  Angular correlation of jets produced in association with a massive scalar,
vector or tensor boson is crucial in the determination of their spin and CP
properties. We study jet angular correlations in events with a high mass bottom
quark pair or a top quark pair and two jets at the LHC, whose cross-section is
dominated by the virtual gluon fusion sub-processes when appropriate kinematic
selection cuts (vector-boson fusion cuts) are applied. We evaluate helicity
amplitudes for sub-processes initiated by qq, qg and gg collisions in the limit
where the intermediate gluons are collinear to the initial partons. We first
obtain a general expression for the azimuthal angle correlations among the
dijets and t t-bar or b b-bar, in terms of the gg to t t-bar or b b-bar
helicity amplitudes in the real gluon approximation of the full matrix
elements, and find simple analytic expressions in the two kinematic limits, the
production of a heavy quark pair near the threshold, and in the relativistic
limit where the invariant mass of the heavy quark pair is much larger than the
quark mass. For b b-bar + 2 jets we find strong azimuthal angle correlations
which are distinct from those expected for events with a CP-even or odd scalar
boson which may decay into a b b-bar pair. For t t-bar + 2 jets we find that
the angular correlations are similar to that of a CP-odd scalar+2 jets near the
threshold M_(t t-bar) ~ 2 m_t, while in the relativistic limit they resemble
the distribution for b b-bar + 2 jets. These correlations in the standard QCD
processes will help establish the experimental technique to measure the spin
and CP properties of new particles produced via gluon fusion at the LHC.
