Is the X(3872) a bound state ?

Abstract

All existing experimental evidence of the bound state nature of the $X(3872)$ relies on considering its decay products with a finite experimental spectral mass resolution which is typically $\Delta m \ge 2 $MeV and much larger than its alleged binding energy, $B_X=0.00(18)$MeV. On the other hand, we have found recently that there is a neat cancellation in the $1^{++}$ channel for the invariant $D \bar D^*$ mass around the threshold between the continuum and bound state contribution. This is very much alike a similar cancellation in the proton-neutron continuum with the deuteron in the $1^{++}$ channel. Based on comparative fits of experimental cross section deuteron and $X(3872)$ prompt production in pp collisions data with a finite $p_T$ to a common Tsallis distribution we find a strong argument questioning the bound state nature of the state but also explaining the large observed production rate likely consistent with a half-bound state.