Applications of chiral perturbation theory: Mass formulas and the decayη→3π

Abstract

Several new results on the breaking of chiral SU(3) × SU(3) are presented within the theoretical framework of chiral perturbation theory. (a) The leading-order corrections to the Gell-Mann-Okubo formula for the baryon octet are shown to be of order ${\epsilon }^{\frac{3}{2}}$, where $\epsilon$ is a chiral symmetry breaking parameter. An explicit exact expression is given for the leading-order corrections, which provides a new development in understanding why this formula works so well. Similarly the corrections to the Gell-Mann-Okubo formula for the ground-state pseudoscalar octet are shown to be of order ${\epsilon }^2\ln \epsilon$ (including $\eta -{\eta }^{\prime }$ mixing). On the basis of these exact results it is argued that SU(3) × SU(3) symmetry is as good as SU(3) symmetry ∼30% except when one considers electromagnetic interactions. (b) We examine the $\eta \to 3\pi$ decay on the assumption that it is regulated by a nonelectromagnetic isospinviolating term of the type ${\epsilon }_3{u}_3$ with $u_3$ a member of $\overline{3}3\oplus 3\overline{3}$. The strength ${\epsilon }_3$ of this term is related to the experimental rate including all leading-order chiral-symmetry corrections. This estimate of ${\epsilon }_3$ leads to $\Delta I=1\mathrm{}$ hadron level shifts about a factor of 2 or 3 too large, although our estimate of ${\epsilon }_3$ depends sensitively on the experimental details. (c) Octet enhancement, an exact formalism to describe $\eta -{\eta }^{\prime }$ mixing, and other topics are discussed.