# SYMMETRIES OF BARYONS AND MESONS

## Abstract

The system of strongly interscting particles is discussed. with electromagnetism, weak interactions, and gravitation considered as perturbations. The electric current j/sub alpha /, the weak current J/sub alpha /. and the gravitational tensor THETA /sub alpha beta / are all well-defined operators, with finite matrix elements obeying dispersion relations. To the extent that the dispersion relations for matrix elements of these operators between the vacuum and other states are highly convergent and dominated by contribut.ons from intermediate one-meson states, relations like the Goldberger-Treiman formula and universality principles like that of Sakurai according to which the p meson is coupled approximately to the isotopic spin exist. Homogeneous linear dispersion relations. even without subtractions, do not suffice to fix the scale of these matrix elements: in particular, for the nonconserved currents. the renormalization factors cannot be calculated. and the universality of strength of the weak interactions is undefined. More information than just the dispersion rela tions must be supplied, for example, by field-theoretie models; the equal- time commutation relations of the various parts of j/sub 4/ and J/sub 4/ are considered. These nonlinear relations define an algebraic system (or a group) that underlies the structure of baryons and mesons. lt is suggestedmore »

- Authors:

- Publication Date:

- Research Org.:
- California Inst. of Tech., Pasadena

- OSTI Identifier:
- 4808615

- NSA Number:
- NSA-16-010880

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

- Additional Journal Information:
- Journal Volume: Vol: 125; Other Information: Orig. Receipt Date: 31-DEC-62

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

- Subject:
- PHYSICS; ANGULAR MOMENTUM; BARYONS; CURRENTS; DIFFERENTIAL EQUATIONS; DISPERSION RELATIONS; ELECTROMAGNETISM; ENERGY LEVELS; FIELD THEORY; GRAVITATION; GROUP THEORY; HAMILTONIAN; HYPERONS; INTERACTIONS; ISOSPIN; KAONS; LAMBDA PARTICLES; MATHEMATICS; MATRICES; MESONS; MOMENTUM; MUONS; NEUTRINOS; NUCLEONS; NUMERICALS; PARTICLE MODELS; PERTURBATION THEORY; PIONS; PSEUDOSCALAR; QUANTUM MECHANICS; RESONANCE; RHO RESONANCES; SAKATA MODEL; SIGMA PARTICLES; STRANGENESS; UNITARY SYMMETRY; VECTORS; WEAK INTERACTIONS; XI PARTICLES

### Citation Formats

```
Gell-Mann, M.
```*SYMMETRIES OF BARYONS AND MESONS*. Country unknown/Code not available: N. p., 1962.
Web. doi:10.1103/PhysRev.125.1067.

```
Gell-Mann, M.
```*SYMMETRIES OF BARYONS AND MESONS*. Country unknown/Code not available. https://doi.org/10.1103/PhysRev.125.1067

```
Gell-Mann, M. Thu .
"SYMMETRIES OF BARYONS AND MESONS". Country unknown/Code not available. https://doi.org/10.1103/PhysRev.125.1067.
```

```
@article{osti_4808615,
```

title = {SYMMETRIES OF BARYONS AND MESONS},

author = {Gell-Mann, M},

abstractNote = {The system of strongly interscting particles is discussed. with electromagnetism, weak interactions, and gravitation considered as perturbations. The electric current j/sub alpha /, the weak current J/sub alpha /. and the gravitational tensor THETA /sub alpha beta / are all well-defined operators, with finite matrix elements obeying dispersion relations. To the extent that the dispersion relations for matrix elements of these operators between the vacuum and other states are highly convergent and dominated by contribut.ons from intermediate one-meson states, relations like the Goldberger-Treiman formula and universality principles like that of Sakurai according to which the p meson is coupled approximately to the isotopic spin exist. Homogeneous linear dispersion relations. even without subtractions, do not suffice to fix the scale of these matrix elements: in particular, for the nonconserved currents. the renormalization factors cannot be calculated. and the universality of strength of the weak interactions is undefined. More information than just the dispersion rela tions must be supplied, for example, by field-theoretie models; the equal- time commutation relations of the various parts of j/sub 4/ and J/sub 4/ are considered. These nonlinear relations define an algebraic system (or a group) that underlies the structure of baryons and mesons. lt is suggested that the group is in fact U(3) x U(3), exemplified by the symmetrical Sakata model. The Hamiltonian density THETA /sub 44/ is not completely invariant under the group; the noninvariant part transforms according to a particular representation of the group; it is possible that this information also is given correctly by the symmetrical Sakata model. Exact relations among form factors follow from the algebraic structure. In addition, the approximate situation in which the strangeness-changing vector currents are conserved and the Hamiltonian is invariant under U(3) is considcred; refering to this limiting case as unitary symmetry.'' In the limit, the banyons and mesons form degenerate supermultiplets, which break up into isotopic multiplets when the symmetry-breaking term in the Hamiltonian is --turned on.'' The mesons are expected to form unitary singlets and octets; each octet breaks up into a triplet. a singlet, and a pair of strange doublets. The known pseudoscalar and vector mesons fit this pattern if there exists also an isotopic singlet pseudoscalar meson x/sup 0/. If unitary symmetry in the abstract is considered rather than in connection with a field theory, then, as an alternative to the Sakata model, the scheme of Ne'eman and Gell-Mann is four, which is called the eightfold way''; the baryons N. DELTA , SIGMA and XI form an octet, like the vector and pseudoscalar meson octets, in the limit of unitary symmetry. Although the violations of unitary symmetry must be quite large, there is a possibility of relating certain violations to others. As an example of the methods advocated, a rough calculation of the rate of K/sup +/ yields mu /sup +/ + v in terms of that of},

doi = {10.1103/PhysRev.125.1067},

url = {https://www.osti.gov/biblio/4808615},
journal = {Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D},

number = ,

volume = Vol: 125,

place = {Country unknown/Code not available},

year = {1962},

month = {2}

}