Møller scattering

As Møller scattering is called the scattering of two electrons to each other. With the exception of very high-energy collisions, such as those be artificially produced in modern particle accelerators, the interaction between the electrons can be considered as a purely electromagnetic. Under this - even the original publication of Christian Møller underlying - Adopt the scattering with quantum electrodynamics ( QED) can be described. At higher energies occur measurable corrections by other interactions, the exchange of Z bosons in the Standard Model of particle physics (SM) or other exchange particles in exotic physics models (the " physics beyond the standard model " ) on.

Quantum electrodynamics

The only existing in quantum electrodynamics interaction is the electromagnetic interaction. In the speech of the quantum field theoretical perturbation theory the momentum exchange between the participating electrons occurs via the exchange of virtual photons.

The incident electrons carry the momentum before the collision and. After the collision, there are two electrons with the pulses and. In the first approximation of perturbation theory two Feynman diagrams that describe the process in place (see illustration at right ). The two diagrams, named after the occurring in the denominator of the respective mathematical expression Mandelstamvariablen t- channel and u - channel, differ only in the context of the pulses. Intuitively, one can imagine this so that the outgoing electron with momentum before the scattering may have had the pulse or the pulse, and therefore both ways to contribute scattering probability ( the cross section ).

In the center of mass system is obtained in the relativistic limit, ie when the energies of the electrons are significantly larger than 512 keV, the differential cross section

Where E is the energy of an electron, the coupling constant of QED, and the scattering angle.

Other interactions

Even in a first approximation, the momentum exchange of the electrons must be done not necessarily have an intermediate photon. Example, allows the standard model of particle physics is also a momentum exchange via an intermediate Z- boson. The corresponding Feynman diagrams are similar to the diagrams from electrodynamics, the inner line is now a Z boson. The associated terms, however, differ in two important ways:

• The contribution of the intermediate particle to the scattering probability depends on its mass. In particular, the contribution of the exchanged Z boson for center of mass energies is significantly below 91 GeV / c ², the mass of the Z boson is negligible compared to the contribution from photon exchange. At sufficiently high energies, as they can be produced, for example, in particle accelerators, but the contribution of the Z boson is measurable.
• In contrast to the photon exchange, the exchange of a Z boson is sensitive to the polarization of the electrons. This leads to a measurable function of the total cross section of the electric polarization.

In addition to the contribution from the exchange of Z bosons also more direct contributions by previously unknown elementary particles are conceivable. Since such contributions have not been measured, these particles must either have little interaction with the electrons, such as a potential graviton, or a high rest mass possess, so that their contributions for focus energies below this mass are strongly suppressed.