Abstract
We smear quenched lattice QCD ensembles with lattice volume $32^3\times 8$ by using Wilson flow. Six ensembles at temperature near the critical temperature $T_c$ corresponding to the critical inverse coupling $\beta_c=6.06173(49)$ are used to investigate the localization of topological charge density. If the effective smearing radius of Wilson flow is large enough, the density, size and peak of Harrington-Shepard (HS) caloron-like topological lumps of ensembles are stable when $\beta\leq 6.050$, but start to change significantly when $\beta\geq6.055$. The inverse participation ratio (IPR) of topological charge density shows similar results, it begins to increase when $\beta\geq 6.055$ and is stable when $\beta\leq 6.050$. The pseudoscalar glueball mass is extracted from the topological charge density correlator (TCDC) of ensembles at $T=1.19T_c,~\textrm{and }1.36T_c$, the masses are $1.915(98)\textrm{ GeV}$ and $1.829(123)\textrm{ GeV}$ respectively, they are consistent with results from conventional methods.
Highlights
Topological properties of the QCD vacuum are believed to play an important role in QCD
We use the HS calorons filter conditions and inverse participation ratio (IPR) to investigate the localization of topological charge density
We find that the three quantities of HS caloron-like topological lumps are consistent at β 1⁄4 6.045
Summary
Topological properties of the QCD vacuum are believed to play an important role in QCD. A usual way to study the topological structure is investigating the localization of topological charge density, such as Belavin-Polyakov-Schwartz-Tyupkin (BPST) instanton-like localized topological lumps at zero temperature. When we use the gluonic definition for the topological charge density qðxÞ to investigate the topological localized structures, such as instantons, a UV filter is needed to remove the short-ranged topological fluctuations and preserve the long-ranged topological structures [7,8,9,10,11]. The topological charge density correlator (TCDC) of quenched QCD can be used to extract pseudoscalar glueball masses at zero temperature with Wilson flow [23]. We extracted the pseudoscalar glueball mass from TCDC at finite temperature with Wilson flow. This method does not need large lattice size in the temporal direction to do fitting, which is hard to be satisfied in ensembles at finite temperature especially at high temperatures
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