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arXiv · 2506.05132

Anomalous dimensions at small spins

A. N. Manashov·S. Moch·L. A. Shumilov
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Abstract

In perturbation theory, the anomalous dimensions of twist-two operators have poles at negative or small positive integer values of spin and therefore must be resummed at these points. It was observed earlier that a certain quadratic combination of the anomalous dimensions remains finite at the right-most singularities, providing an efficient tool for resummation. In this paper, we analyze the small-spin behavior of the anomalous dimensions for all types of twist-two operators in the $O(N)$-symmetric $\varphi^4$ model at the four-loop level, in the complex $\varphi^3$ model at the three-loop level, and the Gross-Neveu-Yukawa model at the two-loop level. We find that the behavior of the anomalous dimensions at singular points is consistent with theoretical expectations, and we present expressions for the resummed anomalous dimensions.

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A. N. Manashov, S. Moch, L. A. Shumilov. 2025-06-05. Anomalous dimensions at small spins. https://doi.org/10.1007/jhep09(2025)106

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