Fermi's interaction
Encyclopedia
In particle physics
, Fermi's interaction also known as Fermi coupling, is an old explanation of the weak force, proposed by Enrico Fermi
, in which four fermions directly interact with one another at one vertex. For example, this interaction explains beta decay of a neutron by direct coupling of a neutron
(two down quark
s and an up quark
) with an electron
, antineutrino and a proton
(two up quarks and a down quark). The interaction could also explain muon decay via a coupling of a muon, electron-antineutrino, muon-antineutrino and electron. Fermi first introduced this coupling in his description of beta decay in 1933.
Tree Feynman diagram
s 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 or Z boson
as explained in the electroweak theory. The electroweak theory is renormalizable.
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) of the four-fermion interaction.
Here g is the coupling constant
of the weak interaction
, and mW is the mass of the W boson which mediates the decay in question.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, Fermi's interaction also known as Fermi coupling, is an old explanation of the weak force, proposed by Enrico Fermi
Enrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...
, in which four fermions directly interact with one another at one vertex. For example, this interaction explains beta decay of a neutron by direct coupling of a neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
(two down quark
Down quark
The down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
s and an up quark
Up quark
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
) with an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
, antineutrino and a proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
(two up quarks and a down quark). The interaction could also explain muon decay via a coupling of a muon, electron-antineutrino, muon-antineutrino and electron. Fermi first introduced this coupling in his description of beta decay in 1933.
Tree Feynman diagram
Feynman diagram
Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
s 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
UV Completion
In theoretical physics, ultraviolet completion, or UV completion, of a quantum field theory is the passing from a lower energy quantum field theory to a more general quantum field theory above a threshold value known as the cutoff...
) — an exchange of a W or Z boson
W and Z bosons
The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
as explained in the electroweak theory. The electroweak theory is renormalizable.
Before the advent of the electroweak theory and the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
, George Sudarshan
George Sudarshan
Ennackal Chandy George Sudarshan , also E.C.G. Sudarshan, is a prominent Indian American physicist, author, and professor at The University of Texas at Austin.-Early life:...
and Robert Marshak
Robert Marshak
Robert Eugene Marshak was an American physicist dedicated to learning, research, and education.-History:...
, and also independently Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
and Murray Gell-Mann
Murray Gell-Mann
Murray Gell-Mann is an American physicist and linguist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles...
, were able to determine the correct tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
structure (vector minus axial vector) of the four-fermion interaction.
Fermi constant
The strength of Fermi's interaction is given by the Fermi coupling constant GF. The most precise experimental determination of the Fermi constant comes from measurements of the muon lifetime, which is inversely proportional to the square of GF. In modern terms:Here g is the coupling constant
Coupling constant
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...
of the weak interaction
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
, and mW is the mass of the W boson which mediates the decay in question.