Renormalization
The integrals over unconstrained momenta, called "loop integrals", in the Feynman graphs typically diverge. This is normally handled by renormalization, which is a procedure of adding divergent counter-terms to the Lagrangian in such a way that the diagrams constructed from the original Lagrangian and counter-terms is finite. A renormalization scale must be introduced in the process, and the coupling constant and mass become dependent upon it. It is this dependence that leads to the Landau pole mentioned earlier, and requires that the cutoff be kept finite. Alternatively, if the cutoff is allowed to go to infinity, the Landau pole can be avoided only by if the renormalized coupling runs to zero, rendering the theory trivial.
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