The vector-meson octet-singlet mixing angle from squared masses is

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Symmetry and Flavour, Ch SU(3) flavour: weights, tensor products and the mass formulas

Problem

The vector-meson octet-singlet mixing angle from squared masses is θ=39.8∘\theta = 39.8^\circ, and the ideal mixing angle is θideal=arctan⁡(1/2)=35.3∘\theta_{\rm ideal} = \arctan(1/\sqrt2) = 35.3^\circ. Near ideal mixing, the physical ω\omega and ϕ\phi are related to the pure non-strange combination nnˉ=(uuˉ+ddˉ)/2n\bar n = (u\bar u+d\bar d)/\sqrt2 and the pure ssˉs\bar s combination by a rotation through Δθ=θ−θideal\Delta\theta = \theta - \theta_{\rm ideal}, so that the fraction of ssˉs\bar s in the physical ω\omega is sin⁡2Δθ\sin^2\Delta\theta. Find the percentage of ssˉs\bar s in the physical ω\omega.

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