One-Loop Renormalization of Lee-Wick Gauge Theory

TL;DR

This paper analyzes the one-loop renormalization of Lee-Wick gauge theory, revealing how the vector boson mass and coupling constants evolve, and compares its behavior to ordinary gauge theories, with implications for unification.

Contribution

It provides the first detailed one-loop renormalization analysis of Lee-Wick gauge theory, including the relationship between mass running and coupling evolution, and extends results to theories with dimension six operators.

Findings

The vector boson mass logarithmically runs with the coupling.

In asymptotically free cases, the vector boson mass diverges in the UV.

Lee-Wick gauge theory exhibits faster coupling running than ordinary gauge theory.

Abstract

We examine the renormalization of Lee-Wick gauge theory to one loop order. We show that only knowledge of the wavefunction renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theory than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.