On the relation between chiralSU 3 ×SU 3 current algebra andSU 6

Abstract

The general structure of the covariant sum rules derived on the basis of chiralSU3×SU3 algebra is investigated in the case in which they are saturated by a finite number of intermediate states. We discuss first the consistency of the saturation with states belonging to anSU6 supermultiplet. We find that consistency is ensured and that theSU6 results for the renormalization ratios are obtained if mass differences betweenSU3 multiplets are neglected. This is due to the fact that for equal masses and parities the matrix elements of the divergences of the axial currents are proportional to the matrix elements of the helicity. We then discuss the situation in which an arbitrary but limited set of states saturates all the matrix elements of the chiralSU3×SU3 algebra taken among them. It is shown that the matrix elements of the chiral algebra coincide with the matrix elements of a collinearSU3×SU3 algebra, so that the states that saturate the chiral algebra are a representation of the collinear one, on the basis of which the coupling constants can be calculated. The collinear group is not the same as the one generally considered as a subgroup of the staticSU6. It coincides with it only in the case of equal parities and masses of all the members of an irreducible representation.