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| ! style="background:#ffdead;" | [[Feynman diagrams]]
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| | align="center" | '''t-channel'''<br>[[Image:MollerScattering-t.svg|220px]]
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| | align="center" | '''u-channel'''<br>[[Image:MollerScattering-u.svg|220px]]
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| |}
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| '''Møller scattering''' is the name given to [[electron]]-electron scattering in [[Quantum Field Theory]], named after the Danish physicist [[Christian Møller]]. The electron interaction that is idealized in Møller scattering forms the theoretical basis of many familiar phenomena such as the repulsion of electrons in the Helium nucleus. While formerly many particle colliders were designed specifically for electron-electron collisions, more recently electron-positron colliders have become more common. Nevertheless Møller scattering remains a paradigmatic process within the theory of particle interactions.
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| We can express this process in the usual notation, often used in [[particle physics]]:
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| :<math>
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| e^{-} e^{-} \longrightarrow e^{-} e^{-}
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| </math>,
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| In [[quantum electrodynamics]], there are two tree-level [[Feynman diagrams]] describing the process: a [[Mandelstam variables|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).
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| <!-- Image with unknown copyright status removed: [[Image:MollerTreeLevelDiagrams.jpg]] -->
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| In the electroweak theory the process is instead described by four tree-level diagrams: 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 (physics)|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.<ref>{{cite journal
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| | title = Precision Measurement of the Weak Mixing Angle in Møller Scattering
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| | author = Anthony, P. L. and others
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| | collaboration = SLAC E158 Collaboration
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| | journal = Phys. Rev. Lett.
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| | volume = 95
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| | issue = 8
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| | pages = 081601
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| | numpages = 5
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| |date=Aug 2005
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| | doi = 10.1103/PhysRevLett.95.081601
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| | url = http://link.aps.org/doi/10.1103/PhysRevLett.95.081601
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| | publisher = American Physical Society|arxiv = hep-ex/0504049 |bibcode = 2005PhRvL..95h1601A }}</ref> The asymmetry in Møller scattering is
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| :<math> | |
| A_{PV}=-m E \frac{G_F}{ \sqrt{2} \pi \alpha } \frac {16 \sin^2 \Theta_{\textrm{cm}}}
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| {\left(3+\cos^2 \Theta_{\textrm{cm}} \right)^2 } \left( \frac{1}{4} - \sin^2 \theta_W \right)
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| </math>,
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| where m is the electron mass, E the energy of the incoming electron (in the reference frame of the other electron), <math>G_F</math> is [[Fermi's interaction|Fermi's constant]], <math>\alpha</math> is the [[fine structure constant]], <math>\Theta_{\textrm{cm}}</math> is the scattering angle in the center of mass frame, and <math>\theta_W</math> is the weak mixing angle, also known as the [[Weinberg angle]].
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| == QED computation ==
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| <!--(to be completed)-->
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| <!-- INTRODUCTION The Moller scattering can be calculated from the QED point-of-view, at the tree-level, with the help of the two diagrams showed on this page. This two diagrams are contributing at leading order from the QED point-of-view. If we are taking in account he weak force, wich is unified with the electromagnetic force at high energy, then we have to add two tree-level diagram for the exchange of a Z^0 boson. Here we will focuse our attention on a strict tree-level QED computation of the cross section, which is rather instructive but maybe not the most accurate description from a physical point-of-view.-->
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| <!-- PRELIMINARY The two feynman diagrams are show on this page. We will redraw it for the purpose of the calculation, with the correct notations we will use for the input/output impulses.-->
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| {{Empty section|date=July 2010}}
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[http://www-project.slac.stanford.edu/e158/ SLAC E158: Measuring the Electron's WEAK Charge]
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| {{QED}}
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| {{DEFAULTSORT:Moller Scattering}}
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| [[Category:Quantum field theory]]
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| [[Category:Quantum electrodynamics]]
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