Studying the scalar bound states of the $K\bar{K}$ system in the Bethe-Salpeter formalism

Abstract

We study the possible bound states of the $K\bar{K}$ system in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. We find that the bound states exist. However, these bound states have very small decay widths. Therefore, besides the possible $K\bar{K}$ component, there may be some other structures in the observed $f_0(980)$ and $a_0(980)$ .

arXiv comment23 pages, LaTeX2e. Discussions on the legitimacy of the ladder approximation and the instantaneous approximation are added. Recognized typos have been corrected. Several references added

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• The Cosmological Parameters 2006
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• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
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• Implications of a DK Molecule at 2.32 GeV
• On the structure of the scalar mesons $f_0(975)$ and $a_0(980)$
• Light Meson Spectroscopy
• Study of the Decay phi --> pi0 pi0 gamma with the KLOE Detector
• Study of the Decay phi --> eta pi0 gamma with the KLOE detector
• The $\varphi (1020)\to {\pi }^0{\pi }^0\gamma$ decay
• Nonperturbative study of generalized ladder graphs in a ϕ^2χtheory
• The $\varphi \to \eta {\pi }^0\gamma$ decay
• Possible Molecular Structure of the Newly Observed Y(4260)
• Possible S-wave Bound-States of Two Pseudoscalar Mesons
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Cited by in corpus (24)

• $Z_c(3900)$ as a resonance from the $D{\bar{D}}^{\ast }$ interaction
• Tetraquark state $X(6900)$ and the interaction between diquark and antidiquark
• Is $Z_c(3900)$ a molecular state
• Bethe-Salpeter equation for doubly heavy baryons in the covariant instantaneous approximation
• The bound state problem of S-wave heavy quark meson-aitimeson systems
• Masses of doubly heavy baryons in the Bethe-Salpeter equation approach
• Is $Z_b(10610)$ a Molecular State?
• Investigation of the possible $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ molecule states
• Possible open-charmed pentaquark molecule ${\Omega }_c(3188)$ --- the $D\Xi$ bound state --- in the Bethe-Salpeter formalism
• Possible molecular states of ${\bar{D}}^{\ast }{K}^{\ast }$ ($D^{\ast }{K}^{\ast }$) and the new exotic states $X_0(2900)$ and $X_1(2900)$ ($T_{cs0}^a(2900{)}^0$ and $T_{cs0}^a(2900{)}^{++}$)
• Understanding Y(4274) and X(4320) in the $J/\psi \varphi$ invariant mass spectrum
• Electromagnetic form factors of ${\Lambda }_b$ in the Bethe-Salpeter equation approach
• Study on possible molecular states composed of ${\Lambda }_c\bar{D}$ (${\Lambda }_{b}B$) and ${\Sigma }_c\bar{D}$ (${\Sigma }_{b}B$) within the Bethe-Salpeter framework
• X(3872) as a molecular $D{\bar{D}}^{\ast }$ state in the Bethe-Salpeter equation approach
• Analyzing $\Xi (1620)$ in the molecule picture in the Bethe-Salpeter equation approach
• Studying the $D_{1}D$ molecule in the Bethe-Salpeter equation approach
• FCNC transitions of ${\Lambda }_b$ to neutron in Bethe-Salpeter equation approach
• The study of possible molecular states of $D_s^{(\ast )}{D}_s^{(\ast )}$ and $B_s^{(\ast )}{B}_s^{(\ast )}$
• Rare ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ decay in the Bethe-Salpeter equation approach
• Studying the bound state of the $K^{-}p$ system in the Bethe-Salpeter formalism
• KKbar molecules with momentum-dependent interactions
• The possible $B\pi$ molecular state and its radiative decay
• Forward-backward asymmetries in ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ in Bethe-Salpeter equation approach
• Electromagnetic form factors of ${\Lambda }_c$ in the Bethe-Salpeter equation approach