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

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.

arXiv comment18 pages, 5 figures, 1 table

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• Meson-baryon scattering up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory
• Pion-nucleon scattering to $\mathcal{O}(p^3)$ in heavy baryon SU(3) chiral perturbation theory
• Pion-nucleon scattering to order $p^4$ in SU(3) heavy baryon chiral perturbation theory
• Phase shifts of the light pseudoscalar meson and heavy meson scattering in heavy meson chiral perturbation theory
• Peripheral nucleon-nucleon scattering at next-to-next-to-leading order in SU(3) heavy baryon chiral perturbation theory
• Pion-nucleon scattering with decuplet contribution in heavy baryon SU(3) chiral perturbation theory
• Octet baryon and heavy meson interactions in chiral effective field theory
• Meson-baryon scattering lengths without annihilation diagrams to order $p^4$ in heavy baryon chiral perturbation theory