Crystal ball function

Dmitry A Romanov Getting energy resolution

Crystal ball function

The Crystal Ball function, named after the Crystal Ball Collaboration (hence the capitalized initial letters), is a probability density function commonly used to model various lossy processes in high-energy physics. 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

N is a normalization factor and α, n, x and σ are parameters which are fitted with the data.

Examples of the Crystal Ball function.

Red: α = 10, Green: α = 1, Blue: α = 0.1.

External links

* J. E. Gaiser, Appendix-F Charmonium Spectroscopy from Radiative Decays of the J/Psi and Psi-Prime, Ph.D. Thesis, SLAC-R-255 (1982). p. 178.

* M. J. Oreglia, A Study of the Reactions psi prime --> gamma gamma psi, Ph.D. Thesis, SLAC-R-236 (1980), Appendix D.

* T. Skwarnicki, Ph.D Thesis, DESY F31-86-02(1986), Appendix E.

Retrieved from "http://en.wikipedia.org/wiki/Crystal_Ball_function"

Crystal region

Etag > 5 GeV, r<1 cm;	Etag > 5 GeV, r<1 cm;

Resolution vs. Energy

The energy resolution as function of energy for different r (radius from HyCal module center) is obtained

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Resolution for different HyCal regions

Crystal region. r < 0.5 cm;	Crystal region.
Crystal region. Transition modules;	Glass region. Transition modules;
Glass region.	Glass region. Edge.

Energy resolution vs. coordinate

The energy resolution as function of relative position inside HyCal module

The energy resolution as function of X coordinate