Correlation and localization properties of topological charge density and the pseudoscalar glueball mass in SU(3) lattice Yang-Mills theory

Towards the goal of extracting the continuum properties, we have studied the Topological Charge Density Correlator (TCDC) and the Inverse Participation Ratio (IPR) for the topological charge density ($q(x)$) in SU(3) Lattice Yang-Mills theory for relatively small lattice spacings including some smaller than those explored before. With the help of recently proposed open boundary condition, it is possible to compute observables at a smaller lattice spacing since {\em trapping problem} is absent. On the other hand, the reference energy scale provided by Wilson flow allows us to study their scaling behavior in contrast to previously proposed smearing techniques. The behavior of TCDC for different lattice spacings at a fixed HYP smearing level shows apparent scaling violations. In contrast, at a particular Wilson flow time $t$ for all the lattice spacings investigated (except the largest one), the TCDC data show universal behavior within our statistical uncertainties. The continuum properties of TCDC are studied by investigating the small flow time behavior. We have also extracted the pseudoscalar glueball mass from TCDC, which appears to be insensitive to the lattice spacings (0.0345 fm $\leq a\leq$ 0.0667 fm) and agrees with the value extracted using anisotropic lattices, within statistical errors. Further, we have studied the localization property of $q(x)$ through IPR whose continuum behavior can be probed through the small values of Wilson flow time and observed the decrease of IPR with decreasing Wilson flow time. A detailed study of $q(x)$ under Wilson flow time revealed that as Wilson flow time decreases, the proximity of the regions of positive and negative charge densities of large magnitudes increases, and the charge density appears to be more delocalized resulting in the observed behavior of IPR.