Teoria efetiva para decaimentos radiativos do X(3872) - Molnar, Daniel Alberto Stanischesk (2015)
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.