Pion-nucleon scattering to $\mathcal{O}(p^3)$ in heavy baryon SU(3) chiral perturbation theory

TL;DR

This paper computes pion-nucleon scattering amplitudes to third order in heavy baryon SU(3) chiral perturbation theory, fitting parameters to experimental data, and predicts scattering observables and sigma terms with good agreement.

Contribution

It provides a complete third-order calculation of $$-matrices in heavy baryon SU(3) chiral perturbation theory, including detailed analysis of contributions and convergence.

Findings

Predicted scattering lengths and volumes agree with experimental data.

Determined sigma terms and proton strangeness content.

Third-order contributions from kaon loops and counterterms are significant.

Abstract

We calculate the complete $T$-matrices of pion-nucleon ($\pi N$) scattering to the third order in heavy baryon SU(3) chiral perturbation theory. The baryon mass in the chiral limit $M_0$ and the low-energy constants are determined by fitting to phase shifts of $\pi N$ and the experimental octet-baryon masses simultaneously. By using these constants, we obtain the pion-nucleon sigma terms, $\sigma_{\pi N}=(34.57\pm 11.85)$ MeV. We also find that a very small strangeness content of the proton, $y \simeq 0$. The scattering lengths and the scattering volumes are predicted, which turn out to be in good agreement with those of other approaches and the available experiment data. The contributions from the third-order amplitudes are discussed in detail. We find that the contributions from the internal kaon lines of one-loop diagrams and the counterterms of the third order are sizeable. In addition, the issue of convergence is also discussed.