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We present a renormalization-group analysis of the $X(3872)$ radiative decaysinto $J/ \psi \gamma$ and $\psi(2S) \gamma$. We assume a $D\bar{D}^{*}$molecule for the $X$ long-distance structure and parametrize its short-distancephysics as contact interactions. Using effective field theory techniques andpower-divergence subtraction scheme, we find that short- and long-distancephysics are equally important in these decays. Our calculations set a lowerlimit to the corresponding decay widths, which can in principle be testedexperimentally. Our results may be used as guide to build models for the $X$short-distance.

Short-distance RG-analysis of $X(3872)$ radiative decays