Chiral corrections to kaon-nucleon scattering lengths

Abstract

We calculate the threshold T-matrices of kaon-nucleon and antikaon-nucleon scattering to one loop order in SU(3) heavy baryon chiral perturbation theory. To that order the complex-valued isospin-1 $\bar{K}N$ threshold T-matrix can be successfully predicted from the isospin-0 and 1 $KN$ threshold T-matrices. As expected perturbation theory fails to explain the isospin-0 $\bar{K}N$ threshold T-matrix which is completely dominated by the nearby subthreshold ${\Lambda }^{\ast }(1405)$-resonance. Cancelations of large terms of second and third chiral order are observed as they seem to be typical for SU(3) baryon chiral perturbation theory calculations. We also give the kaon and eta loop corrections to the $\pi N$ scattering lengths and we investigate $\pi \Lambda$ scattering to one-loop order. The second order s-wave low-energy constants are all of natural size and do not exceed 1 GeV${}^{-1}$ in magnitude.

Comments: 8 pages, 2 figures, published in Phys. Rev. C64, 045204 (2001), corrections of numerical prefactors in Eqs.(10,11,12)