From Operator Product Expansion to Anomalous Dimensions
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| Format: | Preprint |
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2024
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| _version_ | 1866909603255549952 |
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| author | Huang, Rijun Jin, Qingjun Li, Yi |
| author_facet | Huang, Rijun Jin, Qingjun Li, Yi |
| contents | We propose a new method for computing the renormalization functions, which is based on the ideas of operator product expansion and large momentum expansion. In this method, the renormalization $Z$-factors are determined by the ultraviolet finiteness of Wilson coefficients in the dimensional regularization scheme. The ultraviolet divergence is extracted solely from two-point integrals at the large momentum limit. We develop this method in scalar field theories and establish a general framework for computing anomalous dimensions of fields, mass, couplings and composite operators. In particular, it is applied to the 6-dimensional cubic scalar theory and the 4-dimensional quartic scalar theory. We demonstrate this method by computing the anomalous dimension of the $ϕ^Q$ operator in cubic theory up to four loops for arbitrary $Q$, which is in agreement with the known result in the large $N$ limit. The idea of computing anomalous dimensions from the operator production expansion is general and can be extended beyond scalar theories. This is demonstrated through examples of the Gross-Neveu-Yukawa model with generic operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_03283 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From Operator Product Expansion to Anomalous Dimensions Huang, Rijun Jin, Qingjun Li, Yi High Energy Physics - Theory We propose a new method for computing the renormalization functions, which is based on the ideas of operator product expansion and large momentum expansion. In this method, the renormalization $Z$-factors are determined by the ultraviolet finiteness of Wilson coefficients in the dimensional regularization scheme. The ultraviolet divergence is extracted solely from two-point integrals at the large momentum limit. We develop this method in scalar field theories and establish a general framework for computing anomalous dimensions of fields, mass, couplings and composite operators. In particular, it is applied to the 6-dimensional cubic scalar theory and the 4-dimensional quartic scalar theory. We demonstrate this method by computing the anomalous dimension of the $ϕ^Q$ operator in cubic theory up to four loops for arbitrary $Q$, which is in agreement with the known result in the large $N$ limit. The idea of computing anomalous dimensions from the operator production expansion is general and can be extended beyond scalar theories. This is demonstrated through examples of the Gross-Neveu-Yukawa model with generic operators. |
| title | From Operator Product Expansion to Anomalous Dimensions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.03283 |