# What happens in electron-electron collisions?

What are the results of high energy electron electron collisions? Are other particles created?

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As far as I know, nobody has ever done this, at least not at what we currently consider high energy. (Electron-electron collisions happen at low energy all the time, of course.) I doubt that anything interesting would happen, primarily because electrons are mutually repulsive, and they have a low mass. That means two colliding electrons would just bounce away from each other. They would produce some photons from bremsstrahlung radiation, but there wouldn't be any nontrivial interaction.

Even if we did give the electrons high enough energies to get very close and possibly have some sort of interesting interaction - and we're probably talking at least tens or hundreds of TeV here - the possible products are constrained pretty well by conservation of electron lepton number and charge. In particular, the reaction products would have to have total charge -2 and electron lepton number +2. The only configuration of known particles that satisfies that condition is two electrons, and if there were an unknown particle that could change that, it would have to be very strange indeed. Other than that, some number of particle-antiparticle pairs could always be produced, but we get that already at higher energies from $e^+e^-$ and hadron collisions, so there's no particular motivation to build a machine that can produce electron-electron collisions.

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You can pair produce just about anything in higher twist diagrams if enough energy is available, it's just that it doesn't promise much of anything interesting. –  dmckee May 15 '13 at 2:13
I suppose if you produce a couple of quarks you have a pretty clean probe into hadronization, but you get that out of $e^-$--$e^+$, too and with higher cross-section and the ability to use the same pipe for both beams. –  dmckee May 15 '13 at 2:21
What about finding the internal structure of electrons? –  Anixx Nov 6 '14 at 9:50
@Anixx you do not need electron electron scattering for that. great accuracy in the dimensions i gotten from the Bohr magnetons gabrielse.physics.harvard.edu/gabrielse/overviews/… Also storage rings have been used to estimate get a limit on the structure of electrons. –  anna v Nov 6 '14 at 10:38

Let's try just considering what could happen based on conservation laws. The two electrons have a charge of -2e, so the end product must as well. Lepton number conservation is required also, and we have $L_e=2$ here. At this level, it looks difficult to produce additional particles which satisfy just these two conservation laws. If you work in QED the only vertex is the photon one, and so if the energy of the two incoming electrons is large enough you might be able to produce something like

$$e^- +e^-\rightarrow e^-+e^-+(e^++e^-)$$

You can see the term in parenthesis are lepton-number and charge neutral. In principle you could do this with $\mu^++\mu^-$ or $\tau^++\tau^-$ as well.

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No collision is possible in between two electrons because the electron carry negative charge and push each other away with some assumption

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You are presumably arguing that the separation between two electrons can never fall to zero. However collisions between fundamental particles are described using quantum mechanics and because the particles are always delocalised to some extent the separation is ill defined. In this context the term collision means any close interaction causing a significant exchange of momentum. –  John Rennie Nov 6 '14 at 11:05