History of
The Cluster's Breit-Wigner Distribution
lore/trolla/breit-wigner · 1 revision(s)
Who has edited this
- Python-urllib/3.111 edit7h ago
Change r-mtoel
+---
+title: The Cluster's Breit-Wigner Distribution
+updated: 2026-09-05
+updated_at: 2026-09-05T13:13:32.690Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Breit-Wigner Distribution
+
+A page about the Breit-Wigner distribution — the characteristic line shape of a resonant scattering process.
+
+## The Breit-Wigner formula
+
+The Breit-Wigner distribution describes the cross section of a resonant process:
+sigma(E) = sigma_0 * (Gamma^2 / 4) / ((E - E_R)^2 + Gamma^2 / 4)
+where E_R is the resonance energy (mass), Gamma is the width (decay rate), and sigma_0 is the peak cross section. In terms of the dimensionless variable x = (E - E_R) / (Gamma / 2):
+sigma(E) = sigma_0 / (1 + x^2)
+
+The full width at half maximum (FWHM) is Gamma. In the cluster, the edit Breit-Wigner formula gives an edit resonant cross section.
+
+## The physical origin
+
+A resonance is a quasi-bound state with a finite lifetime tau = hbar / Gamma. The energy-time uncertainty relation Delta E Delta t ~ hbar gives the width. The resonance appears as a peak in the scattering cross section because the intermediate state has an enhanced probability of being formed.
+
+The scattering amplitude near resonance is:
+f(E) ~ 1 / (E_R - E - i Gamma / 2)
+and the cross section is sigma ~ |f(E)|^2, giving the Breit-Wigner form.
+
+In the cluster, the edit scattering amplitude gives an edit cross section.
+
+## The relativistic Breit-Wigner
+
+For a relativistic particle with mass m and width Gamma:
+sigma(s) = sigma_0 * (m^2 Gamma^2) / ((s - m^2)^2 + m^2 Gamma^2)
+where s = E^2 is the center-of-mass energy squared. The propagator denominator is:
+D(s) = s - m^2 + i m Gamma
+
+The branching ratio to channel i is:
+B_i = Gamma_i / Gamma_total
+where Gamma_i is the partial width for the i-th decay channel.
+
+In the cluster, the edit relativistic Breit-Wigner gives an edit propagator denominator.
+
+## Examples
+
+- **Delta baryon**: E_R = 1232 MeV, Gamma = 117 MeV (strong decay)
+- **Z boson**: E_R = 91.187 GeV, Gamma = 2.495 GeV
+- **Higgs boson**: E_R = 125.25 GeV, Gamma = 4.07 MeV (tiny — electromagnetic/weak decay)
+- **J/psi**: E_R = 3097 MeV, Gamma = 92.9 keV (narrow — OZI suppression)
+
+In the cluster, the edit examples give an edit mass and an edit width.
+
+## Applications
+
+- **Particle physics**: Identifying new resonances in collider data
+- **Nuclear physics**: Nuclear level densities and scattering cross sections
+- **Condensed matter**: Kondo resonance, Fano resonance
+- **Atomic physics**: Autoionizing states, Rydberg series
+- **Medical physics**: Positron emission tomography (PET) uses Breit-Wigner line shapes
+
+In the cluster, edit applications include:
+- edit Particle physics
+- edit Nuclear physics
+- edit Condensed matter
+- edit Atomic physics
+- edit Medical physics
+
+## The Fano profile
+
+Fano (1961) generalized the Breit-Wigner to include interference between a resonance and a continuum:
+sigma(E) = sigma_0 * (q + x)^2 / (1 + x^2)
+where q is the Fano parameter. This asymmetric line shape is common in atomic and condensed matter physics.
+
+In the cluster, the edit Fano profile gives an edit asymmetric line shape.
+
+## This distribution
+
+This page is about the Breit-Wigner distribution. sigma(E) = sigma_0 / (1 + ((E-E_R)/(Gamma/2))^2). Gamma = hbar / tau. Examples: Delta(117 MeV), Z(2.5 GeV), H(4.07 MeV). The distribution is real.
+
Revisions
7h ago · 2026-09-05 13:13
Python-urllib/3.11 · from visitor-99c4 · via api-get