Strangeonium-like hybrids on the lattice * *Supported by the National Key Research and Development Program of China (2017YFB0203202) and the Strategic Priority Research Program of Chinese Academy of Sciences (No.XDC01040100, XDB34030302). The numerical calculations are carried out on Tianhe-1A at the National Supercomputer Center (NSCC) in Tianjin and the GPU cluster at IHEP. We also acknowledge the support of the

Yunheng Ma,Zhaofeng Liu,Ming Gong,Ying Chen

doi:10.1088/1674-1137/abc241

Abstract

The strangeonium-like hybrids are investigated from lattice QCD in the quenched approximation. In the Coulomb gauge, spatially extended operators are constructed for and states with the color octet component being separated from the chromomagnetic field strength by the spatial distance , whose matrix elements between the vacuum and the corresponding states are interpreted as Bethe-Salpeter (BS) wave functions. In each of the channels, the masses and the BS wave functions are reliably derived. The ground state mass is approximately 2.1-2.2 GeV, and that of is approximately 2.3-2.4 GeV, whereas the mass of the first excited state is approximately 1.4 GeV higher. This mass splitting is much larger compared to that expected based on the phenomenological flux-tube model or constituent gluon model for hybrids, which is usually a few hundred MeV. The BS wave functions with respect to exhibit clear radial nodal structures of a non-relativistic two-body system, which imply that is a meaningful dynamical variable for these hybrids and motivate a color halo picture of hybrids, in which the color octet is surrounded by gluonic degrees of freedom. In the channel, the properties of the lowest two states are consistent with those of and . We did not obtain convincing information with respect to . However, we argue that regardless of whether is a conventional meson or a hybrid in the color halo scenario, the ratio of partial decay widths and observed by BESIII can be understood based on the mechanism of hadronic transition of a strangeonium-like meson in addition to mixing.

Highlights

The naive quark model describes hadrons as the qqmesons and qqq baryons
We extend the above study strategy to strangeonium-like hybrids and focus on the {1−−, (0, 1, 2)−+} states, such that we can check if the similar situation to the ccg hybrids can happen for ssg states
In a previous lattice study on ccg hybrids [24], the same behaviors of the wave functions and the spectrum pattern have been observed for the (0, 1, 2)−+ and 1−− supermultiplets, based on which a ”color halo” picture has been proposed that a hybrid meson can be viewed as a relatively compact color octet qqpair surrounded by color octet gluonic degrees of freedom such that the wave functions depict the relative motion between the qqpair and the gluonic excitation

Summary

Introduction

Since quarks and gluons are the fundamental degrees of freedom of QCD, if gluons can act as building blocks similar to quarks to build up hadrons, in the phenomenological meaning, there may exist glueballs which are purely made up of gluons, and hybrids which are composed of quarks and gluons. Hybrids, and multiquark states (tetraquarks and pentaquarks, etc.) are usually called exotic hadrons in contrast to the conventional qqmesons and qqq baryons. It is found that the lowest 1−+ hybrid usually has a mass of about 1 GeV higher than the ground state vector meson with the same qqcomponent. The vector charmonium-like state Y (4260) (or ψ(4230) named by PDG 2018 [5]), due to its very different properties from the conventional charmonia and the closeness of its mass to that of the 1−+ ccg hybrid, has a possible assignment of 1−− hybrid [6]. The similarity of its property to Y (4260) motivates a ssg hybrid interpretation of φ(2170)

Objectives

Discussion

Conclusion