Color halo scenario of charmonium-like hybrids

TL;DR

This study uses lattice QCD to explore the internal structure of charmonium-like hybrids, proposing a 'color halo' model that challenges traditional flux-tube descriptions and aligns with observed decay patterns.

Contribution

It introduces a novel 'color halo' conceptualization of hybrids based on lattice QCD wave functions, providing new insights into their structure and decay mechanisms.

Findings

Wave functions show no node for ground states and one node for excited states.

Mass splittings of about 1.2-1.4 GeV are obtained for the first time.

Results challenge the flux-tube model, supporting the 'color halo' picture.

Abstract

The internal structures of $J^{PC}=1^{--}, (0,1,2)^{-+}$ charmonium-like hybrids are investigated under lattice QCD in the quenched approximation. We define the Bethe-Salpeter wave function $\Phi_n(r)$ in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator $\bar{c}{c}g$ between the vacuum and $n$-th state for each $J^{PC}$ with $r$ being the spatial separation between a localized $\bar{c}c$ component and the chromomagnetic strength tensor. These wave functions exhibit some similarities for states with the aforementioned different quantum numbers, and their $r$-behaviors (no node for the ground states and one node for the first excited states) imply that $r$ can be a meaningful dynamical variable for these states. Additionally, the mass splittings of the ground states and first excited states of charmonium-like hybrids in these channels are obtained for the first time to be approximately 1.2-1.4 GeV. These results do not support the flux-tube description of heavy-quarkonium-like hybrids in the Born-Oppenheimer approximation. In contrast, a charmonium-like hybrid can be viewed as a "color halo" charmonium for which a relatively localized color octet $\bar{c}c$ is surrounded by gluonic degrees of freedom, which can readily decay into a charmonium state along with one or more light hadrons. The color halo picture is compatible with the decay properties of $Y(4260)$ and suggests LHCb and BelleII to search for $(0,1,2)^{-+}$ charmonium-like hybrids in $\chi_{c0,1,2}\eta$ and $J/\psi \omega (\phi)$ final states.