  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/psi
decay proceeds through the rho^0 meson pole which is caused by the omega-rho^0
mixing. As the result, it is seen that the calculated ratio is compatible with
the measured values of the ratio when X(3872) is an axial-vector tetra-quark
state, while it would be much larger than the measurements when it is a
charmonium. Therefore, the existing data on the ratio seem to favor the
tetra-quark interpretation of X(3872) over the charmonium, although a small
mixing of the charmonium is not excluded.
