Crystal Ball function

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Examples of the Crystal Ball function. CrystalBallFunction.svg
Examples of the Crystal Ball function.

The Crystal Ball function, named after the Crystal Ball Collaboration (hence the capitalized initial letters), is a probability density function (PDF) commonly used to model various lossy processes in high-energy physics such as Bremsstrahlung by electrons. It consists of a Gaussian core portion and a power-law low-end tail, below a certain threshold. The function itself and its first derivative are both continuous.

The Crystal Ball function is given by:

where

,
,
,
,
,

with the error function erf.

The parameters of the function (that are usually determined by a fit) are: