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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.15668 |
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| _version_ | 1866914981385076736 |
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| author | Ishikawa, Ken-Ichi Okawa, Masanori Takei, Hironori |
| author_facet | Ishikawa, Ken-Ichi Okawa, Masanori Takei, Hironori |
| contents | The gradient flow scheme has emerged as a prominent nonperturbative renormalization scheme on the lattice, where flow time is introduced to define the renormalization scale. In this study we perturbatively compute the gradient flow coupling for the SU($N$) Yang-Mills theory in the large-$N$ limit in terms of the lattice bare coupling up to three-loop order. This is achieved by combining the twisted Eguchi-Kawai model with the numerical stochastic perturbation theory. We analyze the flow time dependence of the perturbative coefficients to determine the perturbative beta function coefficients, successfully computing the one-loop coefficient in the large-$N$ limit using three matrix sizes $N=289,441,529$. However, the higher-order coefficients are affected by large statistical errors. We also explore the potential for reducing these statistical errors through variance reduction combined with the large-$N$ factorization property of the SU($N$) Yang-Mills theory, and estimate the required number of samples for the precise determination of the higher-order coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perturbative gradient flow coupling of the twisted Eguchi-Kawai model with the numerical stochastic perturbation theory Ishikawa, Ken-Ichi Okawa, Masanori Takei, Hironori High Energy Physics - Lattice The gradient flow scheme has emerged as a prominent nonperturbative renormalization scheme on the lattice, where flow time is introduced to define the renormalization scale. In this study we perturbatively compute the gradient flow coupling for the SU($N$) Yang-Mills theory in the large-$N$ limit in terms of the lattice bare coupling up to three-loop order. This is achieved by combining the twisted Eguchi-Kawai model with the numerical stochastic perturbation theory. We analyze the flow time dependence of the perturbative coefficients to determine the perturbative beta function coefficients, successfully computing the one-loop coefficient in the large-$N$ limit using three matrix sizes $N=289,441,529$. However, the higher-order coefficients are affected by large statistical errors. We also explore the potential for reducing these statistical errors through variance reduction combined with the large-$N$ factorization property of the SU($N$) Yang-Mills theory, and estimate the required number of samples for the precise determination of the higher-order coefficients. |
| title | Perturbative gradient flow coupling of the twisted Eguchi-Kawai model with the numerical stochastic perturbation theory |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2410.15668 |