Understanding of the Renormalization Program in a mathematically   Rigorous Framework and an Intrinsic Mass Scale
  we show there exists a mathematically consistent framework in which the Renormalization Program can be understood in a natural manner. The framework does not require any violations of mathematical rigor usually associated with the Renormalization program. We use the framework of the non-local field theories [these carry a finite mass scale (\Lambda)]and set up a finite perturbative program. We show how this program leads to the perturbation series of the usual renormalization program [except one difference] if the series is restructured .We further show that the comparison becomes possible if there exists a finite mass scale (\Lambda), with certain properties, in the Quantum Field theory [which we take to be the scale present in the nonlocal theory]. We give a way to estimate the scale (\Lambda). We also show that the finite perturbation program differs from the usual renormalization program by a term; which we propose can also be used to put a bound on (\Lambda). 
Satish D. Joglekar (I.I.T.Kanpur, India)