Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model

Abstract

The more-carefully defined, and more appropriate 2 ++ tensor glueball current is a SUc(3) gaugeinvariant, symmetric, traceless and conserved Lorentz-irreducible tensor. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted, and calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. Besides taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the 2 ++ tensor glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width and coupling constants for the 2 ++ resonance in which the glueball fraction is dominant are obtained.