Is 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 ∆m ≥ 2MeV 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 cancelation in the 1 ++ channel for the invariant DD * mass around the threshold between the continuum and bound state contribution. This is very much alike a similar cancelation 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.

On the precise measurement of the $X(3872)$ mass and its counting rate

“…This undercounting is in complete agreement with our previous study [14,15] on occupation numbers at finite temperature and of relevance in X(3872) in heavy ion-collisions. It also complies with the similarities of production rates at finite p T of deuterons and X(3872) states in pp collisions at ultrahigh energies in the mid-rapidity region [16] which provides, after correcting the effect to a one-to-one production rate, N X /N d ∼ 1.…”

“…The similarities between d and X(3872) already noted in Refs. [45][46][47] have been corroborated on a quantitative level in our recent work [16], were we have pointed out that they are also applicable from the point of view of production at accelerators [16]. However, a crucial and relevant difference for the present work is that while the deuteron is detected directly by analyzing its track and/or stopping power leaving a well-defined trace, the X(3872) is inferred from its decay properties, mainly through the J/ψρ and J/ψω channels.…”

“…6. Therefore, given these suggestive similarities, we have undertaken a comparative study of the deuteron and X(3872) production rates in pp scattering at ultra-high energies (∼ 7 TeV) in the observed p T distributions in colliders, which provides a suitable calibration tool in order to see the effects of the cancellation due to the finite resolution ∆m of the detectors signaling the X(3872) state and deciding on its bound state character [16].…”

“…In this paper, we promote the idea that the precise value of the mass is actually not crucial, since the contribution of nearby states with the same quantum numbers is unavoidable with the current experimental energy resolution detecting its decaying products, and a cancellation mechanism put forward initially by Dashen and Kane [13] is at work in this particular case. We have found in previous works that this has implications to count X(3872) degrees of freedom at finite temperatures of relevance in relativistic heavy ions collisions [14,15] and ultrahigh energies pp prompt X(3872) production at finite p T and mid-rapidity [16]. We will also show how the number of reconstructed states representing the bound X(3872) is smaller than the truly produced ones due to a cancellation mechanism which will be explained below and which provides a natural understanding of the missing decay channels.…”

Measurements of the Absolute Branching Fractions of B±→K±Xcc¯

“…A more refined tetraquark model [7] can accommodate a much smaller branching fraction, but requires another particle, Xð3876Þ, not yet observed. Various molecular models [8][9][10] predict this branching fraction to be ≲10%: Using the Xð3872Þ total width determination based on its line shape, or an upper limit on this quantity, information is provided on the partial width Γ½Xð3872Þ → J=ψπ þ π − ], for which a wide range of predictions exist, from 1.3 MeV in the case of a pure charmonium state [11] to about 100 keV for molecular models [8].…”