Instanton Effects in QCD Sum Rules for the $0^{++}$ Hybrid

Abstract

In this paper, we study instanton contributions to the correlator of the hybrid current $g\bar{q}{\sigma }_{\mu \nu }{G}_{\nu \mu }^a{T}^{a}q$. These contributions are then included in a QCD sum-rule analysis of the isoscalar $0^{++}$ hybrid mass. We find a mass at 1.83 GeV for the $(\bar{u}ug+\bar{d}dg)/\sqrt{2}$ hybrid. However, for the $\bar{s}sg$ hybrid, we find the sum rules are unstable. We also study non-zero width effects, which affect the mass prediction. The mixing effects between these two states are studied and we find QCD sum rules support the existence of a flavor singlet hybrid with mass at around 1.9 GeV. Finally, we study the mixing effects between hybrid and glueball currents. The mixing between the $(\bar{u}ug+\bar{d}dg)/\sqrt{2}$($\bar{s}sg$) and the glueball causes two states, one in the region 1.4-1.8 GeV(1.4-2.2 GeV), and the other in the range 1.8-2.2 GeV(2.2-2.6 GeV).

Comments: 12 pages, revised version