The relativistic Breit–Wigner distribution (after the 1936 nuclear resonance formula[1] of Gregory Breit and Eugene Wigner) is a continuous probability distribution with the following probability density function,[2] where k is a constant of proportionality, equal to (This equation is written using natural units, ħ = c = 1 .)
(Here, p2 is the square of the four-momentum carried by that particle in the tree Feynman diagram involved.)
The propagator in its rest frame then is proportional to the quantum-mechanical amplitude for the decay utilized to reconstruct that resonance, The resulting probability distribution is proportional to the absolute square of the amplitude, so then the above relativistic Breit–Wigner distribution for the probability density function.
It has the standard resonance form of the Lorentz, or Cauchy distribution, but involves relativistic variables s = p 2 , here = E 2 .
is the relativistic counterpart of the similar line-broadening function [6] for the Voigt profile used in spectroscopy (see also § 7.19 of [7]).