  In this paper we consider all possible 1D and 2P ccbar assignments for the
recently discovered X(3872). Taking the experimental mass as input, we give
numerical results for the E1 radiative widths as well as the three principal
types of strong decays; open-charm, ccbar annihilation and closed-charm
hadronic transitions. We find that many assignments may be immediately
eliminated due to the small observed total width. The remaining viable ccbar
assignments are 3D3, 3D2, 1D2, 2 3P1 and 2 1P1. A search for the mode J/psi pi0
pi0 can establish the C-parity of the X(3872), which will eliminate many of
these possibilities. Radiative transitions can then be used to test the
remaining assignments, as they populate characteristic final states. The 3D2
and 1D2 states are predicted to have large (ca.50%) radiative branching
fractions to chi_1 gamma and h_c gamma respectively. We predict that the 3D3
will also be relatively narrow and will have a significant (ca.10%) branching
fraction to chi_2 gamma, and should also be observable in B decay. Tests for
non-ccbar X(3872) assignments are also discussed.
