Abstract
A solvable coordinate-space model is employed to study the \(c\bar{c}\) component of the X(3872) wave function, by coupling a confined 3 P 1 \(c\bar {c}\) state to the almost unbound S-wave \(D^{0}\overline{D}^{*0}\) channel via the 3 P 0 mechanism. The two-component wave function is calculated for different values of the binding energy and the transition radius a, always resulting in a significant \(c\bar{c}\) component. However, the long tail of the \(D^{0}\overline{D}^{*0}\) wave function, in the case of small binding, strongly limits the \(c\bar{c}\) 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 \(D^{0}\overline{D}^{*0}\) scattering length of 11.6 fm. Finally, the \(\mathcal{S}\)-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 \(c\bar{c}\) 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.
Highlights
The Belle Collaboration discovered [1] the charmoniumlike state X(3872) almost a decade ago, observing it in the decay B± → K±π+π−J/ψ, with a significance in excess of 10σ
As for the quantum numbers, the possibilities are JP C = 1++ and JP C = 2−+ according to the PDG [6]
The experimental errors in the average mass of the X(3872) and the D0D∗0 threshold allow for a maximum binding energies (BEs) of 0.57 MeV, i.e., somewhere in between cases X and C
Summary
The Belle Collaboration discovered [1] the charmoniumlike state X(3872) almost a decade ago, observing it in the decay B± → K±π+π−J/ψ, with a significance in excess of 10σ. Once the 1 × 1 S matrix (cf Eq (19)) has been constructed from the wave function, possible bound or virtual states as well as resonances can be searched for These occur at real or complex energies for which S blows up, or equivalently, when cot δlf (E) = i (cf Eq (18)). I.e., the relative momentum has a negative imaginary part From this table we observe that larger and larger couplings are needed to generate a pole close to threshold when a approaches the value 3.5 GeV−1. As a matter of fact, in our prior paper [14], with all relevant two-meson channels included, the X(3872) resonance was found as a confinement pole, whereas dynamical poles were only encountered very deep in the complex energy plane, without any observable effect at real energies. Another feature we can observe for all trajectories is an initial attraction and subsequent repulsion between the dynamical and the confinement poles
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
