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/ψD \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 $ψ(3770)$, $ψ(3770) \to γX(3700) \to γηη'$. The second one proposes the analogous reaction $ψ(4040) \to γX(3700) \to γηη'$ and the third reaction is the $e^+ e^- \to J/ψX(3700) \to J/ψηη'$. Neat peaks are predicted for all the reactions and the calculated rates are found within measurable range in present facilities.