Approximate scale invariance and broken-SU 3 coupling constants

Abstract

Under the assumption that the matrix elements of the divergences of the dilation current ∂μDμ=θμμ are dominated by two poles, it is shown that the present experimental data for the dilation (e) are consistent with an unsubtracted dispersion relation of Г(q2)≡ (=π, K or η), a significantSU3 violation in ePP couplings and no apparent singlet-octet mixing for the scalar mesons. As far as the slope\(\Gamma ' \equiv \Gamma /dq^2 |_{q^2 = 0} \) is concerned, in theSU3 symmetry limit we have Γ′≃1, whileSU3-symmetry-breaking effects change this value to Γ′≃0.5 in consistency with a general theorem given by Okubo. By demanding maximal smoothness we obtain that the scale dimension of the scalar densities (which break chiralSU3×SU3 as well as scale symmetries in the energy density), isdu=1. However, our general relation between the dilaton mass (me) and the dimensiondu (eq. (31)) givesme≃700 MeV, 600 MeV and 400 MeV fordu=1,2 and 3 respectively.