# ARGUS distribution

This article relies largely or entirely on a single source. (March 2011) |

Probability density function c = 1. | |

Cumulative distribution function c = 1. | |

Parameters | cut-off (real) curvature (real) |
---|---|

Support | |

see text | |

CDF | see text |

Mean | where I_{1} is the Modified Bessel function of the first kind of order 1, and is given in the text. |

Mode | |

Variance |

In physics, the **ARGUS distribution**, named after the particle physics experiment ARGUS,^{[1]} is the probability distribution of the reconstructed invariant mass of a decayed particle candidate^{[clarification needed]} in continuum background^{[clarification needed]}.

## Contents

## Definition[edit]

The probability density function (pdf) of the ARGUS distribution is:

for . Here and are parameters of the distribution and

where and are the cumulative distribution and probability density functions of the standard normal distribution, respectively.

## Cumulative distribution function[edit]

The cumulative distribution function (cdf) of the ARGUS distribution is

- .

## Parameter estimation[edit]

Parameter *c* is assumed to be known (the kinematic limit of the invariant mass distribution), whereas *χ* can be estimated from the sample *X*_{1}, …, *X*_{n} using the maximum likelihood approach. The estimator is a function of sample second moment, and is given as a solution to the non-linear equation

- .

The solution exists and is unique, provided that the right-hand side is greater than 0.4; the resulting estimator is consistent and asymptotically normal.

## Generalized ARGUS distribution[edit]

Sometimes a more general form is used to describe a more peaking-like distribution:

where Γ(·) is the gamma function, and Γ(·,·) is the upper incomplete gamma function.

Here parameters *c*, χ, *p* represent the cutoff, curvature, and power respectively.

The mode is:

*p* = 0.5 gives a regular ARGUS, listed above.

## References[edit]

**^**Albrecht, H. (1990). "Search for hadronic b→u decays".*Physics Letters B*.**241**(2): 278–282. Bibcode:1990PhLB..241..278A. doi:10.1016/0370-2693(90)91293-K. (More formally by the ARGUS Collaboration, H. Albrecht et al.) In this paper, the function has been defined with parameter*c*representing the beam energy and parameter*p*set to 0.5. The normalization and the parameter χ have been obtained from data.

## Further reading[edit]

- Albrecht, H. (1994). "Measurement of the polarization in the decay B → J/ψK*".
*Physics Letters B*.**340**(3): 217–220. Bibcode:1994PhLB..340..217A. doi:10.1016/0370-2693(94)01302-0. - Pedlar, T.; Cronin-Hennessy, D.; Hietala, J.; Dobbs, S.; Metreveli, Z.; Seth, K.; Tomaradze, A.; Xiao, T.; Martin, L. (2011). "Observation of the h
_{c}(1P) Using e^{+}e^{−}Collisions above the DD Threshold".*Physical Review Letters*.**107**(4): 041803. arXiv:1104.2025. Bibcode:2011PhRvL.107d1803P. doi:10.1103/PhysRevLett.107.041803. PMID 21866994. - Lees, J. P.; Poireau, V.; Prencipe, E.; Tisserand, V.; Garra Tico, J.; Grauges, E.; Martinelli, M.; Palano, A.; Pappagallo, M.; Eigen, G.; Stugu, B.; Sun, L.; Battaglia, M.; Brown, D. N.; Hooberman, B.; Kerth, L. T.; Kolomensky, Y. G.; Lynch, G.; Osipenkov, I. L.; Tanabe, T.; Hawkes, C. M.; Soni, N.; Watson, A. T.; Koch, H.; Schroeder, T.; Asgeirsson, D. J.; Hearty, C.; Mattison, T. S.; McKenna, J. A.; Barrett, M. (2010). "Search for Charged Lepton Flavor Violation in Narrow Υ Decays".
*Physical Review Letters*.**104**(15): 151802. arXiv:1001.1883. Bibcode:2010PhRvL.104o1802L. doi:10.1103/PhysRevLett.104.151802. PMID 20481982.