Comment on ``Mixing and Decay Constants of Pseudoscalar Mesons''

TL;DR

This paper critically examines a recent assumption about the decay constants of eta and eta' mesons, linking it to axial current identities and highlighting differences between octet and hypercharge currents.

Contribution

It clarifies the relationship between meson decay constants and axial currents, emphasizing the distinction between octet and hypercharge axial currents.

Findings

Reproduces the assumption using hypercharge current identification.

Highlights the inequivalence between octet and hypercharge axial currents.

Provides insight into meson decay constant mixing patterns.

Abstract

The key assumption used recently by Feldmann, Kroll and Stich [Phys.Rev. D58, 114006 (1998)] that the decay constants f_\eta, and f_\eta ' of the respective eta and eta ' mesons in the quark flavor basis follow the pattern of strange and non--strange quarkonia mixing in their wave functions, is reproduced in identifying the non-isotriplet part of the strong neutral axial current with the genuine axial hypercharge current J_{\mu, 5}^Y =\bar q \gamma_\mu\gamma_5 Y/2 q, where Y=C+S+B is defined by the Gell-Mann-Nakano-Nishijima relation as the sum of charm (C), strangeness (S), and baryon (B) quark quantum numbers. The inequivalence between octet and hypercharge axial currents is pointed out.