Pion-nucleon scattering with decuplet contribution in heavy baryon SU(3) chiral perturbation theory

TL;DR

This paper computes pion-nucleon scattering amplitudes including decuplet contributions within heavy baryon SU(3) chiral perturbation theory, fitting to experimental data to determine low-energy constants and predict scattering parameters.

Contribution

It provides a complete calculation of $T$ matrices with decuplet effects at $ ext{O}(\e^3)$, fitting multiple data sets to determine key constants and improve scattering predictions.

Findings

Accurate phase shift descriptions across all partial waves.

Determined $KN$ $\sigma$ terms with statistical errors.

Presented scattering lengths and volumes consistent with data.

Abstract

We calculate the complete $T$ matrices with decuplet contributions for pion-nucleon scattering to order $\mathcal{O}(\epsilon^3)$ 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 $\pi N$, the experimental octet-baryon masses, and the value of $\sigma_{\pi N}$ simultaneously. By using these constants, we obtain the $KN$ $\sigma$ terms, $\sigma_{KN}^{(1)}=(375.07\pm33.02)$ MeV and $\sigma_{KN}^{(2)}=(275.32\pm32.24)$ MeV, with the errors being only statistical. An excellent description of the phase shifts is obtained for all partial waves. We also present results for scattering lengths and scattering volumes. In addition, the convergence of the approach is also discussed.