`scipy.stats._continuous_distns:rel_breitwigner_gen`

source: /scipy/stats/_continuous_distns.py :12388

Signature

   class     rel_breitwigner_gen (    momtype    =  1   ,    a    =  None   ,    b    =  None   ,    xtol    =  1e-14   ,    badvalue    =  None   ,    name    =  None   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

A relativistic Breit-Wigner random variable.

Extended Summary

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Notes

The probability density function for rel_breitwigner is

f (x, ρ) = \frac{k}{( x ^{2} - ρ ^{2} ) ^{2} + ρ ^{2}}

where

k = \frac{2 2 ρ ^{2} ρ ^{2} + 1}{π ρ ^{2} + ρ ρ ^{2} + 1}

The relativistic Breit-Wigner distribution is used in high energy physics to model resonances ^[1]. It gives the uncertainty in the invariant mass, $M$ ^[2], of a resonance with characteristic mass $M_{0}$ and decay-width $Γ$ , where $M$ , $M_{0}$ and $Γ$ are expressed in natural units. In SciPy's parametrization, the shape parameter $ρ$ is equal to $M_{0} /Γ$ and takes values in $(0, \infty)$ .

Equivalently, the relativistic Breit-Wigner distribution is said to give the uncertainty in the center-of-mass energy $E_{cm}$ . In natural units, the speed of light $c$ is equal to 1 and the invariant mass $M$ is equal to the rest energy $M c^{2}$ . In the center-of-mass frame, the rest energy is equal to the total energy ^[3].

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$ρ = M /Γ$ and $Γ$ is the scale parameter. For example, if one seeks to model the $Z^{0}$ boson with $M_{0} \approx 91.1876 GeV$ and $Γ \approx 2.4952 GeV$ ^[4] one can set rho=91.1876/2.4952 and scale=2.4952.

To ensure a physically meaningful result when using the fit method, one should set floc=0 to fix the location parameter to 0.

Aliases

scipy.stats._continuous_distns.rel_breitwigner_gen