Definitions

# Fermi's interaction

In physics, Fermi's interaction is an old explanation of the weak force, proposed by Enrico Fermi. Four fermions directly interact with one another. For example, this interaction is directly able to split a neutron (or two down-quarks and an up-quark) to an electron, antineutrino and a proton (or two up-quarks and a down-quark).

Tree Feynman diagrams describe the interaction remarkably well. Unfortunately, loop diagrams cannot be calculated reliably because Fermi's interaction is not renormalizable. The solution is to replace the four-fermion contact interaction by a more complete theory (see UV completion) — an exchange of a W boson or a Z boson as explained in the electroweak theory. The electroweak theory is renormalizable.

Before the electroweak theory and the Standard Model were constructed, George Sudarshan and Robert Marshak, and also independently Richard Feynman and Murray Gell-Mann were able to determine the correct tensor structure (vector minus axial vector, V−A) of the four-fermion interaction.

## Fermi constant

The strength of Fermi's interaction is given by the Fermi constant $G_F$. In modern terms,

$frac\left\{G_\left\{F\right\}\right\}\left\{\left(hbar c\right)^3\right\}=frac\left\{sqrt\left\{2\right\}\right\}\left\{8\right\}frac\left\{g^\left\{2\right\}\right\}\left\{m_\left\{W\right\}^\left\{2\right\}\right\}=1.16637\left(1\right)times10^\left\{-5\right\}textrm\left\{GeV\right\}^\left\{-2\right\}$

Here $g$ is the coupling constant of the weak interaction, and $m_W$ is the mass of the W boson.

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