Is the Electron a Composite Particle?

In the "Standard Model" of particle physics, the fundamental objects are the leptons (electron, muon, tau lepton and their neutrinos) and the quarks. All the other observed particles, including protons and neutrons, are made up of combinations of quarks, while the quarks and leptons are point-like, with no internal structure.

How do we know other particles are composite?

But can we really be sure that the above picture represents reality? At different times in the past, atoms, nuclei and then protons have been thought of as fundamental objects. It is worth considering evidence which has shown us that this was not the case. Two particular phenomena demonstrate this:-

What about the electron?

One of the simplest stable particles currently held to be fundamental is the electron. Does this show any of the above signs of structure? The search at LEP for excited electrons e*, decaying according to e*   e  or e*   e Z or e*    W (with the Z and W subsequently decaying) has ruled out e* masses up to 46 GeV/c2 (and even up to 92 GeV/c2 - the maximum collision energy - unless the coupling between normal and excited electrons is extremely small). We can, however, extend the search up to considerably higher energies.

At LEP, electrons and positrons collide and annihilate. This normally occurs through the production of a Z0, which then decays into a fermion-antifermion pair. Another process, described in the Feynman diagram below, is annihilation into a pair of photons, e+ e- . In the standard model, the diagram describes two point-like particles exchanging a (virtual) electron. In composite models, the particles are no longer point-like, meaning the description of the interaction must incorporate a form factor, and although there is insufficient energy to produce real e*s, the exchange of virtual e*s must be included in the process. How large an effect the composite nature of the electron makes depends on both the mass of its constituents and upon the strength of the interaction which binds them.

Fig 1  Feynman Diagram showing Electron Positron Annihilation into Two Photons

Searching for an Anomalous Contribution to Two Photon Events in e+ e- Annihilation

Data from the ALEPH detector corresponding to several tens of million e+ e- annihilations were analysed to select the few thousands of events containing a final state composed of photons. This was done using the electromagnetic calorimeters and tracking chambers of the detector. First, two deposits of electromagnetic energy of at least 20 GeV, and separated by an angle of at least 120°, were required. It was then demanded that either both deposits had no charged particle associated with the energy or that only one was connected with a pair of tracks of low invariant mass, consistent with the conversion of a photon into an electron-positron pair. No additional tracks were allowed in the event. Timing cuts were also used to eliminate energy deposits associated with cosmic rays. To allow for the radiation of other photons, possibly passing down the beam pipe and so unobserved, the event was then transformed into the centre of mass frame of the two photons, and their angle, , relative to the initial beam direction was determined.

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

gives a differential cross section
and the lower limit on (at 95% confidence level) is found to be 173 GeV. The lower limit on the mass of the e* (in the 'Low model') is 163 GeV/c2.

Future Compositeness Limits?

The LEP accelerator has now run for 6 years, yielding many tens of millions of Z0 particles, corresponding to a total integrated luminosity of 170 pb-1. From these data, limits on the QED cut-off parameters + and - of 173 and 150 GeV have been obtained, while the lower limit on the mass of an excited electron is found to be 163 GeV/c2.

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 6 pb-1 of data at energies around 130 GeV. From 81 2-photon events, limits on + 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/c2.)

Talk given by Dr. C.N. Booth
April 1996