Resummation of small-spin singularities in anomalous dimensions of twist-two operators

TL;DR

The paper addresses the problem of small-spin ($s\to 0$) singularities in the anomalous dimensions of twist-2 operators and their impact on precision predictions. It develops a resummation framework grounded in conformal Regge theory, applying it to the $O(N)$-symmetric $\varphi^4$ model and to two realizations of the same critical CFT: the Gross-Neveu-Yukawa model in $\epsilon$-expansion and the Gross-Neveu model in $1/N$ expansion. Key contributions include explicit regularized resummed expressions near $s=0$ (e.g., $\gamma^*(s)=-s+\epsilon+\sqrt{(s-\epsilon)^2+\delta m_*^2(s)}$ with $\delta m_*^2(s)=2\gamma^*(s)\bigl(s-\epsilon+\tfrac{1}{2}\gamma^*(s)\bigr)$) and the demonstration that a consistent mixing of Regge trajectories and shadows removes unphysical divergences in both $s$ and the $1/N$ or $\epsilon$ expansions. The work connects perturbative QCD insights with conformal-field-theory techniques, informing higher-loop predictions and suggesting ways to integrate these ideas with BFKL and detector-operator approaches that probe the analytic structure of twist-2 data. Overall, the framework provides a principled path to extend analytic control over twist-2 anomalous dimensions beyond fixed-order perturbation theory.

Abstract

Anomalous dimensions of leading-twist operators in QCD play an important role in precision predictions for high-energy processes, since they govern the scale evolution of parton distributions. Their analytic structure as a function of spin is particularly important due to the complexity of higher-loop computations. In these proceedings, we discuss the resummation of the certain type of such singularities that share common features with those appearing in the quark flavor-nonsinglet sector of QCD. Our main focus is on the interplay between Gross-Neveu-Yukawa model in $ε$ expansion and Gross-Neveu in $1/N$ expansion. Such resummation allows one to predict the higher-loop singular behavior and reveals connections with the conformal Regge theory and recent studies of detector operators in QCD and various conformal field theories.

Figures (1)

• Figure 1: Conformal Chew-Frautschi plot for the Gross-Neveu-Yukawa model in $\epsilon$ expansion (a) and Gross-Neveu model in $1/N$ expansion (b) around point $s = 0$. In Figure the scaling dimensions of the operators \ref{['GN-operators']} and their shadow scaling dimensions in free theory are depicted.