Color halo scenario of charmonium-like hybrids * *Supported by the National Key Research and Development Program of China (2017YFB0203202), the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302, XDC01040100), the National Natural Science Foundation of China (11935017, 11575196, 11775229, 12075253, 12070131001) (CRC 110 by DFG and NSFC). The numerical calculations are carried out on Tianhe-1A at the National

Abstract

The internal structures of charmonium-like hybrids are investigated under lattice QCD in the quenched approximation. We define the Bethe-Salpeter wave function ( ) in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator ( ) between the vacuum and n-th state for each , with r being the spatial separation between a localized 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 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 and suggests LHCb and BelleII to search for charmonium-like hybrids in and final states.