Analysis of the low-energy $\pi^\pm p$ elastic-scattering data

TL;DR

This paper conducts a phase-shift analysis of low-energy $\pi^\pm p$ elastic-scattering data, ensuring data consistency, fitting a theoretical model, and extracting key physical parameters with improved statistical rigor.

Contribution

It introduces a more stringent data acceptance criterion and demonstrates the self-consistency of the low-energy scattering database, refining the extraction of physical parameters.

Findings

Achieved a self-consistent scattering database with only 4.57% data removal.

Determined the pseudovector $\pi N N$ coupling constant as 0.0726 ± 0.0014.

Extracted scattering lengths, volumes, and phase shifts up to 100 MeV, revealing differences with existing solutions.

Abstract

We report the results of a phase-shift analysis (PSA) of the low-energy $\pi^\pm p$ elastic-scattering data. Following the method which we had set forth in our previous PSA (Matsinos et al., 2006), we first investigate the self-consistency of the low-energy $\pi^\pm p$ elastic-scattering databases, via two separate analyses of (first) the $\pi^+ p$ and (subsequently) the $\pi^- p$ elastic-scattering data. There are two main differences to our previous PSA: a) we now perform only one test for the acceptance of each data set (based on its contribution to the overall $\chi^2$) and b) 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 (Goudsmit et al. 1994) to the truncated $\pi^\pm p$ 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 $\pi N N$ coupling constant is $0.0726 \pm 0.0014$. We extract the scattering lengths and volumes, as well as the s- and 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 $\tilde{\delta}_{1-}^{1/2}$ hadronic phase shift.