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As muon colliders do not yet exist, has muon-muon annihilation already been realized experimentally?

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    $\begingroup$ Can you clarify what you are asking? Are you asking if we have observed a muon and anti-muon annihilating, whether we have observed a high energy collision between two (anti)muons, or something else? $\endgroup$ – John Rennie Jan 25 '16 at 8:25
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    $\begingroup$ I am not aware that direct evidence for muon/anti-muon annihilation in a collider experiment exists for the reason that you mentioned, but the inverse process, the creation of a muon/anti-muon pair is a standard process. I am not a theoretical physicist, but I remember seeing the calculation (at least in lowest order) as a standard student exercise in QFT books, so I would guess that it's not hard to estimate the cross sections. $\endgroup$ – CuriousOne Jan 25 '16 at 10:40
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    $\begingroup$ I imagine the odds are pretty decent that the process is actually been recorded in some LHC event from one for the detector packages. But no one is looking for it there and so we probably don't know it. $\endgroup$ – dmckee --- ex-moderator kitten Jan 25 '16 at 19:23
  • $\begingroup$ The interesting fact of the muon collider is not the muon annihilation itself (which from the production process we know to be very similar to electron-positron annihilation), but the possibility to bend muonic beams in storage rings at much higher energies compared to what is feasible with electron machines, therefore achieving very high energy collisions between fundamental (as far as we know) particles. $\endgroup$ – DarioP Jan 26 '16 at 13:42
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    $\begingroup$ Also note that setting up a muon collider experiment, based on two primary beams impinging on two face-to-face targets for the muon production, would actually be easy. But the low energy and collision rate obtained in this way wouldn't bring much (if not any) insight of high energy physics. $\endgroup$ – DarioP Jan 26 '16 at 13:42
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A muon and an anti muon can annihilate but not a muon and a muon. They are not antiparticles. Two muons could exchange energy and momentum between each other though.

Muon antimuon annihilations works like this where the muons annihilate into a Z boson and this Z boson decays to electron neutrino and an antielectron neutrino.

$\mathrm\mu^-+\mu^+=Z^0$

$\mathrm\ Z^0=\nu_e+\bar{v_e} $

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