X(3872) is not a true molecule

Abstract

wave function, in the case of small binding, strongly limits the cc probability, which roughly lies in the range 7-11%, for the average experimental binding energy of 0.16 MeV and a between 2 and 3 GeV −1 . Furthermore, a reasonable value of 7.8 fm is obtained for the X(3872) r.m.s. radius at the latter binding energy, as well as an S-wave D 0 D * 0 scattering length of 11.6 fm. Finally, the S-matrix pole trajectories as a function of coupling constant show that X(3872) can be generated either as a dynamical pole or as one connected to the bare cc confinement spectrum, depending on details of the model. From these results we conclude that X (3872) is not a genuine meson-meson molecule, nor actually any other mesonic system with non-exotic quantum numbers, due to inevitable mixing with the corresponding quark-antiquark states. IntroductionThe Belle Collaboration discovered [1] the charmoniumlike state X(3872) almost a decade ago, observing it in the decay On the theory side, the discussion about the nature of X(3872) continues most vivid. Although the PDG [6] lists 1 ++ and 2 −+ as the meson's possible quantum numbers, and a recent BABAR analysis [9] of the 3π invariant mass distribution in the decay X(3872) → ωJ/ψ even seems to slightly favor the 2 −+ assignment, most model builders describe the state as an axial vector. For instance, model calculations of semi-inclusive B → η c2 + X processes [10] as well as electromagnetic η c2 decays [11] have been shown to disfavor the 2 −+ scenario. The same conclusion was reached in a tetraquark description of X(3872) [12], while pion exchange in a molecular picture would be repulsive in this case [13] and so inhibitive of a bound state. Finally, unquenching a 1 1 D 2 cc state by including meson-meson loops can only further lower the bare mass, which lies in the range 3.79-3.84 GeV for all quenched quark models we know of, thus making a 2 −+ charmonium resonance at 3.872 GeV very unlikely [14]. For further information and more references concerning X(3872), see e.g. a recent review [15], as well as our prior coupled-channel analysis [14].The first suggestion of possible meson-meson molecules bound by pion exchange, in particular a DD * 1 state with quantum numbers 1 ++ or 0 −+ , was due to Törnqvist [13]. With the discovery of X(3872) just below the D 0 D * 0 threshold, this idea was revived, of course. In the present paper, we intend to study the issue, not from Törnqvist's pion-exchange point of view, but rather as regards its possible implications for models based on quark degrees of freedom. In this context, it is worthwhile to quote from Ref. [16], in which a molecular interpretation is advocated (also see Ref.[17]):"Independent of the original mechanism for the resonance, the strong coupling transforms the resonance into a bound state just below the two-particle threshold if a > 0 or into a virtual state just above the two-particle threshold if a < 0. If a > 0, the 1 Henceforth, we omit the bar in DD * , for notational simplicity.

The hidden-charm pentaquark and tetraquark states

“…Later in Ref. [604], Coito, Rupp, and Beveren studied the X(3872) as a confined 3 P 1 cc state coupling to the almost unbound S -wave D 0D * 0 channel via the 3 P 0 mechanism. They calculated the two-component wave function for different values of the binding energy and the transition radius a, and found a significant cc component.…”

Hidden-charm and bottom meson-baryon molecules coupled with five-quark states

“…[53] and references therein). In addition, theDΛ c andD * Λ c thresholds are also located just below theD ( * ) Σ may be explained by this admixture picture of a cc core plus higher Fock components due to the coupling to the meson-meson continuum [56,[65][66][67][68][69][70][71][72][73][74][75][76][77][78]. For those interested in X, Y , and Z exotic states, a general review can be found in [56].…”

A New Hadron Spectroscopy

“…Problems with the two above-mentioned pictures have inspired a number of charmoniummolecular hybrid models, 6 in which the X(3872) is a quantum mechanical mixture of cc, D 0D * 0 and D + D * − components [102,103,104], where the cc component is (mostly) the χ ′ c1 . Hadronic production and radiative transitions to the ψ ′ and J/ψ are hypothesized to proceed ia the cc component and this could explain why X(3872) production properties are similar to those of the ψ ′ and its decay width to γψ ′ is larger than that for γJ/ψ (because of the closer overlap of the χ ′ c1 and ψ ′ radial wavefunctions).…”