η-η′ mixing angle from vector meson radiative decays

The octet-singlet η-η′ mixing mass term could have a derivative O(p2) term as found in recent analysis of the η-η′ system. This term gives rise to an additional momentum-dependent pole contribution which is suppressed by a factor mη2/mη′2 for η relative to the η′ amplitude. The processes with η meson can then be described, to a good approximation, by the momentum-independent mixing mass term which gives rise to a new η-η′ mixing angle θP, like the old η-η′ mixing angle used in the past, but a momentum-dependent mixing term d, like sin(θ0−θ8) in the two-angle mixing scheme used in the parametrization of the pseudo-scalar meson decay constants in the current literature, is needed to describe the amplitudes with η′. In this Letter, we obtain sum rules relating θP and d to the physical vector meson radiative decays with η and η′, as done in our previous work for η meson two-photon decay, and with nonet symmetry for the η′ amplitude, we obtain a mixing angle θP=−(18.76±3.4)°, d=0.10±0.03 from ρ→ηγ and η′→ργ decays, for ω, θP=−(15.81±3.1)°, d=0.02±0.03, and for ϕ, θP=−(13.83±2.1)°, d=0.08±0.03. A larger value of 0.06±0.02 for d is obtained directly from the nonet symmetry expression for the η′→ωγ amplitude. This indicates that more precise vector meson radiative decay measured branching ratios and higher order SU(3) breaking effects could bring these values for θP closer and allows a better determination of d.