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Direct production of the charmonium-like state $X(3872)$ in $e^+e^-$ collisions is considered in the framework of the vector meson dominance model.
- An order-of-magnitude estimate for the width $\Gamma(X\to e^+e^-)$ is found to be $\gtrsim$0.03 eV.
- The same approach applied to the $\chi_{c1}$ charmonium decay predicts the corresponding width of the order 0.1 eV in agreement with earlier estimates.
- Experimental perspectives for the direct production of the $1^{++}$ charmonia in $e^+e^-$ collisions are briefly discussed.
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