Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-10-17
Phys. Rev. D 85, 051503 (2012)
Physics
High Energy Physics
High Energy Physics - Phenomenology
Version shortened and focused on the determination of the sigma-term. References added, mostly to recent LQCD results
Scientific paper
We present a novel analysis of the $\pi N$ scattering amplitude in Lorentz covariant baryon chiral perturbation theory renormalized in the extended-on-mass-shell scheme. This amplitude, valid up to $\mathcal{O}(p^3)$ in the chiral expansion, systematically includes the effects of the $\Delta(1232)$ in the $\delta$-counting, has the right analytic properties and is renormalization-scale independent. This approach overcomes the limitations that previous chiral analyses of the $\pi N$ scattering amplitude had, providing an accurate description of the partial wave phase shifts of the Karlsruhe-Helsinki and George-Washington groups up to energies just below the resonance region. We also study the solution of the Matsinos group which focuses on the parameterization of the data at low energies. Once the values of the low-energy constants are determined by adjusting the center-of-mass energy dependence of the amplitude to the scattering data, we obtain predictions on different observables. In particular, we extract an accurate value for the pion-nucleon sigma term, $ \sigma_{\pi N}$. This allows us to avoid the usual method of extrapolation to the unphysical region of the amplitude. Our study indicates that the inclusion of modern meson-factory and pionic-atom data favors relatively large values of the sigma term. We report the value $\sigma_{\pi N}=59(7)$MeV and comment on implications that this result may have.
Alarcón J. M.
Camalich Martin J.
Oller Jose Antonio
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