Quark, Gluon and Ghost Anomalous Dimensions at O(1/N_f) in Quantum Chromodynamics

TL;DR

This paper calculates the critical exponents for quark, gluon, and ghost anomalous dimensions in QCD at leading order in large N_f, confirming known three-loop results and providing new all-order insights.

Contribution

It derives the critical exponents for key QCD anomalous dimensions at O(1/N_f), offering new all-order information beyond three loops.

Findings

Agreement with known three-loop structure

Provides new all-order information on anomalous dimensions

Calculates exponents at the non-trivial fixed point in QCD

Abstract

By considering the scaling behaviour of various Feynman graphs at leading order in large $\Nf$ at the non-trivial fixed point of the $d$-dimensional $\beta$-function of QCD we deduce the critical exponents corresponding to the quark, gluon and ghost anomalous dimensions as well as the anomalous dimensions of the quark-quark-gluon and ghost-ghost-gluon vertices in the Landau gauge. As the exponents encode all orders information on the perturbation series of the corresponding renormalization group functions we find agreement with the known three loop structure and, moreover, we provide new information at all subsequent orders.