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arXiv · 2410.03283

From Operator Product Expansion to Anomalous Dimensions

Rijun Huang·Qingjun Jin·Yi Li
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Abstract

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 $\phi^Q$ 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.

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Rijun Huang, Qingjun Jin, Yi Li. 2024-10-04. From Operator Product Expansion to Anomalous Dimensions. https://arxiv.org/abs/2410.03283

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