Open Boundary Condition, Wilson Flow and the Scalar Glueball Mass

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 $\leq$ 1/a $\leq$ 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 $\approx$ 5.7 GeV. To smoothen the gauge fields and to reduce the cut off artifacts recently proposed Wilson flow is used. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV $\leq$ 1/a $\leq$ 5.7 GeV.Comment: Replacement agrees with published versio