Revisiting the axial anomaly for light mesons and baryons

The axial anomaly is responsible for the masses and mixing of the mesons $\eta$ and $\eta'$. An open question is if (and to what extent) it affects also other hadrons. We show that anomalous terms can be important to understand the spectroscopy of the pseudotensor mesons $\eta_2 (1645)$ and $\eta_2 (1870)$. In fact, pseudotensor mesons belong to a so-called heterochiral multiplet, for which a quadratic mixing term between nonstrange and strange isoscalar members arises. On the contrary, for so-called homochiral multiplets, such as the ground-state (axial-)vector and tensor mesons, this mixing is not possible, hence one can easily understand why the isoscalar members of these multiplets are almost purely nonstrange and strange, respectively. Moreover, the axial anomaly can be also coupled to baryons (within the mirror assignment), and thus it helps to explain the large decay width $ N^{\ast }(1535)\rightarrow N\eta$ and to clarify which baryons are chiral partners.