Analysis of the Low-Energy π<sup>±</sup>p Elastic-Scattering Data

Abstract

We report the results of a phase-shift analysis (PSA) of the low-energy elastic-scattering data. Following the method which we had set forth in our previous PSA [1], we first investigate the self-consistency of the low-energy elastic-scattering databases, via two separate analyses of (first) the and (subsequently) the elasticscattering data. There are two main differences to our previous PSA: 1) we now perform only one test for the acceptance of each data set (based on its contribution to the overall π p  π p  π p  π p  2 ) and 2) we adopt a more stringent acceptance criterion in the statistical tests. We show that it is possible to obtain self-consistent databases after removing a very small amount of the data (4.57% of the initial database). We subsequently fit the ETH model [38] to the truncated elastic-scattering databases. The model-parameter values show reasonable stability when subjected to different criteria for the rejection of single data points and entire data sets. Our result for the pseudovector coupling constant is. We extract the scattering lengths and volumes, as well as the sand p-wave hadronic phase shifts up to T = 100 MeV. Large differences in the s-wave part of the interaction can be seen when comparing our hadronic phase shifts with the current SAID solution (WI08); there is general agreement in the p waves, save for the π p

Systematic effects in the low-energy behavior of the current SAID solution for the pion-nucleon system

“…The list of the experiments, which are included in our three πN DBs, is available from Refs. [5,8]; the same notation will be used here to identify the individual data sets. Our DBs contain differential cross sections (DCSs), analyzing powers (APs), partial-total cross sections (PTCSs), and total (as well as total-nuclear) cross sections (TCSs) for T ≤ 100 MeV.…”

Aspects of the ETH model of the pion–nucleon interaction

“…The energy dependence of the K-matrix elements K I l± of the model for T ≤ 100 MeV is shown in Figs. 5-8, along with the current solution (as of June 12, 2013) of the SAID analysis [38]; we have already commented on the differences in the s-wave part of the πN interaction between these two solutions [4,5]. Regarding the model amplitudes, the expressions of Subsections 3.1-3.5 have been used, along with the optimal model-parameter vector corresponding to m σ = 475 MeV (the central value of the interval which is currently recommended by the PDG [17]); the fitted uncertainties have not been used.…”

“…The first state in each category (i.e., the D13(1520) and the D33(1700)) could be included in the model without much effort, after applying the formalism of Subsection 3.4 for the propagation of a spin-3 2 particle and standard transformations between the p and d states. The first report on the treatment of the propagation of spin- 5 2 particles has recently appeared [37]. Given the complexity of the subject, the complete development of the formalism and the extraction of amplitudes which can be directly used in our scheme are bound to take some time.…”

“…The quantity m σ (associated with the graphs of Subsection 3.1), which in Ref. [5] had been fixed at 860 MeV [23], is varied herein in the interval which is currently recommended by the PDG [17]. Fits were performed at seven m σ values, from 400 to 550 MeV with an increment of 25 MeV.…”

“…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).…”