Kaon-Nucleon Scattering from Chiral Lagrangians

The s-wave $K^{\pm}N$ scattering amplitude is computed up to one-loop order corresponding to next-to-next-to-leading order (or N$^2$LO in short) with a heavy-baryon effective chiral Lagrangian. Constraining the low-energy constants by on-shell scattering lengths, we obtain contributions of each chiral order up to N$^2$LO and find that the chiral corrections are ``natural" in the sense of viable effective field theories. We have also calculated off-shell $s$-wave $K^-N$ scattering amplitudes relevant to kaonic atoms and $K^-$ condensation in ``nuclear star" matter including the effect of $\Lambda (1405)$. The $K^-p$ amplitude is found to be quite sensitive to the intermediate $\Lambda (1405)$ contribution, while the $K^-n$ amplitude varies smoothly with the C.M. energy. The crossing-even one-loop corrections are found to play an important role in determining the higher-order chiral corrections.