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There are no stable mesons as far as I know. Are there any meson-colliders analogous to for example proton-proton colliders?

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There are no meson colliders as there is no advantage to using them. In a hadron collider (mesons are hadrons) the interesting collisions occur between the constituents of the hadrons, i.e. the quarks. The hadrons themselves don't have much of an effect on the interesting physics. Protons are easy to create and long lived. So we can create them and not worry about the protons disappearing. Furthermore, protons are charged and heavy which makes them easy to accelerate. This makes protons a very convenient choice of particle to use in a collider.

The only other sensible particles to use in a collider are fundamental particles (such as leptons) since they have their own advantages or heavy ions since they study different physics.

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Also, heavier nuclei. –  Jerry Schirmer Jan 14 at 14:30
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I mentioned heavy ion collisions? –  JeffDror Jan 14 at 14:32

The feasibility of colliding a specific particle could be assessed by the following criteria:

  1. Is the particle charged? If the particle is charged you can accelerate it using magnetic fields.
  2. Is the particle stable/long-lived? If the particle is stable then you can collide it before decays.
  3. Can we produce a lot of them to make it worthwhile?

Compared to, say, protons and electrons, mesons aren't a very good choice for a particle collider. Even muons are a better choice:

http://www.fnal.gov/pub/muon_collider/

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The only happy footnote to a meson accelerator is relativistic time dilation. If you can beep it to a few nines of lightspeed within a lab frame microsecond, you've got a presumed linear accelerator,

http://en.wikipedia.org/wiki/File:FrischSmith.svg
"Results of the Frisch-Smith experiment, confirming time dilation by measuring the decay rate of muons in accordance with special relativity."

A muon collider would offer a lepton (point particle) with 105.7 MeV/c^2 rest mass, as opposed to an electron with 0.511 MeV/c^2.

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Muon colliders are planned, but they have little to do with meson colliders. –  dmckee Feb 14 at 2:25
    
arXiv:1308.2143, 1204.3538, hepconf.physics.ucla.edu/higgs2013/talks/eichten.pdf, hepconf.physics.ucla.edu/higgs2013, symmetrymagazine.org/article/october-2010/when-muons-collide. You arew quick with criticism. Let's see how quick you are with apology. –  Uncle Al Feb 14 at 17:44
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Al, despite the earliest name (mu meson) a muon is not a meson, it is a lepton. Muon colliders have been high on the particle physics wishlist for decades, but no one is talking about meson colliders because they are (1) hard and (2) not significantly better than proton and ion colliders. Your links talk about muon colliders, not meson colliders, which is just what I said. –  dmckee Feb 14 at 19:03
    
Sonofagun. I stand corrected. Are we now certain that the poster wanted a meson (same quark problem) not a muon? –  Uncle Al Feb 15 at 3:43

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