  Verifying the existence of bound states of gluons and distinguishing them
from conventional quark-antiquark, hybrid or tetraquark states has remained a
key problem in QCD. We show that QCD counting rules for the power-law fall-off
of production cross sections at high momentum transfer can be used to
distinguish gluonium states from conventional hadrons. The valence two-gluon
contribution to a 0^+ gluonium bound state has L=0 and thus twist (dimension
minus spin of their minimum interpolating operators) tau=2. The competing twist
assignments for scalar f_0 mesons have twist tau = 3 for the valence |q qbar >
configuration or |qqbar g> in an s-wave, and tau >= 4 for |q qbar qbar q >
tetraquarks, etc. Thus, the production cross section for mesons with
quark-containing valence wavefunctions relative to glueball production should
be suppressed by at least a power of momentum transfer. Distinguishing these
processes is feasible in exclusive e^-e^+ --> phi f_0 reactions at 9 and 11 GeV
center of mass energy at Belle-II. In the case of single-particle inclusive
hadroproduction A B --> C X, the cross section for scalar gluonium production
at high transverse momentum p_T and fixed x_T = 2 p_T/sqrt(s) will dominate
meson or tetraquark production by at least two powers of p_T.
