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| Breit–Wigner distribution | |
|---|---|
| Name | Breit–Wigner distribution |
| Caption | Resonance curve illustration |
| Field | Particle physics, Nuclear physics, Spectroscopy |
| Introduced | 1936 |
| Named after | Gregory Breit; Eugene Wigner |
Breit–Wigner distribution The Breit–Wigner distribution is a probability amplitude model used to describe resonant scattering and decays in particle and nuclear processes, originating in mid‑20th century studies by Gregory Breit and Eugene Wigner. It provides a Lorentzian line shape underpinning analyses at facilities such as CERN, Fermilab, SLAC National Accelerator Laboratory, and in experiments by collaborations like ATLAS experiment, CMS experiment, LHCb experiment, and Belle experiment. The distribution is central to interpretation of resonances observed in detectors including those at Large Hadron Collider, Tevatron, KEK, and Brookhaven National Laboratory.
The Breit–Wigner form models resonant enhancements in cross sections measured in scattering experiments performed at institutions such as DESY, Stanford Linear Accelerator Center, Lawrence Berkeley National Laboratory, Argonne National Laboratory, and Los Alamos National Laboratory; its use spans analyses by collaborations including BaBar experiment, CLEO experiment, CDF experiment, D0 experiment, and KLOE experiment. It is compared and contrasted with lineshapes used in spectroscopy at facilities like National Institute of Standards and Technology and in astrophysical spectrometers aboard missions such as Hubble Space Telescope and James Webb Space Telescope. The Breit–Wigner shape connects theoretical frameworks developed in works by Enrico Fermi, Werner Heisenberg, Paul Dirac, Wolfgang Pauli, and Lev Landau.
In its simplest form the distribution for a resonance of mass m0 and width Γ is expressed as a Lorentzian amplitude proportional to 1/((E − m0)^2 + (Γ/2)^2), a formula appearing in derivations by Niels Bohr, John von Neumann, Richard Feynman, and Julian Schwinger. Quantum field theoretic derivations employ propagators and complex poles studied by Paul Dirac, Sin-Itiro Tomonaga, Freeman Dyson, and Gerard 't Hooft, while scattering theory treatments invoke S‑matrix methods pioneered by Eugene Wigner, Hendrik Anthony Kramers, Lev Landau, and Wolfgang Pauli. The relativistic Breit–Wigner introduces energy‑dependent widths and phase space factors used in analyses by Murray Gell‑Mann, Ken Wilson, Yoichiro Nambu, and Shuji Sakai.
Physically, the width Γ relates to resonance lifetime via the uncertainty principle originally formulated by Werner Heisenberg, with operational measurements conducted at accelerators including Large Electron–Positron Collider, Relativistic Heavy Ion Collider, Spallation Neutron Source, and detectors developed by teams at Max Planck Society, Rutherford Appleton Laboratory, CERN NA48, and JINR Dubna. Applications encompass determination of resonance parameters for hadrons such as studies of the Delta baryon, J/ψ particle, Υ meson, Z boson, and W boson in experiments by ALEPH experiment, DELPHI experiment, L3 experiment, and OPAL experiment. In nuclear physics the line shape models resonances observed in reactions studied by Hans Bethe, Lise Meitner, Otto Hahn, and Maria Goeppert Mayer.
Generalizations include the relativistic Breit–Wigner, the Flatté parametrization used for overlapping thresholds introduced in analyses by Stanley Flatté, and extensions incorporating Blatt‑Weisskopf barrier factors used in amplitude analyses by experimental collaborations such as BESIII, NA62 experiment, and COMPASS experiment. Related distributions include the Lorentzian, Voigt profile applied in studies at European Southern Observatory, and Fano resonance profiles described by Ugo Fano and used in atomic, molecular, and condensed matter experiments at institutions like MIT, Caltech, Harvard University, and University of Cambridge. Connections to complex analysis and pole theory draw on mathematics from Bernhard Riemann, Augustin-Louis Cauchy, Sofia Kovalevskaya, and David Hilbert.
Fitting Breit–Wigner–type models to experimental spectra employs maximum likelihood methods developed in statistics influenced by Ronald Fisher, Jerzy Neyman, Egon Pearson, and computational techniques using software frameworks from ROOT (software), GEANT4, MadGraph, and analysis tools created at SLAC National Accelerator Laboratory and CERN. Systematic treatments use covariance estimation and bootstrapping ideas inspired by work at Princeton University, Columbia University, Yale University, and University of Chicago; advanced fits incorporate interference with background models motivated by studies at Brookhaven National Laboratory and Lawrence Livermore National Laboratory. Bayesian approaches leveraging Markov chain Monte Carlo trace back to methods by Thomas Bayes, Pierre-Simon Laplace, Alan Turing, and modern implementations by groups at University of Oxford and University of Edinburgh.
The distribution was introduced in papers by Gregory Breit and Eugene Wigner and was immediately applied to resonant scattering problems investigated by Enrico Fermi and Hans Bethe in nuclear and particle physics contexts at laboratories including CERN, Brookhaven National Laboratory, SLAC National Accelerator Laboratory, and Lawrence Berkeley National Laboratory. Notable uses include extraction of the Z boson width in measurements by the LEP collaborations ALEPH experiment, DELPHI experiment, L3 experiment, OPAL experiment and characterization of quarkonium states by the CLEO experiment, BaBar experiment, Belle experiment, and LHCb experiment. The formalism remains foundational in contemporary resonance studies at Large Hadron Collider experiments such as ATLAS experiment and CMS experiment as well as in nuclear structure measurements at TRIUMF and GANIL.