This article deals with the Lorentz curve in physics, for its occurrence in stochastics see Cauchy distribution . For the Loren z curve in economics see there .
Two parameters go into the Breit-Wigner function. The parameter determines the position of the maximum , the parameter is called the width of the curve. From a physical point of view, the curve can only be interpreted for granted, since a circular frequency is usually associated with it and negative frequencies are physically nonsensical. The functional rule is:
Another form of the curve can be obtained by reparameterization by using the following set of parameters instead of parameters and :
Then
;
in particular, it applies to that the deleted and uncoated parameters become almost identical. The first form is usually preferred in particle physics , the second form in classical physics , since they result in the corresponding forms in their respective fields from physics. The relationships are used for back conversion
Contrary to some belief, neither is nor the full width at half height (FWHM) of the curve. This one is instead
and arises for only about .
For and the Lorentz curve can go through
are approximated. With the exception of a normalization factor, it is then identical to the probability density known as the Cauchy distribution in mathematical probability theory . When the Lorentz curve is mentioned, the approximated version is also sometimes meant.
Physical meaning
Classical physics
The differential equation for the damped harmonic oscillator
In particle physics, the propagators are the inverse functions of the equations of motion for the particles. These have a pole in the mass of these particles. To get around this, a so-called complex mass is introduced, which takes into account the decay width of the respective particle. Then the propagator for a certain four-pulse is proportional to
and its square is the Lorentz curve in the first parameterization:
example
Z 0 boson
The Breit-Wigner formula results
especially for the decay of the Z 0 boson
Here is
the partial width of the input channel (i.e. for the decay Z 0 → e + e - )
the partial width of the output channel
the sum of the partial widths for all possible decays into fermion - anti fermion pairs