Eightfold way (physics)
In physics, the eightfold way is an organizational scheme for a class of subatomic particles known as hadrons that led to the development of the quark model.
There were electrons, protons, neutrons, and photons (the components that make up the vast part of everyday experience such as visible matter and light) along with a handful of unstable (i.e., they undergo radioactive decay) exotic particles needed to explain cosmic rays observations such as pions, muons and the hypothesized neutrinos.
It was known a "strong interaction" must exist to overcome electrostatic repulsion in atomic nuclei.
These particles decay much more slowly than they are produced, a hint that there are two different physical processes involved.
In 1953, Murray Gell-Mann and a collaboration in Japan, Tadao Nakano with Kazuhiko Nishijima, independently suggested a new conserved value now known as "strangeness" during their attempts to understand the growing collection of known particles.
[4][5][b] The discovery of new mesons and baryons continued through the 1950s; the number of known "elementary" particles ballooned.
The eightfold way represented a step out of this confusion and towards the quark model, which proved to be the solution.
Symmetrical patterns appear when these groups of particles have their strangeness plotted against their electric charge.
(This is the most common way to make these plots today, but originally physicists used an equivalent pair of properties called hypercharge and isotopic spin, the latter of which is now known as isospin.)
They consist of The organizational principles of the eightfold way also apply to the spin-3/ 2 baryons, forming a decuplet.
Gell-Mann called this particle the Ω− and predicted in 1962 that it would have a strangeness −3, electric charge −1 and a mass near 1680 MeV/c2.
Gell-Mann received the 1969 Nobel Prize in Physics for his work on the theory of elementary particles.
First, it was noticed (1961) that groups of particles were related to each other in a way that matched the representation theory of SU(3).
Finally (1964), this led to the discovery of three light quarks (up, down, and strange) interchanged by these SU(3) transformations.
The eightfold way may be understood in modern terms as a consequence of flavor symmetries between various kinds of quarks.
and the laws of physics are approximately invariant under a determinant 1 unitary transformation to this space (sometimes called a flavour rotation):
More specifically, these flavour rotations are exact symmetries if only strong force interactions are looked at, but they are not truly exact symmetries of the universe because the three quarks have different masses and different electroweak interactions.
If we apply one of the flavour rotations A to our particle, it enters a new quantum state which we can call
Representation theory is a mathematical theory that describes the situation where elements of a group (here, the flavour rotations A in the group SU(3)) are automorphisms of a vector space (here, the set of all possible quantum states that you get from flavour-rotating a proton).
Therefore, by studying the representation theory of SU(3), we can learn the possibilities for what the vector space is and how it is affected by flavour symmetry.
Since the flavour rotations A are approximate, not exact, symmetries, each orthogonal state in the vector space corresponds to a different particle species.
In the example above, when a proton is transformed by every possible flavour rotation A, it turns out that it moves around an 8 dimensional vector space.
Those 8 dimensions correspond to the 8 particles in the so-called "baryon octet" (proton, neutron, Σ+, Σ0, Σ−, Ξ−, Ξ0, Λ).
After the circulation of the preliminary version of this work (January 1961) the author has learned of a similar theory put forward independently and simultaneously by Y. Ne'eman (Nuclear Physics, to be published).
Earlier uses of the 3 dimensional unitary group in connection with the Sakata model are reported by Y. Ohnuki at the 1960 Rochester Conference on High Energy Physics.
In fact, when I presented this paper to him, he showed me a study he had done on the unitary theory of the Sakata model, treated as a gauge, and thus producing a similar set of vector bosons.
Shortly after the present paper was written, a further version, utilizing the 8 representation for baryons, as in this paper, reached us in a preprint by Prof. M. Gell Mann.After the completion of this work, the authors knew in a private letter from Prof. Nambu to Prof. Hayakawa that Dr. Gell-Mann has also developed a similar theory.
