Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum Electrodynamics

TL;DR

This paper calculates the electron mass anomalous dimension in quantum electrodynamics at order 1/Nf^2, providing a gauge-independent critical exponent that aligns with known perturbative results and extends understanding in arbitrary dimensions.

Contribution

It presents a novel computation of the electron mass anomalous dimension at O(1/Nf^2) in QED across arbitrary dimensions, confirming consistency with three-loop perturbative structures.

Findings

Derived the critical exponent at O(1/Nf^2) in QED.

Confirmed consistency with three-loop perturbative results.

Determined higher-order coefficients in the coupling expansion.

Abstract

The critical exponent corresponding to the renormalization of the composite operator $\bar{\psi}\psi$ is computed in quantum electrodynamics at $O(1/\Nf^2)$ in arbitrary dimensions and covariant gauge at the non-trivial zero of the $\beta$-function in the large $\Nf$ expansion and the exponent corresponding to the anomalous dimension of the electron mass which is a gauge independent object is deduced. Expanding in powers of $\epsilon$ $=$ $2$ $-$ $d/2$ we check it is consistent with the known three loop perturbative structure and determine the subsequent coefficients in the coupling constant