Behavior of Current Divergences under SU_{3}×SU_{3}
Abstract
We investigate the behavior under SU_{3}×SU_{3} of the hadron energy density and the closely related question of how the divergences of the axialvector currents and the strangenesschanging vector currents transform under SU_{3}×SU_{3}. We assume that two terms in the energy density break SU_{3}×SU_{3} symmetry; under SU_{3} 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 SU_{3}×SU_{3} 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 SU_{3}breaking term relative to the chiral symmetrybreaking term. The constant c is found not to be small, as suggested earlier, but instead close to the value (2) corresponding to an SU_{2}×SU_{2} 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.
 Publication:

Physical Review
 Pub Date:
 November 1968
 DOI:
 10.1103/PhysRev.175.2195
 Bibcode:
 1968PhRv..175.2195G