CHIRAL SU3XSU3 ALGEBRA AND APPROXIMATE SU2XSU2 SYMMETRY

The implications of the validity of chiral SU 3×SU3 current algebra and the assumption that the chiral-symmetry breaking term transforms according to the (3,3*)+(3*, 3) representation of SU 3×SU3 are investigated. It is argued that approximate SU 2×SU2 symmetry is expected on the grounds of the smallness of the pion mass together with some reasonably smooth behavior for matrix elements which involve a pion. The PCAC hypothesis, in its pole-dominance form, is applied to the π, K and ν cases in a step-by-step manner. Some results are obtained for the Kℓ3 form factors, including f +(0)=1. Except for the equal-time commutation relations, SU 3 symmetry is not invoked even approximately. Sum rules involving f π, f K, f ν and the pseudoscalar-meson masses are derived, some of which differ significantly from those obtained by authors using approximate SU 3 symmetry. In particular, an expression for f K/f π is inferred which involves pseudoscalar-meson masses alone. © 1969 Società Italiana di Fisica.