### Abstract

We present preliminary result for the step-scaling study of the coupling constant with the Yang-Mills gradient flow, in the twelve-favour SU(3) gauge theory. In this work, the lattice simulation is performed using unimproved staggered fermions and the Wilson plaquette gauge action, from which the gradient flow is also implemented. Imposing twisted boundary condition a'la t'Hooft and Parisi, our calculation is performed at zero fermion mass. The renormalised coupling constant is extracted via the computation of the energy density. In order to examine the reliability of the continuum extrapolation, we investigate this coupling constant using two different lattice discretisations. Our result shows that in order to control the systematic effects in the continuum extrapolation, it is necessary to implement a large enough gradient-flow time. In the current calculation, the gauge-field averaging radius corresponding to the flow time has to be as large as 40% of the lattice size.

Original language | English |
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Article number | 259 |

Journal | Proceedings of Science |

Volume | Part F130500 |

DOIs | |

State | Published - 1 Jan 2014 |

Event | 32nd International Symposium on Lattice Field Theory, LATTICE 2014 - New York, United States Duration: 23 Jun 2014 → 28 Jun 2014 |

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## Cite this

*Proceedings of Science*,

*Part F130500*, [259]. https://doi.org/10.22323/1.214.0259