Chiral anomaly role in $\pi_{1}(1600)\rightarrow\pi\eta^{\prime}$

The ground-state (lightest) hybrid nonet with exotic quantum numbers $J^{PC}=1^{-+}$ and the nonet of their chiral partners with $J^{PC}=1^{+-}$ build a homochiral multiplet involving left- and right-handed currents, which under chiral transformation change just as (axial-)vector mesons. Masses and interactions of hybrids can be obtained in the context of the extended Linear Sigma Model. Here, we concentrate on the decays oh hybrids into two pseudoscalar mesons, such as $\eta\pi$ and $\eta^{\prime}\pi$ modes. Indeed, $\pi_{1}(1400)\rightarrow\pi\eta$ and $\pi_{1}(1600)\rightarrow\pi\eta ^{\prime}$ have been seen in experiments. Assuming that $\pi_{1}(1400)$ and $\pi_{1}(1600)$ correspond to the same state $\pi_{1}^{hyb}$, we show that these decays (and similar ones) follow from a chirally symmetric interaction term that breaks explicitly the axial anomaly. In this respect, these decays would be an additional manifestation of the axial (or chiral) anomaly in the mesonic sector.