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

TL;DR

This paper proposes three experimental methods to detect the predicted $D ar D$ scalar meson X(3700), extending chiral unitary theory to the charm sector, with predicted observable peaks in specific decay and production reactions.

Contribution

It introduces three novel experimental approaches to observe the X(3700) meson, providing measurable predictions for future experiments.

Findings

Predicted clear peaks in proposed reactions.

Calculated rates within current experimental capabilities.

Supports the existence of X(3700) as a quasibound $D ar D$ state.

Abstract

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.