Studying the bound state of the $K^{-}p$ system in the Bethe-Salpeter formalism

Abstract

We study the $s$-wave kaon-nucleon bound state with the strangeness $S=-1$ in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. We solve the Bethe-Salpeter equation of the bound state and obtain the Bethe-Salpeter amplitude. It is shown that the $K^{-}p$ bound state exists in this formalism. We also study the decay width of the bound state based on the Bethe-Salpeter techniques. The mass of this bound state is 1422 MeV and its decay width is obviously smaller than that of $\Lambda (1405)$. These results indicate that there may be some other structures in the observed resonance.

7 pages, 4 Figures

References in corpus (6)

• Effective Kbar N interaction based on chiral SU(3) dynamics
• Lattice QCD Evidence that the Lambda(1405) Resonance is an Antikaon-Nucleon Molecule
• Constraints on the chiral unitary $\bar{K}N$ amplitude from $\pi \Sigma K^{+}$ photoproduction data
• New insights into antikaon-nucleon scattering and the structure of the Lambda(1405)
• Studying the scalar bound states of the $K\bar{K}$ system in the Bethe-Salpeter formalism
• Electromagnetic form factors of ${\Lambda }_b$ in the Bethe-Salpeter equation approach