Improved input for multi-reaction hadronic analyses from elastic pion-nucleon scattering*

In the search for missing baryonic resonances, many analyses include data from a variety of pion and photon induced reactions. For elastic $\pi N$ scattering, however, usually the partial waves of the SAID or other groups are fitted, instead of data. We provide the partial-wave covariance matrices needed to perform correlated $\chi^2$ fits, in which the obtained $\chi^2$ equals the actual $\chi^2$ up to non-linear and normalization corrections. For any analysis relying on partial waves extracted from elastic pion scattering, this is a prerequisite to assess the significance of resonance signals and to assign any uncertainty on results. The compilation of the necessary data to improve hadronic analyses is presented in detail.