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

TL;DR

This paper calculates kaon-nucleon scattering amplitudes to one-loop order in heavy baryon chiral perturbation theory, fitting low-energy constants to experimental data, and predicts scattering phase shifts and lengths with good accuracy.

Contribution

It provides the first comprehensive one-loop order calculation of $KN$ and $ar{K}N$ scattering in SU(3) HB$ ext{χ}$PT, including LEC determination and consistency checks.

Findings

Good description of phase shifts below 200 MeV kaon momentum

Predicted scattering lengths agree with empirical values except for isospin-0 case

Demonstrates the framework's potential for baryon-baryon interaction studies

Abstract

We calculate the T-matrices of kaon-nucleon ($KN$) and antikaon-nucleon ($\overline{K}N$) scattering to one-loop order in SU(3) heavy baryon chiral perturbation theory (HB$\chi$PT). The low-energy constants (LECs) and their combinations are then determined by fitting the phase shifts of $KN$ scattering and the corresponding data. This leads to a good description of the phase shifts below 200 MeV kaon laboratory momentum. We obtain the LEC uncertainties through statistical regression analysis. We also determine the LECs through the use of scattering lengths in order to check the consistency of the HB$\chi$PT framework for different observables and obtain a consistent result. By using these LECs, we predict the $\overline{K}N$ elastic scattering phase shifts and obtain reasonable results. The scattering lengths are also predicted, which turn out to be in good agreement with the empirical values except for the isospin-0 $\overline{K}N$ scattering length that is strongly affected by the $\Lambda(1405)$ resonance. As most calculations in the chiral perturbation theory, the convergence issue is discussed in detail. Our calculations provide a possibility to investigate the baryon-baryon interaction in HB$\chi$PT.