X iv : h ep - p h / 94 04 28 5 v 1 1 8 A pr 1 99 4 Λ ( 1405 ) Contribution to Kaon - Nucleon Scattering Lengths In Chiral Perturbation Theory *

We examine the role of the Λ(1405) in kaon-nucleon scattering lengths using chiral perturbation theory. The leading nonanalytic SU(3) corrections reduce the coupling of the Λ(1405) to KN compared to Σπ. S-wave Kp scattering is the only channel significantly affected by the Λ(1405) pole which substantially cancels against the leading term fixed by the vector current. This cancellation and the close proximity of the Λ(1405) pole makes this SU(3) correction to a(Kp) large and at lowest order leaves the sign of a(Kp) 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. CMU-HEP 94-11 NSF-ITP-94-33 DOE-ER/40682-65 April 1994 * Work supported in part by the Department of Energy under contract DE–FG02– 91ER40682 (CMU) and by the NSF under grant PHY89-04035.