$\Lambda (1405)$ Contribution to Kaon-Nucleon Scattering Lengths In Chiral Perturbation Theory

Abstract

We examine the role of the $\Lambda (1405)$ in kaon-nucleon scattering lengths using chiral perturbation theory. The leading nonanalytic SU(3) corrections reduce the coupling of the $\Lambda (1405)$ to $KN$ compared to $\Sigma \pi$. S-wave $K^{-}p$ scattering is the only channel significantly affected by the $\Lambda (1405)$ pole which substantially cancels against the leading term fixed by the vector current. This cancellation and the close proximity of the $\Lambda (1405)$ pole makes this SU(3) correction to $a(K^{-}p)$ large and at lowest order leaves the sign of $a(K^{-}p)$ undetermined. We extract two linear combinations of constants appearing at higher order in the chiral expansion from measurements of $KN$ scattering lengths. These constants are important for the offshell behaviour of $KN$ scattering amplitudes that play a central role in kaon condensation. The recent claims about the calculability of these constants are discussed.

11 pages, figure not included, uses harvmac, CMU-HEP 94-11, NSF-ITP-94-33

References in corpus (4)

• Strong and Electromagnetic Decays of the Baryon Decuplet
• Kaon-Nucleon Scattering Amplitudes and Z${}^{\ast }$-Enhancements from Quark Born Diagrams
• Chiral Corrections to the S-Wave Pion-Nucleon Scattering Lengths
• Effective Kaon Mass in Baryonic Matter and Kaon Condensation

Cited by in corpus (17)

• Chiral dynamics in the presence of bound states: kaon-nucleon interactions revisited
• Chiral perturbation theory
• Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
• Lattice QCD Evidence that the Lambda(1405) Resonance is an Antikaon-Nucleon Molecule
• An Effective Chiral Lagrangian Approach to Kaon-Nuclear Interactions: Kaonic atom and kaon condensation
• Kaon Condensation in Dense Stellar Matter
• Towards a theory of hadron resonances
• S-wave Meson-Nucleon Interactions and the Meson Mass in Nuclear Matter from Chiral Effective Lagrangians
• Review of the $\mathbf{\Lambda }$(1405): A curious case of a strange-ness resonance
• Properties of Hadrons in the Nuclear Medium
• The Decuplet Revisited in $\chi$PT
• Hyperons in Two Flavor Chiral Perturbation Theory
• Lambda(1405) in the Bound State Soliton Model
• Lattice study on kaon nucleon scattering length in the I=1 channel
• The Role of Lambda(1405) in Kaon-Proton Interactions
• Chiral Dynamics of Low-Energy Kaon-Baryon Interactions with Explicit Resonance
• An Undergraduate Approach to the Quantum Hadrodynamics and the Physics of Neutron Stars Part II: Neutron Stars' Exotic Content