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Since in electron electron scattering if initial energy is quite large then muon antimuon production process can also take place which also contributes thus increases the total cross section.

What does increased cross section mean physically? Does it mean there will be more scattering events or anything more?

And How is this a helpful tool while detecting new particles?

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For high enough energies of the initial electrons, the muon pair production becomes possible which means that some fraction of the electron-electron collisions will lead to the production of the muons.

The fraction will depend on the energy as well as the impact factor – how accurately the electrons are hitting each other.

It doesn't make sense to discuss the change of the "total cross section" in this particular process because the total elastic cross section is infinite because the electromagnetism is a long-range force. Even if the impact factor is one meter and the electrons are "clearly missing each other", their momenta will be changed by a tiny amount which means that some (tiny) reaction has taken place and the event – every event of this kind – must be included to the cross section. This paragraph is meant to prove that the cross section is greater than a squared meter – it is greater than anything.

On the other hand, an interesting new feature of quantum mechanics we have to keep in mind is that the cross section is actually finite for short-range forces. This wouldn't be true in classical scattering. In classical scattering, even if the force (remains nonzero but) decreases very quickly with the distance, e.g. exponentially, the momenta of the particles are always changed at least a little bit when the particles interact (repel). In quantum mechanics, however, the probability that the particles' momenta are exactly the same as the initial ones is actually finite and close to one if the force between them is a short-range force. So in a big fraction of the reactions, nothing happens at all even though the force is formally nonzero at every distance!

While classical physics always favors some effects that tend to be extremely and arbitrarily weak if the interaction is very weak etc., quantum mechanics likes to quantize things and do something else. The effect that may occur – e.g. the production of an extra photon or a muon pair – may be finitely strong but it's the probability of this effect that goes to zero if the interaction is very weak (e.g. if the electrons are very far from one another).

High-energy scattering may produce new muons which is clearly useful for studying muons. It may also similarly produce other new particles which may be helpful for studying these other new particles. Collisions of particles are a tool to produce any particles and convince them to undergo any process that is possible in Nature. That's why particle colliders effectively probe everything about particle physics that may be probed in principle.

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