Fermi's interaction
Fermi's interaction
In particle physics, Fermi's interaction (also the Fermi theory of beta decay) is an explanation of the beta decay, proposed by Enrico Fermi in 1933.[1] The theory posits four fermions directly interacting with one another (at one vertex of the associated Feynman diagram). This interaction explains beta decay of a neutron by direct coupling of a neutron with an electron, a neutrino (later determined to be an antineutrino) and a proton.[2]
Fermi first introduced this coupling in his description of beta decay in 1933.[3] The Fermi interaction was the precursor to the theory for the weak interaction where the interaction between the proton–neutron and electron–antineutrino is mediated by a virtual W− boson.
History of initial rejection and later publication
Fermi first submitted his "tentative" theory of beta decay to the famous science journal Nature, which rejected it "because it contained speculations too remote from reality to be of interest to the reader.[4]" Nature later admitted the rejection to be one of the great editorial blunders in its history.[5] Fermi then submitted revised versions of the paper to Italian and German publications, which accepted and published them in those languages in 1933 and 1934.[6][7][8][9] The paper did not appear at the time in a primary publication in English.[5] An English translation of the seminal paper was published in the American Journal of Physics in 1968.[9]
Fermi found the initial rejection of the paper so troubling that he decided to take some time off from theoretical physics, and do only experimental physics. This would lead shortly to his famous work with activation of nuclei with slow neutrons.
The "tentativo"
Definitions
Electron state
Neutrino state
Similarly,
Heavy particle state
represents a neutron, and
The operators that change a heavy particle from a proton into a neutron and vice versa are respectively represented by
and
Hamiltonian
![{\displaystyle H_{\text{int.}}=g\left[Q\psi (x)\phi (x)+Q^{*}\psi ^{*}(x)\phi ^{*}(x)\right],}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b1bc38c2db0878585fd0891e8dadde6e92dba26)
![{\displaystyle H_{\text{int.}}=g\left[Q{\tilde {\psi }}^{*}\delta \psi +Q^{*}{\tilde {\psi }}\delta \psi ^{*}\right],}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b03c8d3668dbc6810fd1ac03661cfccf273b378a)
Matrix elements
Transition probability
According to Fermi's golden rule, the probability of this transition is
Fermi makes three remarks about this function:
Since the neutrino states are considered to be free, and thus the upper limit on the continuous -spectrum is .
Since for the electrons , in order for -decay to occur, the proton–neutron energy difference must be
The factor
Forbidden transitions
Influence
Later developments
 |
| Fermi's interaction showing the 4-point fermion vector current, coupled under Fermi's Coupling ConstantGF. Fermi's Theory was the first theoretical effort in describing nuclear decay rates for β decay. |
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 Vector Current Conservation hypothesis.[14]
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.[15][16]
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.[17][18]
Fermi coupling constant
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.
In the Standard Model, Fermi's constant is related to the Higgs vacuum expectation value
- .[21]
More directly, approximately (tree level for the standard model),
