  We study the two-point Topological Charge Density Correlator (TCDC) in
lattice QCD with two degenerate flavours of unimproved Wilson fermions and
Wilson gauge action at two values of lattice spacings and different volumes,
for a range of quark masses. Configurations are generated with DDHMC algorithm
and smoothed with HYP smearing. In order to shed light on the mechanisms
leading to the observed suppression of topological susceptibility with respect
to the decreasing quark mass and decreasing volume, in this work, we carry out
a detailed study of the two-point TCDC. We have shown that, (1) the TCDC is
negative beyond a positive core and radius of the core shrinks as lattice
spacing decreases, (2) as the volume decreases, the magnitude of the contact
term and the radius of the positive core decrease and the magnitude of the
negative peak increases resulting in the suppression of the topological
susceptibility as the volume decreases, (3) the contact term and radius of the
positive core decrease with decreasing quark mass at a given lattice spacing
and the negative peak increases with decreasing quark mass resulting in the
suppression of the topological susceptibility with decreasing quark mass, (4)
increasing levels of smearing suppresses the contact term and the negative peak
keeping the susceptibility intact and (5) both the contact term and the
negative peak diverge in nonintegrable fashion as lattice spacing decreases. It
is gratifying to note that observations similar to 1 and 5 have been made using
topological charge density operator based on chiral fermion. The observations 2
and 3 may be confirmed more precisely by using formulations based on chiral
fermions.
