Evangelos Matsinos, Guenther Rasche
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, we first investigated 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 differences to our previous PSA: a) we now perform only \emph{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, by raising the minimal p-value (for the acceptance of the null hypothesis) from the equivalent of a $3 \sigma$ effect in the normal distribution to $2.5 \sigma$; the new value is closer to the 'common' preference for the outset of statistical significance ($1.00 \cdot 10^{-2}$). 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 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.
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http://arxiv.org/abs/1203.3625
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