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Radiative Decays X(3872) -> psi(2S)+gamma and psi(4040) -> X(3872)+gamma in Effective Field Theory

Heavy hadron chiral perturbation theory (HHchiPT) and XEFT are applied to the decays X(3872) -> psi(2S) + gamma and psi(4040) -> X(3872) + gamma under the assumption that the X(3872) is a molecular bound state of neutral charm mesons. In these decays the emitted photon energies are 181 MeV and 165 MeV, respectively, so HHchiPT can be used to calculate the underlying D^0 bar{D}^{0*}+ bar{D}^0 D^{0*} -> psi(2S) + gamma or psi(4040) -> (D^0 bar{D}^{0*}+ bar{D}^0 D^{0*}) + gamma transition. These amplitudes are matched onto XEFT to obtain decay rates. The decays receive contributions from both long distance and short distance processes. We study the polarization of the psi(2S) in the decay X(3872) -> psi(2S) + gamma and the angular distribution of X(3872) in the decay psi(4040) -> X(3872) + gamma and find they can be used to differentiate between different decay mechanisms as well as discriminate between 2^{-+} and 1^{++} quantum number assignments of the X(3872).