How the axial anomaly controls flavor mixing among mesons

Abstract

It is well known that, because of the axial anomaly in QCD, mesons with J P ¼ 0 − are close to SUð3Þ V eigenstates; the η 0 ð958Þ meson is largely a singlet, and the η meson an octet. In contrast, states with J P ¼ 1 − are flavor diagonal; e.g., the ϕð1020Þ is almost puress. 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 ¼ SUð3Þ L × SUð3Þ 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 Zð3Þ A subgroup of the axial Uð1Þ A enter. For heterochiral multiplets, which begin with that including the η and η 0 ð958Þ, there are Zð3Þ A invariant terms with low mass dimension which cause states to mix according to SUð3Þ V flavor. For homochiral multiplets, which begin with that including the ϕð1020Þ, there are no Zð3Þ 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.

Revisiting the axial anomaly for light mesons and baryons

“…In the mesonic sector one can -for the so-called "heterochiral" multiplets [3]-write down anomalous terms similar to the one which are usually introduced for (pseudo)scalar mesons. Hence, a large strange-nonstrange mixing in the pseudotensor nonet and in the pseudovector nonet are possible (in the former some experimental evidence already exists [5]).…”

“…(dots refer to other terms [3]). Here, for simplicity we keep only the "third" term of that work (by using the same notation).…”

“…And what about the role of the axial anomaly for baryons? In these proceedings, we report on two recent works in which the role of the axial anomaly was studied in the mesonic and baryonic sectors [3,4].…”

“…2, based on Ref. [3], light meson nonets are grouped into chiral multiplets and classified according to their chiral transformations: there are "heterochiral" mesons (such as the (pseudo)scalar states) and 'homochiral' mesons (such as (axial-)vector states). For all heterochiral multiplets, the axial anomaly allows for mixing of nonstrange and strange isoscalar members, as well known for the η and η mesons mentioned above.…”

Chiral anomaly and strange-nonstrange mixing

“…This fact can be nicely understood by the homochirality of the corresponding chiral multiplets, which involve left-and right-handed currents. For homochiral multiplets, no anomalous mixing is realized [4].…”