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

Abstract

Several new results on the breaking of chiral SU(3) \ifmmode\times\else\texttimes\fi{} 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 ${\ensuremath{\epsilon}}^{\frac{3}{2}}$, where $\ensuremath{\epsilon}$ 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 ${\ensuremath{\epsilon}}^{2}\mathrm{ln}\ensuremath{\epsilon}$ (including $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing). On the basis of these exact results it is argued that SU(3) \ifmmode\times\else\texttimes\fi{} SU(3) symmetry is as good as SU(3) symmetry \ensuremath{\sim}30% except when one considers electromagnetic interactions. (b) We examine the $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay on the assumption that it is regulated by a nonelectromagnetic isospinviolating term of the type ${\ensuremath{\epsilon}}_{3}{u}_{3}$ with ${u}_{3}$ a member of $\overline{3}3\ensuremath{\bigoplus}3\overline{3}$. The strength ${\ensuremath{\epsilon}}_{3}$ of this term is related to the experimental rate including all leading-order chiral-symmetry corrections. This estimate of ${\ensuremath{\epsilon}}_{3}$ leads to $\ensuremath{\Delta}I=1$ hadron level shifts about a factor of 2 or 3 too large, although our estimate of ${\ensuremath{\epsilon}}_{3}$ depends sensitively on the experimental details. (c) Octet enhancement, an exact formalism to describe $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing, and other topics are discussed.