Structure of the X(3872) as explained by a diffusion Monte Carlo calculation

M C Gordillo,F De Soto,J Segovia

doi:10.1103/physrevd.104.054036

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 $c \bar c n \bar n$ ($n=u$ or $d$ quark) system. This approach accounts for multi-particle 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 masses are given by the mechanism responsible of the dynamical breaking of chiral symmetry. The same mechanisms gives rise to Goldstone-boson exchange interactions between quarks that have been fixed in the last 10-20 years reproducing hadron, hadron-hadron and multiquark phenomenology. It appears that a meson-meson molecular configuration is preferred but, contrary to the usual assumption of $D^0\bar{D}^{\ast0}$ molecule for the $X(3872)$, our formalism produces $\omega J/\psi$ and $\rho J/\psi$ clusters as the most stable ones, which could explain in a natural way all the observed features of the $X(3872)$.

Highlights

A very successful classification scheme for hadrons in terms of their valence quarks and antiquarks was independently proposed by Murray Gell-Mann [1] and George Zweig [2] in 1964
The quark model received experimental verification beginning in the late 1960s and, despite extensive experimental searches, no unambiguous candidates for exotic configurations were identified until the turn of this century, with the discovery by the Belle Collaboration in 2003 [3] of the Xð3872Þ in the invariant mass spectrum of πþπ−J=ψ produced in BÆ → KÆXð3872Þ → KÆðπþπ−J=ψÞ decays
Xð3872Þ as a ccnntetraquark system with quantum numbers JPC 1⁄4 1þþ. This approach avoids the usual quark-clustering assumed in any theoretical technique applied to the same problem and, provides information about the hadron’s wave function and structural properties

Summary

Introduction

A very successful classification scheme for hadrons in terms of their valence quarks and antiquarks was independently proposed by Murray Gell-Mann [1] and George Zweig [2] in 1964. The quark model received experimental verification beginning in the late 1960s and, despite extensive experimental searches, no unambiguous candidates for exotic configurations were identified until the turn of this century, with the discovery by the Belle Collaboration in 2003 [3] of the Xð3872Þ in the invariant mass spectrum of πþπ−J=ψ produced in BÆ → KÆXð3872Þ → KÆðπþπ−J=ψÞ decays. More than two dozens of unconventional charmonium- and bottomoniumlike states, the so-called XYZ mesons, have been observed at B-factories (BABAR, Belle and CLEO), τ-charm facilities (CLEO-c and BESIII) and proton-(anti)proton

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