Shedding light on the $ X(3930) $ and $ X(3960) $ states with the $B^- \to K^- J/\psi \omega $ reaction

TL;DR

This paper investigates the nature of the $X(3930)$ and $X(3960)$ states through the $B^- o K^- J/\psi \omega$ decay, aiming to clarify if they are the same or different resonances.

Contribution

It provides a theoretical analysis predicting the $J/\psi \omega$ mass distribution, offering a method to distinguish between the $X(3930)$ and $X(3960)$ states.

Findings

A clear signal expected around 3930 MeV in the $J/\psi \omega$ mass distribution.

No additional resonance signal at 3960 MeV supports the hypothesis of a single state.

Supports the idea that the $D_s^+ D_s^-$ peak is a threshold effect, not a new resonance.

Abstract

We have studied the contribution of the state $X(3930)$, coming from the interaction of the $D \overline{D}$ and $D^{+}_s D^{-}_s$ channels, to the $B^- \to K^- J/\psi \omega $ decay. The purpose of this work is to offer a complementary tool to see if the $X(3930)$ state observed in the $D^+ D^-$ channel is the same or not as the $X(3960)$ resonance claimed by the LHCb collaboration from a peak in the $D^{+}_s D^{-}_s$ mass distribution around threshold. We present results for what we expect in the $J/\psi \omega $ mass distribution in the $B^- \to K^- J/\psi \omega $ decay and conclude that a clear signal should be seen around $3930\,\rm MeV$. At the same time, finding no extra resonance signal at $3960\,\rm MeV$ would be a clear indication that there is not a new state at $3960\,\rm MeV$, supporting the hypothesis that the near-threshold peaking structure peak in the $D^{+}_s D^{-}_s$ mass distribution is only a manifestation of a resonance below threshold.