Meson-baryon scattering to one-loop order in heavy baryon chiral perturbation theory

Abstract

We calculate the T-matrices of pseudoscalar meson octet-baryon scattering to one-loop order in SU(3) heavy baryon chiral perturbation theory. The pertinent combinations of low-energy constants are determined by fitting to phase shifts of $πN$ and $K N$ scattering and the corresponding data. By using these low-energy constants, we obtain the strong phase shift difference of $πΛ$ scattering at the $Ξ$ mass, $δ_P-δ_S=(8.8 \pm 0.2)$ degrees, in agreement with experimental results. We find that the phase shifts in the $S_{01}$($πΣ$), $S_{01}$($K Ξ$), $S_{01}$($\overline{K} N$), and $S_{11}$($\overline{K} Σ$) waves are so strong that resonances may be generated dynamically in all these channels. We also predict the scattering lengths and make comparisons with the results obtained from the threshold T-matrices in heavy baryon chiral perturbation theory and the method of covariant infrared regularization. The issue of convergence is also discussed in detail.

25 pages, 8 figures, 1 table