me again... what are next to next leading order calculations in the standard model?
That just means the two loops corrections to the lowest order diagram you can draw for a given process. So you consider a certain process and draw the diagram with the fewest number of loops possible; this is your leading order diagram (this leading order diagram could be a tree level diagram but it may also contain loops since some processes are only possible with loops). Then you consider all the diagrams containing two extra loops relative to the leading order diagram. These are the next to next leading order corrections.
It depends if you count loop-order L or coupling-constant-order N. You can add vertices increasing N keeping L fixed.
Good point. But this possibility arises only in the context of infrared effects, where we do not observe the low energy particles (for example photons). Otherwise, having a differenr number of coupling constant does not give the same diagram as the lowest order diagram (the asymptotic particle content is different).
Yes, I agree.
All what I say is that talking about "the order" is ambiguous unless you specify whether it is the number of verices or the number of loops.
It's right that if you count loop-order L or coupling-constant-order N.
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