The ratio of decay widths of X(3872) to ψ′γ and J/ψγ as a test of the X(3872) dynamical structure

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Radiative decays of X(3872) with JPC=1⁺⁺ are studied in the coupled-channel approach, where the c c states are described by relativistic string Hamiltonian, while for the decay channels DD* a string breaking mechanism is used. Within this method a sharp peak and correct mass shift of the 2 ³P₁ charmonium state just to the D⁰D*⁰ threshold was already obtained for a prescribed channel coupling to the DD* decay channels. For the same value of coupling the normalized wave function (w.f.) of X(3872) acquires admixture of the 1 ³P₁ component with the w.f. fraction c₁=0.153 (θ=8.8∘), which increases the transition rate Γ(X(3872)→ J/ψγ) up to 50-70 keV, making the ratio R=B(X(3872)→ ψ′γ)B(X(3872)→ J/ψγ)=0.8± 0.20 (th) significantly smaller, as compared to R≃ 5 for X(3872) as a purely 2 ³P₁ state.