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

TL;DR

This work studies $S$-wave $KN$ scattering within a renormalizable covariant chiral EFT using time-ordered perturbation theory, treating the leading-order interaction nonperturbatively and higher-order terms perturbatively with subtractive renormalization to obtain a renormalized $T$-matrix. The authors extend the framework to next-to-leading order in the SU(3) sector, constraining four low-energy constants from scattering lengths and lattice inputs, and projecting onto $s$-wave states to extract phase shifts and the effective-range expansion. They find that the LO nonperturbative treatment is essential in the $KN$ system, with the $I=1$ channel described reasonably well at NLO and a negative effective range $r<0$, while the $I=0$ interaction remains weak with large uncertainties; comparisons to HAL QCD suggest that reproducing the small lattice-scattering length can yield $r$ values in agreement with their results. The work demonstrates the applicability and convergence of renormalizable ChEFT in SU(3) meson-baryon scattering and provides quantitative guidance for future experiments and lattice simulations of $KN$ dynamics.

Abstract

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.

Figures (4)

• Figure 1: Time-ordered diagrams for $KN$ scattering up to NLO. The dashed, solid and double-solid lines correspond to kaon, octet baryons and vector mesons, respectively. The dots (boxes) denote the $\mathcal{O}(p^1)$ ($\mathcal{O}(p^2)$) vertices.
• Figure 2: Predictions for the $s$-wave $KN$ scattering phase shifts at LO. The solid red lines denote the non-perturbative LO results with $T$-matrix given as Eq. (\ref{['Eq:TLO']}), and the dotted blue lines are the perturbative results at LO with $T=V_\mathrm{LO}$. The triangle, circle, and box datapoints represent the energy-dependent PWAs from Refs. Martin:1975gsHyslop:1992csGibbs:2006ab, respectively.
• Figure 3: Left panel: description of $KN$ phase shifts in the $S_{11}$ channel up to NLO. Right panel: $\left(p_\mathrm{cm}\cot\delta\right)^{-1}$ as function of $p_\mathrm{cm}/M_\pi$ for the $S_{11}$$KN$ channel. The solid lines denote the NLO results, and the corresponding light green bands represent the uncertainties at the 68% confidence level. The narrow band with $p_{cm}=0$ represents the scattering length summarized in Ref. Dover:1982zh. The notations of the datapoints are the same as those given in Fig. \ref{['Fig:KN_LOPS']}.
• Figure 4: Left panel: description of $KN$ phase shifts in the $S_{01}$ channel up to NLO. Right panel: $\left(p_\mathrm{cm}\cot\delta\right)^{-1}$ as function of $p_\mathrm{cm}/M_\pi$ for the $S_{01}$$KN$ channel. The solid lines denote the NLO results, and the corresponding light green bands represent the uncertainties at the 68% confidence level. The narrow band with $p_{cm}=0$ represents the scattering length summarized in Ref. Dover:1982zh. The notations of the datapoints are the same as those given in Fig. \ref{['Fig:KN_LOPS']}.