We present a novel analysis of the πN scattering amplitude in Lorentz covariant baryon chiral perturbation theory renormalized in the extended-on-mass-shell scheme. This amplitude, valid up to O(p 3 ) in the chiral expansion, systematically includes the effects of the ∆(1232) in the δ-counting, has the right analytic properties and is renormalization-scale independent. This approach overcomes the limitations that previous chiral analyses of the πN 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, σπN . 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 σπN = 59(7) MeV and comment on implications that this result may have.PACS numbers: 13.75. Gx, 11.30.Rd, 12.39.Fe, 13.85.Dz The sigma terms, σ πN and σ s , are observables of fundamental importance that embody the internal scalar structure of the nucleon, becoming an essential piece to understand the origin of the mass of the ordinary matter. The pion-nucleon sigma term, σ πN , is a key ingredient in investigations of the QCD phase diagram and in the study of nuclear systems [1,2]. On the other hand, σ πN and σ s appear as hadronic matrix elements in the neutralino-nucleon elastic scattering cross section. Unfortunately, our current knowledge of the sigma terms is far from satisfactory. With the advent of experimental results on dark-matter searches, different authors have pled for a more accurate experimental determination of these quantities [3][4][5].The σ πN is defined as the nucleon matrix element of the light-quark scalar current,The sigma term can be obtained from the πN scattering data by extrapolating the scattering amplitude to the Cheng-Dashen point [6,7], which lies in the unphysical region of the Mandelstam plane. The usual method to perform this extrapolation is by means of an energy-dependent parameterization of the data in partial waves (PW) supplemented by dispersion relations that impose strong analyticity and unitarity constraints onto the scattering amplitude at low energies. The current uncertainty in σ πN originates from discrepancies between the classical PW analysis of the Karlsruhe-Helsinki (KH) [8] group and the more modern one performed by the George-Washington [9] (GW) group. More precisely, the KH amplitudes were used by Gasser et al. to obtain the canonical result σ πN ≃ 45 MeV [10], whereas the analysis o...
We revisit the classical relation between the strangeness content of the nucleon, the pion-nucleon sigma term and the SU (3)F breaking of the baryon masses in the context of Lorentz covariant chiral perturbation theory with explicit decuplet-baryon resonance fields. We find that a value of the pion-nucleon sigma term of ∼60 MeV is not necessarily at odds with a small strangeness content of the nucleon, in line with the fulfillment of the OZI rule. Moreover, this value is indeed favored by our next-to-leading order calculation. We compare our results with earlier ones and discuss the convergence of the chiral series as well as the uncertainties of chiral approaches to the determination of the sigma terms.
We present a novel analysis of the πN scattering amplitude in covariant baryon chiral perturbation theory up to O(p 3 ) within the extended-on-mass-shell renormalization scheme and including the ∆(1232) explicitly in the δ-counting. We take the hadronic phase shifts provided by partial wave analyses as basic experimental information to fix the low-energy constants. Subsequently, we study in detail the various observables and low-energy theorems related to the πN scattering amplitude. In particular, we discuss the results and chiral expansion of the phase shifts, the threshold coefficients, the Goldberger-Treiman relation, the pion-nucleon sigma term and the extrapolation onto the subthreshold region. The chiral representation of the amplitude in the theory with the ∆ presents a good convergence from very low energies in the subthreshold region up to energies well above threshold, leading also to a phenomenological description perfectly consistent with the one reported by the respective partial wave analyses and independent determinations. We conclude that a model-independent and systematic framework to analyze πN-scattering observables using directly experimental data shall be possible in covariant baryon chiral perturbation theory.
We obtain leading-and next-to-leading order predictions of chiral perturbation theory for several prominent moments of nucleon structure functions. These free-parameter free results turn out to be in overall agreement with the available empirical information on nearly all of the considered moments, in the region of low-momentum transfer (Q 2 < 0.3 GeV 2 ). Especially surprising is the situation for the spin polarizability δ LT , which thus far was not reproducible in chiral perturbation theory for proton and neutron simultaneously. This problem, known as the "δ LT puzzle," is not seen in the present calculation.
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