  We investigate the well-known $c\bar{c}$ vector state $\psi(4040)$ in the
framework of a quantum field theoretical model. In particular, we study its
spectral function and search for the pole(s) in the complex plane. Quite
interestingly, the spectral function has a non-standard shape and two poles are
present. The role of the meson-meson quantum loops (in particular $DD^*$ ones)
is crucial and could also explain the not yet confirmed state $Y(4008)$.
