Lattice gradient flow with tree-level $\mathcal{O}(a^4)$ improvement in pure Yang-Mills theory

Understand

Following a recent paper by Fodor et al.

• (arXiv:1406.0827), we reexamine several types of tree-level improvements on the flow action with various gauge actions in order to reduce the lattice discretization errors in the Yang-Mills gradient flow method.
• We propose two types of tree-level, $\mathcal{O}(a^4)$ improved lattice gradient flow including the rectangle term in both the flow and gauge action within the minimal way.
• We then perform numerical simulations with the simple plaquette gauge action for testing our proposal.