How the axial anomaly controls flavor mixing among mesons

Abstract

It is well known that, because of the axial anomaly in QCD, mesons with JP=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 JP=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 Gfl=SU(3)L×SU(3)R. We construct effective Lagrangians from terms invariant under Gfl 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 the heterochiral multiplet with spin 1 as well as for hetero- and homochiral multiplets with spin 2 and spin 3.