Gell-Mann-Okubo mass formula
Encyclopedia
In physics
, the Gell-Mann–Okubo mass formula provides a sum rule for baryon
and meson
masses within a specific multiplet determined by particle spin. The rule was first formulated by Murray Gell-Mann
in 1961 and independently proposed by Susumu Okubo
in 1962. Spin, in its simplest generalization is generated by SU(3), which can be represented by eight unitary and traceless matrices corresponding to the "components" of spin. Three of the matrices correspond to the three components of spin, while four correspond to flavor change, and the final to hypercharge.
For the baryon octet, the final matrix for hypercharge can be transformed to provide two mass difference matrices relating the masses of the baryons within the octet. Using these matrices the Gell-Mann-Okubo formula can be written for the baryon octet,
where mN is the average mass of the proton and neutron, mΞ the average mass of the Ξ0 and Ξ−, and mΣ the average mass of Σ0, Σ+, and Σ−.
The same mass relation can be found for the meson octet, but now the masses are squared.
For the baryon decuplet, the mass formula is given by three relations,
where mX is the average mass between the neutral and charged instances of particle X, just as is done in the baryon octet formulation. The baryon decuplet formula allowed Gell-Mann to successfully predict the mass of the yet undiscovered Ω−.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, the Gell-Mann–Okubo mass formula provides a sum rule for baryon
Baryon
A baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...
and meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
masses within a specific multiplet determined by particle spin. The rule was first formulated by 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...
in 1961 and independently proposed by Susumu Okubo
Susumu Okubo
is a Japanese theoretical physicist at the University of Rochester.Ōkubo began study at the University of Tokyo in 1949 and received his bachelor's degree there in 1952. He became a graduate student at the University of Rochester in 1954, where he earned his PhD in 1958 with Robert Marshak as...
in 1962. Spin, in its simplest generalization is generated by SU(3), which can be represented by eight unitary and traceless matrices corresponding to the "components" of spin. Three of the matrices correspond to the three components of spin, while four correspond to flavor change, and the final to hypercharge.
For the baryon octet, the final matrix for hypercharge can be transformed to provide two mass difference matrices relating the masses of the baryons within the octet. Using these matrices the Gell-Mann-Okubo formula can be written for the baryon octet,
where mN is the average mass of the proton and neutron, mΞ the average mass of the Ξ0 and Ξ−, and mΣ the average mass of Σ0, Σ+, and Σ−.
The same mass relation can be found for the meson octet, but now the masses are squared.
For the baryon decuplet, the mass formula is given by three relations,
where mX is the average mass between the neutral and charged instances of particle X, just as is done in the baryon octet formulation. The baryon decuplet formula allowed Gell-Mann to successfully predict the mass of the yet undiscovered Ω−.