2016/09/30 by Norihiko Kamata, Shoichi Sasaki
Physics and Astronomy · #hep-lat
paper · pdf · doi:10.1103/physrevd.95.054501
published as Phys. Rev. D 95, 054501 (2017) · 16 pages, 14 figures. v3: a version published in PRD
arxiv created 2017/03/12 · arxiv updated 2017/03/15
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with Fodor et al. [arXiv:1406.0827]. The tree-level O(a2) improvement can be achieved in a simple manner, where an appropriate weighted average is computed between two definitions of the action density ⟨ E(t)⟩ measured at every flow time t. We further develop the idea of achieving the tree-level O(a4) improvement. For testing our proposal, we present numerical results for ⟨ E(t) ⟩ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings (a≈ 0.1, 0.07, and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections on t2⟨ E(t)⟩ in the relatively small-t regime. To demonstrate the feasibility of our tree-level improvement proposal, we also study the scaling behavior of the dimensionless combinations of the Λ_\textrmMS parameter and the new reference scale tX, which is defined through tX2⟨ E(tX)⟩=X for the smaller X, e.g., X= 0.15. It is found that √t0.15Λ_\textrmMS shows a nearly perfect scaling behavior as a function of a2 regardless of the types of gauge action and flow, after tree-level improvement is achieved up to O(a4). Further detailed study of the scaling behavior exposes the presence of the remnant O(g2n a2) corrections, which are beyond the tree level. Although our proposal is not enough to eliminate all O(a2) effects, we show that the O(g2n a2) corrections can be well under control even by the simplest tree-level O(a2) improved flow.