Open boundary condition, Wilson flow and the scalar glueball mass

Abstract

A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV ≤ 1 a ≤ 5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale ≈ 5.7 GeV. To smoothen the gauge fields we have used recently proposed Wilson flow which, compared to HYP smearing, exhibits better systematics in the extraction of glueball mass. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV ≤ 1 a ≤ 5.7 GeV.

The running coupling of 8 flavors and 3 colors

“…The application of the gradient flow is not by any means limited to running coupling studies, applications also include scale setting in QCD [33][34][35][36], thermodynamics [37], renormalized energy momentum tensor [38][39][40], various aspects of chiral symmetry [41][42][43] and scalar glueballs [44].…”

Multilevel algorithm for flow observables in gauge theories

“…On a related note, we also point out that it has been suggested to extract the masses of glueballs from the large distance behavior of two-point functions of the smoothed topological charge and energy density [8]. For this approach to work, it is highly beneficial to have a precise determination of the tail of the correlator at large distances.…”

Physical observables from boundary artifacts: scalar glueball in Yang-Mills theory

“…An observable which we have extensively studied in our previous work [14] is the time slice energy density E(x 0 ) which was used as an interpolating operator to calculate the scalar glueball mass. We adopt a symmetric definition of the time slice energy density as…”

“…with t and T being respectively the Wilson flow time and the temporal extent of the lattice, defines a reference flow time t 0 which provides a reference scale to extract physical quantities from lattice calculations. The effectiveness of the Wilson flow in the extraction of topological susceptibility [13], glueball mass [14] and topological charge density correlator [15] has been demonstrated recently. In fig.…”