Møller scattering
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t-channel |
u-channel |
Møller scattering is the name given to electron-electron scattering in Quantum Field Theory. The electromagnetic and electroweak forces that govern electron interactions produce wonderful effects like electricity and electric fields, and at the same time result in the three body problem in atomic Helium. Since in quantum field theory there can be no force without a mediating particle, Møller scattering describes virtually all electron-electron interactions. True Møller scattering is now less common in experimental particle physics, having given way to electron-positron scattering (as in the International Linear Collider).
In quantum electrodynamics, there are two tree-level Feynman diagrams describing the process: a t-channel diagram in which the electrons exchange a photon and a similar u-channel diagram. Crossing symmetry, one of the tricks often used to evaluate Feynman diagrams, in this case implies that Møller scattering should have the same cross section as Bhabha scattering (electron-positron scattering).
In the electroweak theory the process is instead described by four tree-level diagrams (see image): the two from QED and an identical pair in which a Z boson is exchanged instead of a photon. The weak force is purely left handed, but the weak and electromagnetic forces mix into the particles we observe. The photon is symmetric by construction, but the Z boson prefers left-handed particles to right-handed particles. Thus the cross sections for left-handed electrons and right-handed differ. The difference was first noticed by the Russian physicist Yakov Zel'dovich in 1959, but at the time he believed the parity violating asymmetry (a few hundred parts per billion) was too small to be observed. This parity violating asymmetry can be measured by firing a polarized beam of electrons through an unpolarized electron target (liquid hydrogen, for instance), as was done by an experiment at the Stanford Linear Accelerator Center, SLAC-E158[1]. The asymmetry in Møller scattering is
,
where m is the electron mass, α is the fine structure constant, Θcm is the scattering angle in the center of mass frame, and θW is the weak mixing angle, also known as the Weinberg angle.
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