η–η′ Mixing Angle from Vector Meson Radiative Decays

Abstract

The η–η′ mixing from the derivative coupling SU(3)×SU(3) symmetry breaking term, produces an additional momentum-dependent pole term for processes with η′, but is suppressed in the η amplitude by a factor mη2/mη′2. Thus processes with η meson could then be described, to first order in SU(3) breaking, by the usual η–η′ mixing angle, while processes with η′ could be effectively described by a new mixing angle as in the two-angle mixing scheme used in the parametrization of the pseudo-scalar meson decay constants in the current literature. In this talk, I would like to present a recent work in which we show that, by diagonalizing both the mixing mass term and the momentum-dependent mixing term, the η–η′ system could be described by a meson field renormalization and a new mixing angle θ. From the sum rules relating θ and d to the measured vector meson radiative decays amplitudes, we obtain θ=−(13.99±3.1)°, d=0.12±0.03 from ρ→ηγ and η′→ργ decays, for ω, θ=−(15.47±3.1)°, d=0.11±0.03, and for ϕ, θ=−(12.66±2.1)°, d=0.10±0.03. It seems that vector meson radiative decays would favor a small η−η′ mixing angle as found in previous analysis.