Eur. Phys. J. C (2013) 73: 2351
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

Abstract

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.