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The ratio of branching fractions Br(X(3872) --> gamma J/psi)/ Br(X(3872) -->pi^+ pi^- J/psi) is studied by assuming that the X(3872) --> pi^+ pi^- J/psidecay proceeds through the rho^0 meson pole which is caused by the omega-rho^0mixing. As the result, it is seen that the calculated ratio is compatible withthe measured values of the ratio when X(3872) is an axial-vector tetra-quarkstate, while it would be much larger than the measurements when it is acharmonium. Therefore, the existing data on the ratio seem to favor thetetra-quark interpretation of X(3872) over the charmonium, although a smallmixing of the charmonium is not excluded.

omega-rho^0 mixing as a possible origin of the hypothetical isospin non-conservation in the X(3872) --> pi^+ pi^- J/psi decay