Width and Partial Widths of Unstable Particles

TL;DR

This paper proposes a gauge-invariant definition of branching ratios and partial widths for unstable particles, aligning theoretical consistency with experimental measurements, especially for the Z^0 boson.

Contribution

It introduces a gauge-independent framework for defining partial widths and branching ratios, and validates its applicability to experimental data at the Z^0 resonance.

Findings

The new definitions satisfy additivity and gauge independence.

The approach aligns with LEP measurements at NNLO accuracy.

Using pole mass and width improves experimental-theoretical consistency.

Abstract

In the gauge theory context, a definition of branching ratios and partial widths of unstable particles is proposed that satisfies the basic principles of additivity and gauge independence. A simpler definition, similar to the conventional one, is examined in the Z^0-boson case. In order to establish contact with experiment, we show that it leads to a peak cross section that justifies the expression used by the LEP Electroweak Working Group through next-to-next-to-leading order, provided that the pole rather than the on-shell mass and width of the Z^0 boson are employed.