How the axial anomaly controls flavor mixing among mesons

Here, it is well known that, because of the axial anomaly in QCD, mesons with J ^P = 0 ^– are close to SU(3) _V eigenstates; the η'(958) meson is largely a singlet, and the η meson an octet. In contrast, states with J ^P = 1 ^– are flavor diagonal; e.g., the Φ(1020) is almost pure ¯ss. Using effective Lagrangians, we show how this generalizes to states with higher spin, assuming that they can be classified according to the unbroken chiral symmetry of G _fl = SU(3) _L × SU(3) _R. We construct effective Lagrangians from terms invariant under G _fl and introduce the concept of hetero- and homochiral multiplets. Because of the axial anomaly, only terms invariant under the Z(3) _A subgroup of the axial U(1) _A enter. For heterochiral multiplets, which begin with that including the η and η'(958), there are Z(3) _A invariant terms with low mass dimension which cause states to mix according to SU(3) _V flavor. For homochiral multiplets, which begin with that including the Φ(1020), there are no Z(3) _A invariant terms with low mass dimension, and so states are diagonal in flavor. In this way, we predict the flavor mixing for themore » heterochiral multiplet with spin 1 as well as for hetero- and homochiral multiplets with spin 2 and spin 3.