Chiral anomaly and strange-nonstrange mixing

TL;DR

This paper reviews the role of the axial anomaly in meson mixing, highlighting differences between heterochiral and homochiral multiplets, and discusses the implications for pseudoscalar, vector, tensor, and pseudotensor states.

Contribution

It provides a pedagogical analysis of meson mixing and the influence of the axial anomaly across different multiplet types, including new insights into pseudotensor states.

Findings

a-a0 ext{eta} ext{ is close to the octet, } ext{eta'} ext{ to the singlet.

a-a0 ext{vector and tensor states} ext{ have negligible anomalous contributions.

a-a0 ext{pseudotensor states} ext{ exhibit sizable anomalous mixing.}

Abstract

As a first step, a simple and pedagogical recall of the $\eta$-$\eta'$ system is presented, in which the role of the axial anomaly, related to the heterochiral nature of the multiplet of (pseudo)scalar states, is underlined. As a consequence, $\eta$ is close to the octet and $\eta'$ to the singlet configuration. On the contrary, for vector and tensor states, which belong to homochiral multiplets, no anomalous contribution to masses and mixing is present. Then, the isoscalar physical states are to a very good approximation nonstrange and strange, respectively. Finally, for pseudotensor states, which are part of an heterochiral multiplet (just as pseudoscalar ones), a sizable anomalous term is expected: $\eta_2 (1645)$ roughly corresponds to the octet and $\eta_2 (1870)$ to the singlet.