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

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 $\pi NN$ 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.

Comments: J. Mod. Phys. 3 (2012) 1369-87