Nature of X (3872) from its radiative decay

We study the radiative decay of X(3872) based on the assumption that X(3872) is regarded as a cc charmonium with quantum number J(PC) = 1(++) (J, P, C represent the spin, parity and charge conjugation, respectively). The form factors of X(3872) transitions to J/Psi gamma and Psi 'gamma (Psi ' denotes Psi(2S) throughout the paper) are calculated in the framework of the covariant light-front quark model. The phenomenological wave function of a meson depends on the parameter beta, whose inverse essentially describes the confinement scale. In the present work, the parameters beta for the vector J/Psi and Psi ' mesons will be determined through their decay constants, which are obtained from the experimental values of their partial decay widths to the electron-positron pair. For X(3872), we determined the value of beta by the decay width of X(3872) -> Psi 'gamma. Then, we examined the width of X(3872) -> J/Psi gamma in a manner of parameter-free prediction and compared it with the experimental value. As a result, an inconsistency or contradiction occurs between the widths of X(3872) -> J/Psi gamma and X(3872) -> Psi 'gamma. We thus conclude that X(3872) cannot be a pure cc resonance and that other components are necessary in its wave function.