Proper Wilson flow time for calculating the topological charge density and the pseudoscalar glueball mass in quenched lattice QCD

Abstract: The proper Wilson flow time for calculating the topological charge density correlator (TCDC) of the gluonic definition by the Wilson flow is analyzed using the matching procedure. The relationship has been established between the proper Wilson flow time for calculating TCDC and the proper Wilson flow time at which the topological charge defined by the gluon fields is closest to an integer. The properties of TCDC defined by the bosonic field are investigated, and the pseudoscalar glueball mass was extracted from the TCDC computed at the proper Wilson flow time. It is further demonstrated that the proper Wilson flow time determined by the matching procedure can be applied to compute the topological susceptibility in the gluonic definition.