Three-flavor symmetry of hadrons in consistent with the Okubo-Zweig-Iizuka rule
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It is argued that the only three-flavor symmetry which is consistent with the Okubo-Zweig-Iizuka (OZI) rule, and is therefore dictated by the gluon gauge dynamics, is the heavy c quark limit of a certain U(4)F subgroup (called SOZI here) and defined as SOZI = limmc→Ac SU(2)ud ⊗ SU(2)cd ⊗ U(1) with the two SU(2) groups acting in turn onto the first and second quark generations rather than Gell-Mann%27s eightfold SU(3)F. Within this scheme, the presence of non-strange quarkonium components in the wave function of the physical η and f1(1285) mesons appears necessarily through the violation of the OZI rule for the pseudoscalar and axial vector mesons by the anomalous axial U(1)A baryon number current and not by a primordial octet flavor symmetry. The physical observable which selects the SOZI over the SU(3)F scheme is the non-isotriplet part of the neutral axial current. In the case of the SOZI symmetry, the only non-isotriplet neutral axial current having a well-defined chiral limit is purely strange, while within the SU(3)F framework it is the octet axial current which is supposed to be partially conserved. Accordingly, while in the latter case the tree level ηΝ coupling is of significant strength, it almost vanishes in the former, in agreement with data, thus confirming the relevance of the SOZI symmetry.
It is argued that the only three-flavor symmetry which is consistent with the Okubo-Zweig-Iizuka (OZI) rule, and is therefore dictated by the gluon gauge dynamics, is the heavy c quark limit of a certain U(4)F subgroup (called SOZI here) and defined as SOZI = limmc→Ac SU(2)ud ⊗ SU(2)cd ⊗ U(1) with the two SU(2) groups acting in turn onto the first and second quark generations rather than Gell-Mann's eightfold SU(3)F. Within this scheme, the presence of non-strange quarkonium components in the wave function of the physical η and f1(1285) mesons appears necessarily through the violation of the OZI rule for the pseudoscalar and axial vector mesons by the anomalous axial U(1)A baryon number current and not by a primordial octet flavor symmetry. The physical observable which selects the SOZI over the SU(3)F scheme is the non-isotriplet part of the neutral axial current. In the case of the SOZI symmetry, the only non-isotriplet neutral axial current having a well-defined chiral limit is purely strange, while within the SU(3)F framework it is the octet axial current which is supposed to be partially conserved. Accordingly, while in the latter case the tree level ηΝ coupling is of significant strength, it almost vanishes in the former, in agreement with data, thus confirming the relevance of the SOZI symmetry.
