Spontaneous Breakdown of Conformal and Chiral Invariance

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included by .pdf document. We discuss the implications of a theory in which scale and chiral invariance are spontaneously broken, and the dilaton [...] appears as a mixture of the two isoscalar members of the scalar nonet. From standard assumptions for the conformal properties of the axial-vector current, we predict the ratio of the [...] and [...] coupling constants, and test the hypothesis of f-dominance. At first, we neglect the effects of scale violation. Then, the calculated width of the dilaton, [...], appears to exceed the limit given by the Adler-Weisberger sum rule for [...] scattering, while f-dominance seems to work. Using the method of collinear dispersion relations, we estimate scalebreaking effects, which are found to be large. In the real world, our result for [...] agrees with other expectations, both experimental and theoretical. However, the spin-2 gravitational radius of the pion is found to be double the prediction of f-dominance. This is consistent with experimental indications that f-dominance fails. We discuss meson-baryon scattering and its relation to parameters measuring the breaking of chiral symmetry in the energy density. Our interpretation of a recent result of Cheng and Dashen is that scale invariance is spontaneously broken, and chiral SU(2) x SU(2) is a much better summetry than SU(3). By requiring consistency, with a sum rule of von Hippel and Kim, we find that data for [...] scattering are not consistent with the dimension of the chiral-violating scalar being -1.