Some Aspects of (8,8) Chiral Symmetry Breaking

Abstract

It is assumed that the chiral-symmetry-breaking Hamiltonian density transforms as part of the (8,8) representation of SU(3) ⊗ SU(3). We then derive a spectral-function sum rule for the model and make use of SU(3) assumptions to determine the symmetry-breaking parameter $z$. We find $z\approx -0.565\mathrm{}$, in agreement with previous evaluations which made use of different techniques. The analogy to the $(\overline{3}, 3)\oplus (3, \overline{3})$ model of SU(3) ⊗ SU(3)-symmetry breaking is stressed. Other values of $z$ for which the (8,8) model exhibits distinct qualitative features are also discussed. We conclude by presenting the soft-pion calculation of the $K_{l3\mathrm{}}$ form factors in the (8,8) model.