Regularization and error assignment to unfolded distributions

The commonly used approach to present unfolded data only in graphical form with the diagonal error depending on the regularization strength is unsatisfactory. It does not permit the adjustment of parameters of theories, the exclusion of theories that are admitted by the observed data and does not allow the combination of data from different experiments. We propose fixing the regularization strength by a p-value criterion, indicating the experimental uncertainties independent of the regularization and publishing the unfolded data in addition without regularization. These considerations are illustrated with three different unfolding and smoothing approaches applied to a toy example.