The Octet Meson and Octet Baryon Interaction with strangeness and the $\Lambda (1405)$

Abstract

The octet meson and baryon interaction with strangeness $S=-1$ is studied fully relativistically with chiral Lagrangian. In this work, a Bethe-Salpeter equation approach with spectator quasipotential approximation is applied to study the reactions $K^{-}p\to MB$ with $MB=K^{-}p,{\bar{K}}^{0}n,{\pi }^{-}{\Sigma }^{+},{\pi }^0{\Sigma }^0,{\pi }^{+}{\Sigma }^{-}$ and $\eta \Lambda$ with all possible partial waves and theoretical results are comparable with experimental data. It is found that the Weinberg-Tomozawa potential derived from the lowest order chiral Lagrangian only provides the contributions from partial waves with spin-parities $J^P=1/2^{+}$ and $1/2^{-}$. Two-pole structure of the $\Lambda (1405)$ is confirmed with poles at $1383+99i$ and $1423+14i$ MeV. The lower and higher poles originate from $\Sigma \pi$ interaction as a resonance and $\bar{K}N$ interaction as a bound state, respectively.

13 pages, 4 figures

References in corpus (9)

• Big-Bang Nucleosynthesis
• Lattice QCD Evidence that the Lambda(1405) Resonance is an Antikaon-Nucleon Molecule
• On the Strangeness -1 S-wave Meson-Baryon Scattering
• Lineshape of the Lambda(1405) Hyperon Measured Through its Sigma0 pion0 Decay
• $Z_c(3900)$ as a resonance from the $D{\bar{D}}^{\ast }$ interaction
• Study of the $B{\bar{B}}^{\ast }/D{\bar{D}}^{\ast }$ bound states in a Bethe-Salpeter approach
• The internal structures of the nucleon resonances $N(1875)$ and $N(2120)$
• New structure around 3250 MeV in the baryonic B decay and the $D_0^{\ast }(2400)N$ molecular hadron
• Strangeness in the proton and N*(1535)

Cited by in corpus (13)

• Nucleon resonances $N(1875)$ and $N(2100)$ as strange partners of LHCb pentaquarks
• Understanding spin parity of $P_c(4450)$ and $Y(4274)$ in a hadronic molecular state picture
• Molecular picture for $X_0(2900)$ and $X_1(2900)$
• Interpretation of $Y(4390)$ as an isoscalar partner of $Z(4430)$ from $D^{\ast }(2010){\bar{D}}_1(2420)$ interaction
• Hidden-strange molecular states and the $N\varphi$ bound state via a QCD van der Waals force
• Possible ${\Lambda }_c{\bar{\Lambda }}_c$ molecular states and their productions in nulceon-antinulceon collision
• The $X(2239)$ and $\eta (2225)$ as hidden-strange molecular states from $\Lambda \bar{\Lambda }$ interaction
• Possible molecular states from the $N\Delta$ interaction
• Pole trajectories from $S$- and $P$-wave $D{\bar{D}}^{\ast }$ interactions
• Role of ${\Sigma }^{\ast }(1/2^{-})$ baryons in ${\Lambda }_c\to \Lambda {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• $\bar{D}{\Sigma }_c^{\ast }$ and ${\bar{D}}^{\ast }{\Sigma }_c$ interactions and LHCb pentaquarks
• $\Xi$(2030) and $\Xi$(2120) as ${\bar{K}}^{\ast }\Sigma$ molecular states
• Kaon-induced production of strange hidden-charm molecular pentaquarks $P_{\psi s}^{\Lambda }$ from proton