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

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.

18 pages, 7 figures, 3 tables

References in corpus (16)

• Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• 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
• 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
• Extracting the sigma-term from low-energy pion-nucleon scattering
• The lowest-lying baryon masses in covariant SU(3)-flavor chiral perturbation theory
• On the chiral effective meson-baryon Lagrangian at third order
• Hadronic shift in pionic hydrogen
• Meson-baryon scattering lengths in HB$\chi$PT
• Evaluation of pion-nucleon sigma term in Dyson-Schwinger equation approach of QCD
• Kaon-nucleon scattering to one-loop order in heavy baryon chiral perturbation theory
• Flavor decomposition of the pion-nucleon $\sigma$-term
• Phenomenological analysis of nucleon strangeness and meson-nucleon sigma terms
• Isospin breaking in pion-deuteron scattering and the pion-nucleon scattering lengths

Cited by in corpus (11)

• Cross-channel constraints on resonant antikaon-nucleon scattering
• Light pseudoscalar meson and heavy meson scattering lengths to $\mathcal{O}(p^4)$ in heavy meson 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
• Revisiting Theoretical Analysis of Electric Dipole Moment of ${}^{129}$Xe
• Relations for low-energy coupling constants in baryon chiral perturbation theory derived from the chiral quark model
• Pion-nucleon scattering with decuplet contribution in heavy baryon SU(3) chiral perturbation theory
• Peripheral nucleon-nucleon scattering at next-to-next-to-leading order in SU(3) heavy baryon 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
• Contribution of the Weinberg-type Operator to atomic and nuclear electric dipole moments