From Operator Product Expansion to Anomalous Dimensions
Journal of High Energy Physics(2025)
Nanjing Normal University
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 ϕQ 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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Key words
Renormalization and Regularization,Renormalization Group,Scattering Amplitudes
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