$S$-wave $KN$ scattering in a renormalizable chiral effective field theory

We investigate the $s$-wave $KN$ scattering up to next-to-leading order within a renormalizable framework of covariant chiral effective field theory. Using time-ordered perturbation theory, the scattering amplitude is obtained by treating the leading-order interaction non-perturbatively and including the higher-order corrections perturbatively via the subtractive renormalization. We demonstrate that the non-perturbative treatment is essential, at least at lowest order, in the SU(3) sector of $KN$ scattering. Our NLO study achieves a good description of the empirical $s$-wave phase shifts in the isospin $I=1$ channel. An analysis of the effective range expansion yields a negative effective range, consistent with some partial wave analyses but opposite in sign to earlier phenomenological summaries. For the $I=0$ counterpart, the $KN$ interaction is found to be rather weak and exhibits large uncertainties. Further low-energy $KN$ scattering experiments and lattice QCD simulations are needed to better constrain both $s$-wave channels.