A brief history of mass

Abstract It has been known since the 1950s that an unstable particle is associated with a complex pole in the propagator. This had to be rediscovered twice: in the early 1970s in the context of hadronic resonances, and in the early 1990s in the context of the Z boson. The physical mass of the particle is the real part of the pole in the complex energy plane. In hadronic physics, this replaced the “Breit–Wigner mass,” which was found to depend on the parameterization of the “energy-dependent width.” In Z physics, it replaced the “on-shell” mass, which was found to be gauge dependent. Although the mass defined from the complex pole position has been widely discussed in the literature, it has not yet made its way into quantum field theory textbooks.

Authors

Institutions

Publication Details

Journal
The European Physical Journal Plus
Published
2025-06-08
DOI
https://doi.org/10.1140/epjp/s13360-025-06450-6
Primary Topic
Particle physics theoretical and experimental studies
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

A brief history of mass

S. Willenbrock
The European Physical Journal Plus
Particle physics theoretical and experimental studies
article

A brief history of mass

S. Willenbrock
article en

Abstract

Abstract It has been known since the 1950s that an unstable particle is associated with a complex pole in the propagator. This had to be rediscovered twice: in the early 1970s in the context of hadronic resonances, and in the early 1990s in the context of the Z boson. The physical mass of the particle is the real part of the pole in the complex energy plane. In hadronic physics, this replaced the “Breit–Wigner mass,” which was found to depend on the parameterization of the “energy-dependent width.” In Z physics, it replaced the “on-shell” mass, which was found to be gauge dependent. Although the mass defined from the complex pole position has been widely discussed in the literature, it has not yet made its way into quantum field theory textbooks.

The European Physical Journal PlusVol. 140(6)
University of Illinois Urbana-Champaign (US)
Openalex Percentile: Top 94%
Particle physics theoretical and experimental studies
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.