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

Abstract

In analogy to the f ₀(500), which appears as a ππ 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 $e^ + e^ - \to {J \mathord{\left/ {\vphantom {J {\psi D\bar D}}} \right. \kern-\nulldelimiterspace} {\psi D\bar D}}$ 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 ψ(3770), ψ(3770) → γX(3700) → γηη′. The second one proposes the analogous reaction ψ(4040) → γX(3700) → γηη′ and the third reaction is the e ⁺ e− → J/ψX(3700) → J/ψηη′. Neat peaks are predicted for all the reactions and the calculated rates are found within measurable range in present facilities.