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) \ensuremath{\bigotimes} 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 $z\ensuremath{\approx}\ensuremath{-}0.565$, in agreement with previous evaluations which made use of different techniques. The analogy to the $(\overline{3}, 3)\ensuremath{\bigoplus}(3, \overline{3})$ model of SU(3) \ensuremath{\bigotimes} 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 ${K}_{l3}$ form factors in the (8,8) model.