Investigation of the Lightest Hybrid Meson Candidate with a Coupled-Channel Analysis of $\bar{p}p$-, $\pi^- p$- and $\pi\pi$-Data

A sophisticated coupled-channel analysis is presented that combines different processes: the channels $\pi^0\pi^0\eta$, $\pi^0\eta\eta$ and $K^+K^-\pi^0$ from $\bar{p}p$ annihilations, the P- and D-wave amplitudes of the $\pi\eta$ and $\pi\eta^\prime$ systems produced in $\pi^- p$ scattering, and data from $\pi\pi$-scattering reactions. Hence our analysis combines the data sets used in two independent previous analyses published by the Crystal Barrel experiment and by the JPAC group. Based on the new insights from these studies, this paper aims at a better understanding of the spin-exotic $\pi_1$ resonances in the light-meson sector. By utilizing the K-matrix approach and realizing the analyticity via Chew-Mandelstam functions the amplitude of the spin-exotic wave can be well described by a single $\pi_1$ pole for both systems, $\pi\eta$ and $\pi\eta^\prime$. The mass and width of the $\pi_1$-pole are measured to be $(1623 \, \pm \, 47 \, ^{+24}_{-75}\,)\, \mathrm{MeV/c}^2$ and $(455 \, \pm \, 88 \, ^{+144}_{-175}\,)\, \mathrm{MeV}$.