Three methods to detect the predicted $D \bar{D}$ scalar meson X(3700)

In analogy to the f_0(500), which appears as a $\pi \pi$ resonance in chiral unitary theory, and the f_0(980), which appears as a quasibound $K \bar K$ state, the extension of this approach to the charm sector also predicts a quasibound $D \bar D$ state with mass around 3720 MeV, named as X(3700), for which some experimental support is seen in the $e^+ e^- \to J/\psi D \bar D$ reaction close to the $D \bar D$ threshold. In the present work we propose three different experiments to observe it as a clear peak. The first one is the radiative decay of the $\psi(3770)$, $\psi(3770) \to \gamma X(3700) \to \gamma \eta \eta '$. The second one proposes the analogous reaction $\psi(4040) \to \gamma X(3700) \to \gamma \eta \eta '$ and the third reaction is the $e^+ e^- \to J/\psi X(3700) \to J/\psi \eta \eta '$. Neat peaks are predicted for all the reactions and the calculated rates are found within measurable range in present facilities.