Computing QED amplitudes in a collider

[eoghan]

Hi there,

While reviewing the theory of Feynman diagrams for QED, a question came into my mind. In the textbooks, one usually deals with processes involving two incoming particles. But I could imagine a process where four particles are interacting (e.g. attached picture) and this can give a contribution that is of the same order as a loop diagram with only two interacting particles. Since in a collider two beams of particles collide I can expect to have interactions between any even number of particles. So in order to compute the cross section should one compute also these interactions? Or for some reasons the diagrams with more than two particles cancel away?

 

[Orodruin]

It is hard enough to get two particles to collide. Having four particles interact is practically impossible.

 

[mfb]

Exercise for you: The typical size of the interaction region of hadron collisions is 1 fm². Ignoring correlations, how likely is it that four particles are within 1 fm of each other? How does that compare to two particles?
For leptons the effective interaction region is even smaller.

In practice even the “~0“ answer is an overestimate as particles in a beam don’t get that close.