# Collision Between Three or More Particles

Collisions between two particles happen all the time.
But can there be three or more particles colliding at the same time ? Has such an event been observed so far ? And if that can't happen, why not ?

Thank you

Of course it CAN happen, but it is very unlikely to, and doesn't really tell you anything new or interesting (that I know of). In terms of say building a 3-way particle collider, the decrease in the energy of collisions between any pair of particles far outweighs any benefit you would get from any rare extra-high energy collisions between three, and likewise the cost of building a third stretch of accelerator for the extra beam makes it way not worth it.

You can also imagine :
electron+positron -> quark+antiquark+gluon
or more jets
and then you can imagine that if you prepare all the final particles in the 3 jets carefully in opposite momenta, you could in principle obtain the initial electron+positron state.

But I am too sure how this question should be answered.

For definiteness, take :
neutron -> proton + electron + antineutrino
In principle you can collide the final state with enough energy to produce the initial state.

However at a fundamental level, the standard model tells us that this is a 2-2 scattering

All elementary processes in the standard model proceed in 2-2 fundamental scatterings.

String theory can accommodate 1->3 (or more) processes but dodges the question since there is no unique fundamental vertices anymore there (no unique way to cut the worldsheet).

mathman
from
http://en.wikipedia.org/wiki/Carbon
Formation in stars
Main articles: Triple-alpha process and CNO cycle

Formation of the carbon atomic nucleus requires a nearly simultaneous triple collision of alpha particles (helium nuclei) within the core of a giant or supergiant star which is known as the triple-alpha process, as the products of further nuclear fusion reactions of helium with hydrogen or another helium nucleus produce lithium-5 and beryllium-8 respectively, both of which are highly unstable and decay almost instantly back into smaller nuclei.[49] This happens in conditions of temperatures over 100 megakelvin and helium concentration that the rapid expansion and cooling of the early universe prohibited, and therefore no significant carbon was created during the Big Bang. Instead, the interiors of stars in the horizontal branch transform three helium nuclei into carbon by means of this triple-alpha process.[50] In order to be available for formation of life as we know it, this carbon must then later be scattered into space as dust, in supernova explosions, as part of the material which later forms second, third-generation star systems which have planets accreted from such dust.[51] The Solar System is one such third-generation star system. Another of the fusion mechanisms powering stars is the CNO cycle, in which carbon acts as a catalyst to allow the reaction to proceed.

Rotational transitions of various isotopic forms of carbon monoxide (for example, 12CO, 13CO, and C18O) are detectable in the submillimeter wavelength range, and are used in the study of newly forming stars in [[molecular clouds.[52]

"nearly simultaneous triple collision" is not good enough as I was looking for examples of exactly simultaneous triple collision. Also I'm more interested in examples with elementary particles.

I'm starting to believe that a simultaneous triple collision of elementary particles is not possible.
The argument given by humanino, that:
"All elementary processes in the standard model proceed in 2-2 fundamental scatterings."
seems convincing enough.

But is there a theoretical reason for only having 2-2 fundamental scatterings, or is that based on observation ?

There are experimental results suggesting a three-particle force component inside nuclei, but as far as I know there is no conclusive proof of that.

But is there a theoretical reason for only having 2-2 fundamental scatterings, or is that based on observation ?
I do not think this is based upon observation. Rather, it is based upon a perturbative expansion (Feynman diagram) of renormalizable interactions.

But, you can always write down effective interactions (and hopefully even derive them) which are non-renormalizable (they loose their validity at certain scale). The three body forces in nuclei is a good example, and there is very strong evidence that it is really there
Origin of the anomalous long lifetime of 14C

Last edited:
Hepth
Gold Member
Yes, in the standard model there are vertices corresponding at tree level to an interaction that has 3 in and one out, so a 4-body interaction. This happens NOT with fermions, but with the gauge bosons. Take a look at the electroweak theory page on wikipedia. There are terms in the SM such as [A (photon) Z, W+, W-]
where:

W+W-ZZ
ZZZZ
etc
So a w+w- and a Z can "collide exactly" and create an outgoing Z.

That is an important point. However, I am not sure those qualify as "collisions" in the sense that intermediate vector bosons are never outside the S-matrix, they never appear in asymptotic states.

Hepth
Gold Member
Yeah, I wouldn't call anything a real "collision" but just thought I'd point out that there ARE 4-point interactions.