Troubles of describing multiple pion production in chiral dynamics

Generalized Hidden Local Symmetry (GHLS) model as the chiral model of pseudoscalar, vector, and axial vector mesons and their interactions containing also the couplings of strongly interacting particles with electroweak gauge bosons, is confronted with the ALEPH data on the decay $τ^-\toπ^-π^-π^+ν_τ$ and BABAR and CMD data on the reaction $e^+e^-\toπ^+π^-π^+π^-$. It is shown that both the invariant mass spectrum of final pions in $τ$ decay calculated in the GHLS framework with the single $a_1(1260)$ resonance and the cross section $e^+e^-\toπ^+π^-π^+π^-$ calculated in the above framework with the single $ρ(770)$ resonance, disagree with the experimental data. The modifications of GHLS model based on inclusion of two additional heavier axial vector mesons $a_1^\prime$, $a_1^{\prime\prime}$ in the $τ$ decay and the vector mesons $ρ^\prime$, $ρ^{\prime\prime}$ in $e^+e^-\toπ^+π^-π^+π^-$ are shown to be necessary for the good description of the above data.

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