- Excited states - when atoms, nuclei or protons are given sufficient energy, they can be excited into higher states, which are often unstable, decaying back to the ground state with the emission of a photon or other particles.
- Form factors - the scattering of high energy particles from a nucleus or proton cannot be accurately described by scattering from a point object. To explain the angular (or momentum) distribution of the scattered beam requires a form factor, which is the Fourier transform of the target particle's spatial distribution.

At LEP, electrons and positrons collide and annihilate.
This normally occurs through the production of a Z^{0}, which then
decays into a fermion-antifermion pair.
Another process, described in the Feynman diagram
below, is annihilation into a pair of photons,
^{+} e^{-}

Fig 1 Feynman Diagram showing Electron Positron Annihilation into Two Photons

The observed angular distribution, corrected for detector effects, is shown in figure 2. Superimposed on this is the distribution predicted by the Standard Model. It can be seen that the agreement is very good.

Fig 2 Differential Cross-Section (Corrected for Detector Acceptance)
as a Function of

This is clearer in figure 3, showing the ratio of observed to predicted cross-section as a function of . Clearly there is no need for extra effects, introduced by the compositeness of the electron. This does not, however, mean that we can rule out any structure to the particle. Composite models of the electron can be parametrised in various ways, and we can put limits on these parameters. We can determine the maximum allowed anomalous contribution (at the two standard deviation level) as a function of , and so deduce lower limits on the energy scale of the form factor and, in particular models, on the mass of the e*.

Fig 3 Ratio of Observed to Predicted Cross-Section as a Function
of

Expressing the form factor as

Unfortunately, the limit on parameters such as only improves proportional to the eighth root of the integrated luminosity, so even if LEP were to run at the same energy for many years more, the improvement in would be rather small. However, the limit on also depends on the centre-of-mass collision energy, being proportional to the energy to the power three-quarters for a given integrated luminosity. Making measurements at a higher energy is therefore the best way to improve our searches for the effects of compositeness in the electron.

LEP is now being upgraded to run at gradually increasing energies, from
161 GeV in 1996 to over 190 GeV in a few years' time (compared with previous
operation at 91 GeV - the rest-mass energy of the Z).
As an indication
of what may be achieved, a very short run in the Autumn of 1995 produced
less than ^{-1}_{+}
and _{-}
of 169 and 132 GeV were obtained, competitive with the values above extracted
from 80 times as many events (30 times as large an integrated luminosity)
at lower energy.
(The limit on the excited electron mass, which does
not rise quite so quickly with energy, was found to be 136 GeV/c^{2}.)