On the Gauge Invariance of the Z-Boson Mass

TL;DR

This paper examines different definitions of the Z boson mass, demonstrating that some schemes lead to gauge-dependent results while others maintain gauge invariance, clarifying conceptual issues in electroweak theory.

Contribution

It compares various mass schemes for the Z boson, showing that the pole position in the complex plane yields gauge-independent parameters, unlike the real-part scheme.

Findings

Pole scheme in the complex plane is gauge independent.

Real-part scheme results in gauge-dependent mass and width.

Gauge dependence does not violate gauge invariance of the amplitude.

Abstract

The different schemes for the definition of the Z boson mass are analyzed. It is shown that the scheme, defining the mass as pole of the real part of the Z boson propagator and the width as the imaginary part of the propagator at the same point results in the gauge dependent results for these parameters in a two-loop approximation. On the other hand, the scheme, where the mass and width are related to the position of the pole of the propagator in the complex plane leads to the gauge independent result. It is argued that the gauge dependence of mass and width does not contradicts to the gauge invariance of the amplitude.