The chiral representation of the $\pi N$ scattering amplitude and the pion-nucleon sigma term

By J. M. Alarcón, J. A. Oller, J. Camalich. 2011

344 citations recorded by the source corpus.

We present a novel analysis of the $\ensuremath{\pi}N$ 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 $\ensuremath{\Delta}(1232)$ in the $\ensuremath{\delta}$-counting, has the right analytic properties, and is renormalization-scale independent. This approach overcomes the limitations that previous chiral analyses of the $\ensuremath{\pi}N$ 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, ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}$. 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 ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}=59(7)\text{ }\text{ }\mathrm{MeV}$ and comment on implications that this result may have.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2eba2dd8055f3c1302914ab1428460eddde4b55e

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Citations in the corpus

Baryons as relativistic three-quark bound states (2016, result): “9 σ depending on which lattice result is taken (see also [411] for an earlier, similar result).”
Renormalisation-group improved analysis of μ → e processes in a systematic effective-field-theory approach (2017, methodology): “See [47, 48] for analogous results obtained from a computation in an effective-field theoretical framework.”
Focus Point Supersymmetry Redux (2011, positive): “More recent calculations support older determinations of the pion-nucleon sigma term [48].”