Fitting and selecting scattering data

The main purpose of scattering experiments is to unveil the underlying structure of the colliding particles and their interaction. Typically one measures scattering observables (cross sections and polarizations) at discrete angles and energies and mutually consistent data may validate or falsify proposed theories or models. However, the accumulation of data from different laboratories while potentially improves the statistical significance it may sometimes generate mutually inconsistent data as a side-effect. Thus, some decision has to be made on what are the maximal amount of data which are mutually compatible. We show elastic $\pi N$ and $NN$ scattering as prominent examples where this selection is called for. We discuss how it can be done in a self-consistent manner invoking a principle of maximal consensus of the database and with the help of a sufficiently flexible model involving a minimal number of theoretical assumptions. In the NN case this has become possible with a combination of long distance field theoretical constraints at the hadronic level such as pion exchanges and electromagnetic effects and a coarse graining of the unknown interaction over the shortest de Broglie wavelength being probed in the scattering process.