Phase-shift analysis of low-energy elastic-scattering data

Abstract

Using electromagnetic corrections previously calculated by means of a potential model, we have made a phase-shift analysis of the π ± p elastic-scattering data up to a pion laboratory kinetic energy of 100 MeV. The hadronic interaction was assumed to be isospin invariant. We found that it was possible to obtain self-consistent databases by removing very few measurements. A pion-nucleon model, based on sand u-channel diagrams with N and ∆ in the intermediate states, and σ and ρ t-channel exchanges, was fitted to the elastic-scattering database obtained after the removal of the outliers. The model-parameter values showed an impressive stability when the database was subjected to different criteria for the rejection of experiments. Our result for the pseudovector πN N coupling constant (in the standard form) is 0.0733 ± 0.0014. The six hadronic phase shifts up to 100 MeV are given in tabulated form. We also give the values of the s-wave scattering lengths and the p-wave scattering volumes. Big differences in the s-wave part of the interaction were observed when comparing our hadronic phase shifts with those of the current GWU solution. We demonstrate that the hadronic phase shifts obtained from the analysis of the elastic-scattering data cannot reproduce the measurements of the π − p charge-exchange reaction, thus corroborating past evidence that the hadronic interaction violates isospin invariance. Assuming the validity of the result obtained Preprint submitted to Elsevier Science within the framework of chiral perturbation theory, that the mass difference between the u-and the d-quark has only a very small effect on the isospin invariance of the purely hadronic interaction, the isospin-invariance violation revealed by the data must arise from the fact that we are dealing with a hadronic interaction which still contains residual effects of electromagnetic origin. PACS: 13.75.Gx; 25.80.Dj; 25.80.Gn

Improved description of the πN-scattering phenomenology in covariant baryon chiral perturbation theory

“…This gives information about the scalar coupling of the nucleon and is an important quantity for hadronic physics as well as for direct detection of dark matter [13]. Using this approach we showed in [6] that the modern N partial wave analyses (PWAs) [14,15] point to a relatively large value of the sigma term,…”

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

“…For the partial wave analysis of the pion-nucleon scattering amplitudes results of several groups are available: Karlsruhe [66,67], Matsinos [68] and GWU [45]. Unfortunately, none of these groups provide uncertainties of their results.…”

Relativistic chiral representation of the πN scattering amplitude II: The pion–nucleon sigma term

“…We then fix the values of the LECs fitting the CM energy dependence of the 2 S-and 4 P -wave phase shifts obtained from the chiral amplitude to the latest solutions of the KH [11] and GW [12] groups. In addition, we include the analysis of the Matsinos' group (EM) [22] which focuses in the PW parameterization of the data at very low energies without imposing dispersive constraints from the high-energy region. The fits are done from the lowest CM energies above threshold, W th ≃ 1.08 GeV, up to W max = 1.2 GeV which is below the ∆(1232) region (the EM analysis only reaches W max ≃ 1.16 GeV).…”

“…For a thoughtful discussion on the discrepancy of the isovector scattering length extracted from the low-energy scattering data by the EM analyses, a − 0+ = 0.0797(11) m −1 π , see Refs. [22]. We have explored the subthreshold region and obtained the subthreshold coefficients which result from a Taylor expansion of the amplitudes about the point W cd and t = 0 [7].…”

“…The consistency between the results derived from the GW and EM solutions is very remarkable since these are quite different analyses having both in common the implementation of the wealth of low-energy data collected along the last 20 years in meson factories [12,22] with many points not included in KH [11]. Besides that, the positive values determined from pionic-atom data for a + 0+ , which are consistent with those extracted from the GW and EM PWs, strongly constrain σ πN , raising it for 7 MeV as compared with the KH values [13,9].…”