Troubles of describing multiple pion production in chiral dynamics

TL;DR

This paper evaluates the GHLS model's ability to describe multi-pion production in tau decays and electron-positron annihilation, finding that including additional heavier mesons improves agreement with experimental data.

Contribution

It introduces modifications to the GHLS model by adding heavier axial and vector mesons, enhancing its accuracy in describing experimental multi-pion production data.

Findings

Single-resonance GHLS model disagrees with data.

Adding heavier mesons improves data description.

Modified model aligns better with experimental results.

Abstract

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 $\tau^-\to\pi^-\pi^-\pi^+\nu_\tau$ and BABAR and CMD data on the reaction $e^+e^-\to\pi^+\pi^-\pi^+\pi^-$. It is shown that both the invariant mass spectrum of final pions in $\tau$ decay calculated in the GHLS framework with the single $a_1(1260)$ resonance and the cross section $e^+e^-\to\pi^+\pi^-\pi^+\pi^-$ calculated in the above framework with the single $\rho(770)$ 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 $\tau$ decay and the vector mesons $\rho^\prime$, $\rho^{\prime\prime}$ in $e^+e^-\to\pi^+\pi^-\pi^+\pi^-$ are shown to be necessary for the good description of the above data.