The eta-eta' system in the two mixing angle scheme

Abstract

A two mixing angle description of the pseudoscalar decay constants associated to the η-η system is used to parametrize the theoretical amplitudes of the radiative decays (η, η ) → γγ and the coupling constants g V (η,η )γ with V = ρ, ω, φ . The parametrization is performed in both the "octet-singlet" basis and the "quark-flavour" basis. An excellent agreement with the most recent experimental data is achieved. Our analysis reveals that at the present experimental accuracy the two mixing angles differ significantly in the former basis but not in the latter, in accordance with the expectations of large N c Chiral Perturbation Theory where the difference between the two mixing angles are due to a SU(3) f -breaking effect and a violation of the OZI rule respectively.

Electromagnetic transitions in an effective chiral Lagrangian with the $ \eta^{{\prime}}_{}$ and light vector mesons

“…This agrees with the leading-order result of large-N c chiral perturbation theory [10,33], but contrasts to phenomenological analyses which suggest two mixing angles for the octet-singlet basis, but seem to be compatible with one mixing angle in the flavor basis (see e.g. [47]).…”

“…As a striking consequence we have found an unconventionally small mixing angle θ ±2 • of the η-η system. Phenomenological analyses prefer a two-mixing-angle scenario with significantly larger mixing angles [40,41,47]. Going beyond leading order in our scheme provides us with the possibility of two mixing angles.…”

“…The situation is comparable to large-N c chiral perturbation theory. Also there a two-mixing angle scenario emerges only at next-to-leading order [10,33] and even then is not in full agreement with the phenomenological extraction [47].…”

Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball

“…Different mixing schemes used to determine these decay constants imply that the decay constants follow a particular symmetry (e.g., quark-flavor or octetsinglet) and effectively impose different restrictions on the decay constants [13], reducing the number of parameters which describe the mixing. In our numerical analysis, we use the decay constant sets f (8,0) η,η ′ obtained in several analyses using quark-flavor mixing scheme [53] as well as mixing scheme-free analyses [13,54].…”

“…In the present paper, we will confirm this observation. Nevertheless, neglecting the effects of π 0 and η − η ′ mixing until the time-like region considerations (Section 4), we list in Table 1 the non-zero values of α P , β P , γ P for different decay constants sets, obtained using different mixing schemes (analyzes) [13,53,54]. Mix.…”