New analysis of the low-energy π^±p differential cross-sections of the CHAOS Collaboration

Abstract

In a previous paper, we reported the results of a partial-wave analysis (PWA) of the pion–nucleon (πN) differential cross-sections (DCSs) of the CHAOS Collaboration and came to the conclusion that the angular distribution of their π+p data sets is incompatible with the rest of the modern (meson factory) database. The present work, re-addressing this issue, has been instigated by a number of recent improvements in our analysis, namely regarding the inclusion of the theoretical uncertainties when investigating the reproduction of experimental data sets on the basis of a given "theoretical" solution, modifications in the parametrization of the form factors of the proton and of the pion entering the electromagnetic part of the πN amplitude, and the inclusion of the effects of the variation of the σ-meson mass when fitting the ETH model of the πN interaction to the experimental data. The new analysis of the CHAOS DCSs confirms our earlier conclusions and casts doubt on the value for the πN Σ term, which Stahov, Clement and Wagner have extracted from these data.

Evaluation of the pion–nucleon sigma term from CHAOS data

“…The combination 2a + 1+ + a + 1− has been stable during the last three decades. Our result 2a + 1+ + a + 1− = (199 ± 14) · 10 −3 m −3 π , obtained from (7) using our values for coefficient c 1 , effective range b + 0+ and scattering length a + 0+ , is in good agreement with those obtained in partial wave analyses performed during the last several years [37,38,39], e.g. 2a + 1+ + a + 1− = (203.9 ± 1.9) · 10 −3 m −1 π [39].…”

“…Our result 2a + 1+ + a + 1− = (199 ± 14) · 10 −3 m −3 π , obtained from (7) using our values for coefficient c 1 , effective range b + 0+ and scattering length a + 0+ , is in good agreement with those obtained in partial wave analyses performed during the last several years [37,38,39], e.g. 2a + 1+ + a + 1− = (203.9 ± 1.9) · 10 −3 m −1 π [39]. In view of the spread among the various isoscalar scattering lengths mentioned above, we performed two tests to study the sensitivity of our determination of σ πN to a variation of the scattering length.…”

Roy–Steiner-equation analysis of pion–nucleon scattering

“…In more detail, the discrepancy could be attributed to about equal parts to the πN coupling constant, a + 0+ , and the dispersive integrals. 14 A similar picture emerged from the subthreshold parameters extracted with dispersive techniques from PWAs in [213][214][215][297][298][299], where the input from the GWU group [296,[300][301][302] consistently produced a larger σ-term than the PWAs from [76][77][78] (see also [303][304][305][306][307] in this context). Similarly, extractions of the σ-term from ChPT [20,308] tend to reproduce the value corresponding to the PWA that is used to determine the LECs in the physical region.…”

Aspects of the ETH model of the pion–nucleon interaction

“…In a series of subsequent papers, two πN-related issues were mainly addressed: a) the reproduction of the low-energy (T ≤ 100 MeV) π ± p elastic-scattering and charge-exchange π − p → π 0 n (CX) data [4,5,6,7], including the extraction of the values of the low-energy constants (LECs) of the πN system, and b) the violation of isospin invariance in the hadronic part of the πN interaction 1 [4,7,9]. The model was also involved in an iterative procedure which resulted in the determination of the electromagnetic (em) corrections [10,11], i.e., of the corrections which must be applied to the πN phase shifts and to the partialwave amplitudes on the way to the evaluation of the low-energy observables, namely of the differential cross section (DCS) and of the analysing power (AP).…”

“…The model was also involved in an iterative procedure which resulted in the determination of the electromagnetic (em) corrections [10,11], i.e., of the corrections which must be applied to the πN phase shifts and to the partialwave amplitudes on the way to the evaluation of the low-energy observables, namely of the differential cross section (DCS) and of the analysing power (AP). The long-term use of this model has demonstrated that it can account for the experimental information available at low energies almost as successfully as simple parameterisations of the K-matrix elements [4,5,6,7,12], which do not contain theoretical constraints other than the expected low-energy behaviour of these elements. One may thus conclude that the model constitutes a firm basis for the parameterisation of the dynamics of the πN system at low energies.…”