Gluon Correlators in the Kogan-Kovner Model

The Lorentz-invariant gluon correlation functions and , corresponding to scalar and pseudoscalar glueballs, are calculated for Kogan's and Kovner's variational ansatz for the pure SU(N) Yang–Mills wave functional. One expects only one dynamical mass scale should be present in QCD; the ansatz generates the expected scale for both glueballs, as well as an additional scale for the scalar glueball coming from the correlator of the color electric field. The additional mass scale must therefore vanish, or be close to the expected one. This is shown to constrain the nature of the phase transition in the Kogan–Kovner ansatz.