We re-examine the problem of simultaneously describing in a consistent way all radiative and leptonic decays of light mesons (V → P γ, P → V γ, P → γγ, V → e + e − ). For this purpose, we rely on the Hidden Local Symmetry model in both its anomalous and non-anomalous sectors. We show that the SU(3) symmetry breaking scheme proposed by Bando, Kugo and Yamawaki, supplemented with nonet symmetry breaking in the pseudoscalar sector, allows one to reach a nice agreement with all data, except for the K * ± radiative decay. An extension of this breaking pattern allows one to account for this particular decay mode too. Considered together, the whole set of radiative decays provides a pseudoscalar mixing angle θ P ≃ −11 • and a value for θ V which is ≃ 3 • from that of ideal mixing. We also show that it is impossible, in a practical sense, to disentangle the effects of nonet symmetry breaking and those of glue inside the η ′ , using only light meson decays. * Work supported by Department of Energy contract DE-AC03-76SF00515.When in doubt, tell the truth . . .
Mark Twain
I. INTRODUCTION.Defining an accurate framework in which the study of all radiative decays of light flavor mesons can be performed successfully is a long standing question. There are a few kinds of different models which have been proposed so far. The most popular modelling is in terms of magnetic moments of quarks [1,2]. It includes, to some extent, SU(3) breaking effects by having a magnetic moment for the s quark, slightly different to that of the d quark. It also depends on overlap integrals which are hard to estimate theoretically, and are thus arbitrarily chosen equal [3]. This, at least, allows one to have a reasonable number of free parameters. Another traditional approach is to use SU(3) relations among coupling constants [4]. However, the assumption of exact SU(3) symmetry still yields reasonable descriptions of radiative decays [5], though the success is never complete.Recently, several models including SU(3) symmetry breaking effects have been proposed [6-8], motivated in part by effective Lagrangian approaches to the interactions of vector mesons [9,10], sometimes with additional SU(2) symmetry breaking effects [7]. Including SU(3) symmetry breaking as per Bando, Kugo and Yamawaki (hereafter referred to as BKY) [11,12], these models give a special role to all decay constants (f K , f η , f η ′ ) in the breaking procedure; some additional corrections are also allowed. More recently, a new kind of model has been proposed [13], where additional symmetry breaking effects are introduced by means of the (measured) leptonic decay constants of vector mesons.The study of radiative decays of light flavor mesons is also connected with the long standing problem of η/η ′ mixing [5,8,[14][15][16][17] and to its possible association with a glue content [13,18]. The two-photon decay of the η(η ′ ) is also connected with the problem of anomalies [18][19][20][21]. Recent developments seem to advocate a more complicated η/η ′ mixing scheme [22,23], which has rece...