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Behavior of current divergences under SU3×SU3

Gell-Mann, Murray and Oakes, R. J. and Renner, B. (1968) Behavior of current divergences under SU3×SU3. Physical Review, 175 (5). pp. 2195-2199. ISSN 0031-899X. doi:10.1103/PhysRev.175.2195.

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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 (-sqrt[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.

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Additional Information:©1968 The American Physical Society. Received 22 July 1968. We wish to thank Professor R. P. Feynman for interesting discussions on the subject of this paper. Work supported in part by the U.S. Atomic Energy Commission. Prepared under Contract No. AT(11-1)-68 for the San Francisco Operations Office, U.S. Atomic Energy Commission. The research described here was performed at the Institute for Advanced Study, Princeton, N.J. The authors would like to thank Professor Carl Kaysen for his hospitality at the Institute.
Issue or Number:5
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3634
Deposited By: Tony Diaz
Deposited On:22 Jun 2006
Last Modified:08 Nov 2021 20:11

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