Breit-Wigner distribution

The Breit-Wigner distribution ( according to Gregory Breit and Eugene Wigner ) is a continuous probability distribution with probability density

Γ is the full width of the curve at half maximum height ( FWHM), M is the value of the abscissa of the maximum of E.

The Breit-Wigner distribution is sometimes referred to as the Lorentz - curve or Cauchy distribution (in particular of mathematical probability theory).

Physical meaning

The distribution has physical significance in the description of resonance curves, for example, in nuclear physics, particle physics and for the driven harmonic oscillator.

In particle physics, the relativistic Breit-Wigner formula is often used for the energy spectra of short-lived particles used particularly

Example: Z0 boson

Especially for the decay of the Z0 boson, the Breit-Wigner formula is to

Here, the partial width of the input channel is ( partial width for the decay Z0 -> e e-), the partial width of the outlet channel, the energy in the center of mass system and the sum of the partial widths for all possible decays into fermion - antifermion pairs.

For example, the resonance curve of an oscillator

The resonance curve can be described by the Lorentz - curve or Cauchy distribution:

Here, the resonance frequency and the parameter describing the quality of the curve. The maximum is reached and in weight.

For the special case of the integral is detachable and has the real interval the value 1:

The ratio Q is called the quality of the oscillator and s can be expressed in function of the parameter

It is the geometric mean of the upper and lower limiting frequency. The cut-off frequencies or are those frequencies at which the quantity (eg voltage) at the times the value of the maximum value decline. The cut-off frequencies can be expressed in function of the parameter s as follows:

The bandwidth is the difference between the cut-off frequencies. The s parameter can be expressed as a function of Q as follows: