Five-loop anomalous dimensions of $\phi^Q$ operators in a scalar theory with $O(N)$ symmetry

TL;DR

This paper calculates the five-loop anomalous dimensions of symmetric tensor operators in an $O(N)$ scalar theory, providing detailed $Q$-dependence and confirming previous large-$Q$ results through advanced unitarity methods.

Contribution

It presents the first complete five-loop computation of $Q$-dependent anomalous dimensions for $ ext{O}(N)$ scalar operators using form factors and unitarity cuts.

Findings

Anomalous dimensions match previous large-$Q$ semiclassical results.

Complete $Q$-dependence of anomalous dimensions obtained at five loops.

Method demonstrates the effectiveness of unitarity cuts in high-loop calculations.

Abstract

We compute the complete $Q$-dependence of anomalous dimensions of traceless symmetric tensor operator $\phi^Q$ in $O(N)$ scalar theory to five-loop. The renormalization factors are extracted from $\phi^Q\rightarrow Q\phi$ form factors, and the integrand of form factors are constructed with the help of unitarity cut method. The anomalous dimensions match the known results in \cite{Badel:2019oxl, Antipin:2020abu}, where the leading and subleading terms in the large $Q$ limit were obtained using a semiclassical method.