https://doi.org/10.1140/epjc/s10052-013-2351-8
Regular Article - Theoretical Physics
X(3872) is not a true molecule
1
Centro de Física das Interacções Fundamentais, Instituto Superior Técnico, Technical University of Lisbon, 1049-001, Lisbon, Portugal
2
Centro de Física Computacional, Departamento de Física, Universidade de Coimbra, 3004-516, Coimbra, Portugal
* e-mail: george@ist.utl.pt
Received:
3
February
2013
Revised:
27
February
2013
Published online:
21
March
2013
A solvable coordinate-space model is employed to study the component of the X(3872) wave function, by coupling a confined 3
P
1
state to the almost unbound S-wave
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
component. However, the long tail of the
wave function, in the case of small binding, strongly limits the
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
scattering length of 11.6 fm. Finally, the
-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
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.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013