If you've ever heard of Feynman diagrams, you've probably seen the simplest sort - the ones with the fewest possible interactions. What you may not have seen much of are loop diagrams - Feynman diagrams with the same starting and ending states but with extra, seemingly-extraneous interactions in the middle. The funky thing about the Feynman path integral formulation of particle physics is that in order to calculate the amplitude (related to the probability) for an interaction, you need to account for all possible diagrams with start and end states you care about. That means, yes, all of those loops on loops on loops, which we call higher-order diagrams. Luckily, for forces like the weak force and electromagnetism, the amount that higher-order diagrams contribute to the amplitude decreases with complexity. As a result, it's often a reasonable approximation to use only the simplest diagram to describe an interaction, and even professionals often content themselves with fourth- or fifth-order diagram contributions.
Less fortunately, the strong nuclear force is less obliging. Rather than higher-order diagrams contributing less and less to the total amplitude, they contribute increasingly large amounts. This trouble with gluons (those are the force carriers for the strong force) is one of a couple of traits that makes the strong nuclear force such a pain to work with for theorists.
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