Prediction of the SU(3) x SU(3) configuration mixing as a relativistic effect in the naive quark model
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Abstract: (APS)
The harmonic-oscillator quark model of hadrons implies relativistic internal volocities for the quarks. If, consequently, we use a relativistic treatment of the quark spin (by replacing Pauli spinors with Dirac spinors), we obtain not only corrections to the "static SU(6)" results for the axial-vector matrix elements GAGV or G* (as shown by Bogoliubov), but the whole SU(3)⊗SU(3) configuration mixing at pz=∞, in a semiquantitative manner. The mixing operator is just the product of the Wigner rotations of quark spins. For the low-lying 12+ octet, the dominant representations are (6, 3), (3,3¯), and (8, 1), in agreement with the phenomenological analysis of Buccella, De Maria, and Lusignoli. The SU(6) classification of hadrons is preserved; at rest, the hadron wave function corresponds to an SU(6) group whose spin generators are the sum of the mean spin operators (of Foldy and Wouthuysen) of the quarks.References(0)
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