Fermi's Interaction - The Nature of The Interaction

The Nature of The Interaction

The interaction could also explain muon decay via a coupling of a muon, electron-antineutrino, muon-neutrino and electron, with the same fundamental strength of the interaction. This hypothesis was put forward by Gershtein and Zeldovich and is known as the Conserved Vector Current hypothesis.

Fermi's four-fermion theory describes the weak interaction remarkably well. Unfortunately, the calculated cross-section grows as the square of the energy, making it unlikely that the theory is valid at energies much higher than about 100 GeV. The solution is to replace the four-fermion contact interaction by a more complete theory (UV completion)—an exchange of a W or Z boson as explained in the electroweak theory.

In the original theory, Fermi assumed that the form of interaction is a contact coupling of two vector currents. Subsequently, it was pointed out by Lee and Yang that nothing prevented the appearance of an axial, parity violating current, and this was confirmed by experiments carried out by Chien-Shiung Wu.

The inclusion of Parity violation in Fermi's interaction was done by George Gamow and Edward Teller in the so-called Gamow-Teller Transitions which described Fermi's interaction in terms of Parity violating "allowed" decays and Parity conserving "superallowed" decays in terms of anti-parallel and parallel electron and neutrino spin states respectively. Before the advent of the electroweak theory and the Standard Model, 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.