Perturbative S-matrices that depend on parameters of a realistic   regularization
  We propose a partial answer to the question of what kind of ultrahigh-energy physics has to be taken into account to circumvent the appearance of ultraviolet divergencies; a more than sixty years old open question in quantum electrodynamics. To this end we introduce a new theoretical concept to the theory of quantum scattering: Perturbative S-matrices that depend on parameters of a realistic regularization--realistic in the sense of Pauli and Villars [Rev. Mod. Phys. 21, 434 (1949)]. We expect that these additional parameters may provide some new information about the physics of quantum scattering. There are such perturbative S-matrices also in the presence of non-renormalizable interaction terms with no counterterms. 
Marijan Ribaric and Luka Sustersic