Strangeonium-like hybrids on the lattice *

Abstract

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.