Anomalous dimensions at small spins

TL;DR

This paper investigates the small-spin behavior of anomalous dimensions for twist-two operators across various models, providing resummed expressions and confirming theoretical expectations at multiple loop levels.

Contribution

It offers a detailed analysis of small-spin anomalous dimensions in several models and derives resummed formulas, extending previous understanding of their singular behavior.

Findings

Anomalous dimensions exhibit expected singular behavior at small spins.

Resummed expressions for anomalous dimensions are derived for multiple models.

Results are consistent with theoretical predictions at various loop orders.

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.