar{D}}^{\ast }$ threshold, the binding energy of it equals to zero approximately. Therefore, the coupling constant in the $D{\bar{D}}^{\ast }$ Yukawa potential is determined, which is related to the first zero point of the zero order Bessel function. Similarly to the $K{\bar{K}}^{\ast }$ case, four resonance states are produced as solutions of the Schrodinger equation with the outgoing wave condition. It is assumed that the resonance states at $3885-i1$MeV, $4029-i108$ MeV, $4328-i191$MeV and $4772-i267$MeV might be associated with the $Zc(3900)$, the $X(3940)$, the ${\chi }_{c1}(4274)$ and ${\chi }_{c1}(4685)$ particles, respectively. It is noted that all solutions are isospin degenerate.

arXiv comment9 pages, 2 tables, 4 figures, to be published in Communications in Theoretical Physics

References in corpus (37)

• 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
• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• Diquark-Antidiquarks with Hidden or Open Charm and the Nature of X(3872)
• Pentaquark and Tetraquark states
• Heavy-Quark QCD Exotica
• An updated review of the new hadron states
• Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson
• Charmonium Options for the X(3872)
• Low lying axial-vector mesons as dynamically generated resonances
• Low-energy Universality and the New Charmonium Resonance at 3870 MeV
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• X(3872) and Other Possible Heavy Molecular States
• Masses of heavy tetraquarks in the relativistic quark model
• Is X(3872) {\sl Really} a Molecular State?
• Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons
• Is X(3872) a molecule?
• Coupled-channel model for charmonium levels and an option for X(3872)
• Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state
• Hadron Loops: General Theorems and Application to Charmonium
• Coupled-Channel and Screening Effects in Charmonium Spectrum
• Isospin breaking, coupled-channel effects, and X(3872)
• Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
• Different pole structures in line shapes of the $X(3872)$
• Interplay of quark and meson degrees of freedom in a near-threshold resonance
• Ambiversion of X(3872)
• Charmonium spectroscopy above thresholds
• Scattering of an Ultrasoft Pion and the X(3872)
• QCD Sum-Rule Interpretation of X(3872) with $J^{PC}=1^{++}$ Mixtures of Hybrid Charmonium and $\bar{D}{D}^{\ast }$ Molecular Currents
• Quark mass dependence of the X(3872) binding energy
• A Refined Analysis on the $X(3872)$ Resonance
• Revising the $f_1(1420)$ resonance
• X(3872) as a 1D2 charmonium state
• $X(3872)$ as virtual companion pole of the charm-anticharm state ${\chi }_{c1}(2P)$
• The $D{\bar{D}}^{\ast }$ interaction with isospin zero in an extended hidden gauge symmetry approach