Many-Body Coulomb Gauge Exotic and Charmed Hybrids

Abstract

Utilizing a QCD Coulomb gauge Hamiltonian with linear confinement specified by lattice, we report a relativistic many-body calculation for the light exotic and charmed hybrid mesons. The Hamiltonian successfully describes both quark and gluon sectors, with vacuum and quasiparticle properties generated by a BCS transformation and more elaborate TDA and RPA diagonalizations for the meson ($q\bar{q}$) and glueball ($gg$) masses. Hybrids entail a computationally intense relativistic three quasiparticle ($q\bar{q}g$) calculation with the 9 dimensional Hamiltonian matrix elements evaluated variationally by Monte Carlo techniques. Our new TDA (RPA) spectrum for the nonexotic $1^{--}$ charmed ($c\bar{c}$ and $c\bar{c}g$) system provides an explanation for the overpopulation of the observed $J/\psi$ states. For the important $1^{-+}$ light exotic channel we obtain hybrid masses above 2 $GeV$, in broad agreement with lattice and flux tube models, indicating that the recently observed resonances at 1.4 and 1.6 $GeV$ are of different, perhaps four quark, structure.