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Suppose you have a λφ

But what about 3 particles scattering into 3 particles? Do the counter-terms determined by renormalizing the 2-pt and 4-pt functions cancel divergences in 3x3 scattering?

For example, take the graph below:

Is it obvious that the counter-terms from 2x2 and scattering, along with counter-terms from the 2-pt function, can cancel this graph?

^{4}theory. Books only seem to calculate counter-terms for 2-pt and 4-pt functions.But what about 3 particles scattering into 3 particles? Do the counter-terms determined by renormalizing the 2-pt and 4-pt functions cancel divergences in 3x3 scattering?

For example, take the graph below:

Is it obvious that the counter-terms from 2x2 and scattering, along with counter-terms from the 2-pt function, can cancel this graph?