Fermi interaction

In particle physics , the Fermi interaction is an effective description of the weak interaction , which was historically the first of its kind. Enrico Fermi proposed this theory, in which four fermions interact directly with each other (hence the name four-fermion interaction ). She is z. B. directly able to split a neutron (two down quarks and one up quark ) into an electron , an antineutrino and a proton (two up quarks and one down quark).

The Fermi interaction results as an effective theory from the electroweak interaction if all energies can be considered to be small compared to the mass of the W boson . The lowest order describes z. B. the muon decay very well. Higher orders, i.e. loop diagrams , cannot be calculated reliably because the Fermi interaction cannot be renormalized . As a solution, it is replaced by a more complete theory - the exchange of a W and a Z boson as described in the renormalizable electroweak interaction .

Before the electroweak theory and the Standard Model were established, George Sudarshan and Robert Marshak and independently Richard Feynman and Murray Gell-Mann were able to determine the correct tensor structure of the four-fermion interaction: vector minus pseudo vector , V - A .

Fermi constant

The strength of the Fermi interaction is determined by the Fermi coupling constant  . In modern notation: ${\displaystyle G_{\mathrm {F} }}$

${\displaystyle G_{\mathrm {F} }={\frac {\sqrt {2}}{8}}{\frac {g^{2}}{m_{\text{W}}^{2}}}=1{,}16637(1)\times 10^{-5}{\textrm {GeV}}^{-2}\ ,}$

It is

• ${\displaystyle g}$the coupling constant of the weak interaction
• ${\displaystyle m_{W}}$the mass of the W boson .

The Fermi constant is related to the vacuum expectation value of the Higgs field : ${\displaystyle v}$

${\displaystyle G_{\mathrm {F} }={\frac {1}{{\sqrt {2}}v^{2}}}}$.

Individual evidence

1. ↑ K. Nakamura et al. (Particle Data Group): Review of Particle Physics . (pdf) In: Journal of Physics G . 37, 2010, p. 075021. Retrieved March 23, 2011.