Bose symmetry interference effects of4πfinal states

Abstract

We analyze the relative branching ratios of $4\ensuremath{\pi}$ final states ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}},$ ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0},$ and ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0},$ from various resonances with ${J}^{\mathrm{PC}}{=0}^{++},$ ${0}^{\ensuremath{-}+},$ ${2}^{++}.$ We find that in some cases the interference effects due to Bose symmetry make their ratios obviously different from the naive counting values without these effects. The results allow an accurate estimate of the $4\ensuremath{\pi}$ branching ratios of relevant resonances when only one (or two) modes are measured in a given experiment.