ARGUS distribution

ARGUS

Probability density function No image available
Cumulative distribution function No image available
Parameters	c > 0 cut-off (real) χ > 0 curvature (real)
Support
PDF	see text
CDF	see text
Mean	where I1 is the Modified Bessel function of the first kind of order 1, and Ψ(x) is given in the text.
Mode
Variance

This article relies largely or entirely upon a single source. Please help improve this article by introducing citations to additional sources. Discussion about the problems with the sole source used may be found on the talk page. (March 2011)

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

Definition

The probability density function of the ARGUS distribution is:

for 0 ≤ x < c. Here χ, and c are parameters of the distribution and

and Φ(·), ϕ(·) are the cumulative distribution and probability density functions of the standard normal distribution, respectively.

Cumulative distribution function

The cdf of the ARGUS distribution is

Parameter estimation

Parameter c is assumed to be known (the speed of light), whereas χ can be estimated from the sample X₁, …, 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

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.

mode =

p = 0.5 gives a regular ARGUS, listed above.

References

1. ^ Albrecht, H. (1990). "Search for hadronic b→u decays". Physics Letters B 241 (2): 278–282. doi:10.1016/0370-2693(90)91293-K.  edit (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

Please expand this article. Some suggested sources are given below. More information might be found in a section of the talk page. (February 2012)

• Albrecht, H. (1994). "Measurement of the polarization in the decay B → J/ψK*". Physics Letters B 340 (3): 217–220. doi:10.1016/0370-2693(94)01302-0.  edit
• Pedlar, T.; Cronin-Hennessy, D.; Hietala, J.; Dobbs, S.; Metreveli, Z.; Seth, K.; Tomaradze, A.; Xiao, T. et al (2011). "Observation of the h_{c}(1P) Using e^{+}e^{-} Collisions above the DD[over ¯] Threshold". Physical Review Letters 107 (4). doi:10.1103/PhysRevLett.107.041803.  edit
• Lees, J. P.; Poireau, V.; Prencipe, E.; Tisserand, V.; Garra Tico, J.; Grauges, E.; Martinelli, M.; Palano, A. et al (2010). "Search for Charged Lepton Flavor Violation in Narrow Υ Decays". Physical Review Letters 104 (15). doi:10.1103/PhysRevLett.104.151802.  edit

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