Structure of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> as explained by a diffusion Monte Carlo calculation
M. C. Gordillo, F. De Soto, J. Segovia
Abstract
Two decades after its unexpected discovery, the properties of the $X(3872)$ exotic resonance are still under intense scrutiny. In particular, there are doubts about its nature as an ensemble of mesons or having any other internal structure. We use a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation that describes this state as a $c\overline{c}n\overline{n}$ ($n=u$ or $d$ quark) system. This approach accounts for multiparticle correlations in physical observables avoiding the usual quark-clustering assumed in other theoretical techniques. The most general and accepted pairwise Coulomb + linear-confining + hyperfine spin-spin interaction, with parameters obtained by a simultaneous fit of around 100 masses of mesons and baryons, is used. The $X(3872)$ contains light quarks whose constituent masses are given by the dynamical breaking of chiral symmetry. The same mechanism gives rise to Goldstone-boson exchange interactions between light quarks whose contribution, derived from a well extended chiral quark model, has been included in this analysis but plays a marginal role. It appears that a meson-meson molecular configuration is preferred but, contrary to the usual assumption of ${D}^{0}{\overline{D}}^{*0}$ molecule for the $X(3872)$, our formalism produces $\ensuremath{\omega}J/\ensuremath{\psi}$ and $\ensuremath{\rho}J/\ensuremath{\psi}$ clusters as the most stable ones, which could explain in a natural way all the observed features of the $X(3872)$.