In this thesis we study radiative decays of the exotic meson X(3872) into $J/ \psi \gamma$ and $\psi(2S) \gamma$ using an effective field theory framework. Assuming the exotic meson to be primarily a molecular state of the mesons $D$ and $ \bar{D}^{*}$, we perform a renormalization analysis to estimate the contribution of the short-distance physics. This is done using two different prescriptions, the popular $\overline{MS}$ scheme, valid only for perturbative calculations, and the PDS scheme, used in EFTs for loosely-bound systems and intrinsically non-perturbative. We show that, without a short-distance contact interaction, the observables become very dependent on the regularization scale, therefore demanding proper renormalization. We include two short-distance contact terms, one for each decay channel, and impose the renormalization condition within both $\overline{MS}$ and PDS schemes. We obtain the behavior of the contact term with the renormalization scale $\mu$, which can be useful in guiding models for the short-distance part. We note, however, distinct behaviors between $\overline{MS}$ and PDS. Both also lead to lower limits in the decay widths that could, in principle, be tested experimentally.

In this thesis we study radiative decays of the exotic meson X(3872) into $J/ \psi \gamma$ and $\psi(2S) \gamma$ using an effective field theory framework. Assuming the exotic meson to be primarily a molecular state of the mesons $D$ and $ \bar{D}^{*}$, we perform a renormalization analysis to estimate the contribution of the short-distance physics. This is done using two different prescriptions, the popular $\overline{MS}$ scheme, valid only for perturbative calculations, and the PDS scheme, used in EFTs for loosely-bound systems and intrinsically non-perturbative. We show that, without a short-distance contact interaction, the observables become very dependent on the regularization scale, therefore demanding proper renormalization. We include two short-distance contact terms, one for each decay channel, and impose the renormalization condition within both $\overline{MS}$ and PDS schemes. We obtain the behavior of the contact term with the renormalization scale $\mu$, which can be useful in guiding models for the short-distance part. We note, however, distinct behaviors between $\overline{MS}$ and PDS. Both also lead to lower limits in the decay widths that could, in principle, be tested experimentally.