### Abstract

Following a recent paper by Fodor et al. (arXiv:1406.0827), we reexamine several types of treelevel 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, 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. Our numerical results of the expectation value of the action density, E(t), show that two O(a^{4}) improved flows significantly eliminate the discretization corrections in the small flow time t regime. On the other hand, the values of t^{2}E(t) in the large t regime, where the lattice spacing dependence of the tree-level term dies out as inverse powers of ta^{2}, are different between the results given by two optimal flows leading to the same O(a^{4}) improvement at tree level. This may suggest that non-negligible O(g^{2}a^{4}) effect sets in the large t regime, where the running coupling g(1/√ 8t) becomes large.

Original language | English |
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Article number | 301 |

Journal | Proceedings of Science |

Volume | 14-18-July-2015 |

Publication status | Published - 2015 Jan 1 |

Event | 33rd International Symposium on Lattice Field Theory, LATTICE 2015 - Kobe, Japan Duration: 2015 Jul 14 → 2015 Jul 18 |

### ASJC Scopus subject areas

- General

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## Cite this

*Proceedings of Science*,

*14-18-July-2015*, [301].