Behavior of Current Divergences under SU3×SU3

Murray Gell-Mann, R. J. Oakes, and B. Renner
Phys. Rev. 175, 2195 – Published 25 November 1968
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Abstract

We investigate the behavior under SU3×SU3 of the hadron energy density and the closely related question of how the divergences of the axial-vector currents and the strangeness-changing vector currents transform under SU3×SU3. We assume that two terms in the energy density break SU3×SU3 symmetry; under SU3 one transforms as a singlet, the other as the member of an octet. The simplest possible behavior of these terms under chiral transformations is proposed: They are assigned to a single (3,3*)+(3*,3) representation of SU3×SU3 and parity together with the current divergences. The commutators of charges and current divergences are derived in terms of a single constant c that describes the strength of the SU3-breaking term relative to the chiral symmetry-breaking term. The constant c is found not to be small, as suggested earlier, but instead close to the value (2) corresponding to an SU2×SU2 symmetry, realized mainly by massless pions rather than parity doubling. Some applications of the proposed commutation relations are given, mainly to the pseudoscalar mesons, and other applications are indicated.

  • Received 22 July 1968

DOI:https://doi.org/10.1103/PhysRev.175.2195

©1968 American Physical Society

Authors & Affiliations

Murray Gell-Mann

  • California Institute of Technology, Pasadena, California 91109

R. J. Oakes

  • Northwestern University, Evanston, Illinois 60201

B. Renner*

  • California Institute of Technology, Pasadena, California 91109

  • *On leave from Gonville and Caius College, Cambridge, England.

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Vol. 175, Iss. 5 — November 1968

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