Topological charge density correlator in Lattice QCD with two flavours of unimproved Wilson fermions

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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.