Irrelevance of Anomalous Breaking of Axial U(1) Symmetry and the U(1) Problem

The eta and eta’ mesons are conventionally known to receive contribution from the anomalous breaking of axial U(1) symmetry, and they are considered to not be the Nambu-Goldstone (NG) bosons of the spontaneous chiral SU(3)_L x SU(3)_R symmetry breaking of QCD. However, it has recently been shown that this axial U(1) anomaly is not actually physical. In this contribution, we first review this statement and then propose a mechanism in which eta and eta’ mesons are indeed NG bosons while being consistent with the axial U(1) problem.