scipy.stats._continuous_distns:rel_breitwigner_gen

Notes

The probability density function for rel_breitwigner is

where

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 $\Gamma$, where $M$, $M_0$ and $\Gamma$ are expressed in natural units. In SciPy's parametrization, the shape parameter $\rho$ is equal to $M_0/\Gamma$ and takes values in $(0,\infty )$.

Equivalently, the relativistic Breit-Wigner distribution is said to give the uncertainty in the center-of-mass energy $E_{\text{cm}}$. 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].

%(after_notes)s

$\rho =M/\Gamma$ and $\Gamma$ is the scale parameter. For example, if one seeks to model the $Z^0$ boson with $M_0\approx 91.1876\text{ GeV}$ and $\Gamma \approx 2.4952\text{ GeV}$ ^[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.