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Heavy hadron chiral perturbation theory (HHchiPT) and XEFT are applied to thedecays X(3872) -> psi(2S) + gamma and psi(4040) -> X(3872) + gamma under theassumption 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^0bar{D}^{0*}+ bar{D}^0 D^{0*} -> psi(2S) + gamma or psi(4040) -> (D^0bar{D}^{0*}+ bar{D}^0 D^{0*}) + gamma transition. These amplitudes are matchedonto XEFT to obtain decay rates. The decays receive contributions from bothlong distance and short distance processes. We study the polarization of thepsi(2S) in the decay X(3872) -> psi(2S) + gamma and the angular distribution ofX(3872) in the decay psi(4040) -> X(3872) + gamma and find they can be used todifferentiate between different decay mechanisms as well as discriminatebetween 2^{-+} and 1^{++} quantum number assignments of the X(3872).

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