Flavour Stability of the Chiral Vacuum and Scalar Meson Dynamics

Abstract

Previous work relating the flavour variation of the chiral order parameters $F_{\pi }$, $<\bar{u}u>$ and S-wave scattering data, based on chiral sum rules and chiral perturbation theory at order $p^4$, is extended to include $O(p^6)$ corrections. The finding of a significant decrease of these order parameters, particularly $<\bar{u}u>$, with the number of flavours increasing from $N_F=2$ to $N_F=3$ is confirmed, modulo an assumption on the convergence of the chiral expansion. The connection between scalar resonance physics and the phase structure of the chiral vacuum is also illustrated on the basis of the linear sigma-model. We allow for a very general symmetry breaking sector compatible with softness. The result depends strongly on the input scalar meson masses, in particular, on the presence, or not, of a light sigma.}

Comments: 27 Pages, 1 figure, v2: references added, minor improvements