Chiral shielding

Abstract

We demonstrate how a chiral soft pion theorem (SPT) shields the scalar meson ground-state isoscalar $\ensuremath{\sigma}(600\ensuremath{-}700)$ and isospinor $\ensuremath{\kappa}(800\ensuremath{-}900)$ from detection in ${a}_{1}\ensuremath{\rightarrow}\ensuremath{\pi}(\ensuremath{\pi}\ensuremath{\pi}{)}_{\mathrm{swave}},$ $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}2{\ensuremath{\pi}}^{0},$ ${\ensuremath{\pi}}^{\ensuremath{-}}\stackrel{\ensuremath{\rightarrow}}{p}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}n$ and ${K}^{\ensuremath{-}}\stackrel{\ensuremath{\rightarrow}}{p}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}n$ processes. While pseudoscalar meson $\mathrm{PVV}$ transitions are known to be determined by (only) quark loop diagrams, the above SPT also constrains scalar meson $\mathrm{SVV}$ transitions to be governed (only) by meson loop diagrams. We apply this latter $\mathrm{SVV}$ theorem to ${a}_{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and ${f}_{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ decays.