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

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, ${\sigma }_{KN}^{(1)}=(375.07\pm 33.02)$ MeV and ${\sigma }_{KN}^{(2)}=(275.32\pm 32.24)$ 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.

arXiv comment29 pages, 6 figures, 5 tables

References in corpus (44)

• On the Foundations of Chiral Perturbation Theory
• The chiral representation of the $\pi N$ scattering amplitude and the pion-nucleon sigma term
• Error Estimates of Theoretical Models: a Guide
• Pion-nucleon scattering in chiral perturbation theory I: Isospin-symmetric case
• Renormalization of relativistic baryon chiral perturbation theory and power counting
• Recent Developments in Chiral Perturbation Theory
• Aspects of chiral pion-nucleon physics
• Chiral expansion of baryon masses and $\sigma$-terms
• High-precision determination of the pion-nucleon $\sigma$-term from Roy-Steiner equations
• Roy-Steiner-equation analysis of pion-nucleon scattering
• A percent-level determination of the nucleon axial coupling from Quantum Chromodynamics
• Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam
• Matching Heavy Particle Approach to Relativistic Theory
• Uncertainty analysis and order-by-order optimization of chiral nuclear interactions
• Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Leading SU(3)-breaking corrections to the baryon magnetic moments in Chiral Perturbation Theory
• Strong and Electromagnetic Decays of the Baryon Decuplet
• The hidden charm pentaquark states and ${\Sigma }_c{\bar{D}}^{(\ast )}$ interaction in chiral perturbation theory
• Parameterization dependence of T matrix poles and eigenphases from a fit to piN elastic scattering data
• Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory
• Critical Analysis of Baryon Masses and Sigma-Terms in Heavy Baryon Chiral Perturbation Theory
• Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme
• Axial, induced pseudoscalar, and pion-nucleon form factors in manifestly Lorentz-invariant chiral perturbation theory
• Compton Scattering and the Spin Structure of the Nucleon at Low Energies
• Pion-nucleon scattering in an effective chiral field theory with explicit spin-3/2 fields
• Hidden-charm and hidden-bottom molecular pentaquarks in chiral perturbation theory
• Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances
• The lowest-lying baryon masses in covariant SU(3)-flavor chiral perturbation theory
• Baryon axial currents
• Uncertainties in WIMP Dark Matter Scattering Revisited
• Chiral Prediction for the $\pi N$ Scattering Length $a^{-}$ to Order $\mathcal{O}(M_{\pi }^4)$
• Hadronic shift in pionic hydrogen
• Meson-baryon scattering lengths in HB$\chi$PT
• Chiral corrections to kaon-nucleon scattering lengths
• Decuplet contribution to the meson-baryon scattering lengths
• Meson-baryon scattering to one-loop order in heavy baryon chiral perturbation theory
• 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
• Kaon-nucleon scattering to one-loop order in heavy baryon chiral perturbation theory
• Three and Two-Point One-Loop Integrals in Heavy Particle Effective Theories
• Pion-nucleon scattering to order $p^4$ in SU(3) heavy baryon chiral perturbation theory
• One-loop vertex integrals in heavy-particle effective theories
• Flavor decomposition of the pion-nucleon $\sigma$-term

Cited by in corpus (2)

• Electromagnetic polarizabilities of the spin-$\frac{3}{2}$ baryons in heavy baryon chiral perturbation theory
• Meson-baryon scattering lengths without annihilation diagrams to order $p^4$ in heavy baryon chiral perturbation theory