  We further explore the consequences of treating the X(3872) meson as a
tetraquark bound state by analyzing its one-photon decay X => \gamma + J/psi in
the framework of our approach developed in previous papers which incorporates
quark confinement in an effective way. To introduce electromagnetism we gauge a
nonlocal effective Lagrangian describing the interaction of the X(3872) meson
with its four constituent quarks by using the P-exponential path-independent
formalism. We calculate the matrix element of the transition X => \gamma+ J/psi
and prove its gauge invariance. We evaluate the X=> \gamma + J/psi decay width
and the longitudinal/transverse composition of the J/psi in this decay. For a
reasonable value of the size parameter of the X(3872) meson we find consistency
with the available experimental data. We also calculate the helicity and
multipole amplitudes of the process, and describe how they can be obtained from
the covariant transition amplitude by covariant projection.
