Statistical equations and methods applied to the precision muon (g - 2) experiment at BNL

G. W. Bennett, B. Bousquet, H. N. Brown, G. Bunce, R. M. Carey, P. Cushman, G. T. Danby, P. T. Debevec, M. Deile, H. Deng, W. Deninger, S. K. Dhawan, V. P. Druzhinin, L. Duong, E. Efstathiadis, F. J.M. Farley, G. V. Fedotovich, S. Giron, F. Gray, D. GrigorievM. Grosse-Perdekamp, A. Grossmann, M. Hare, D. W. Hertzog, X. Huang, V. W. Hughes, M. Iwasaki, K. Jungmann, D. Kawall, M. Kawamura, B. I. Khazin, J. Kindem, F. Krienen, I. Kronkvist, A. Lam, R. Larsen, Y. Y. Lee, I. B. Logashenko, R. McNabb, W. Meng, J. Mi, J. P. Miller, W. M. Morse, D. Nikas, C. J.G. Onderwater, Yu F. Orlov, C. Ozben, J. Paley, Q. Peng, C. Polly, J. Pretz, R. Prigl, G. zu Putlitz, T. Qian, S. I. Redin*, O. Rind, B. L. Roberts, N. M. Ryskulov, S. Sedykh, Y. K. Semertzidis, P. Shagin, Yu M. Shatunov, E. P. Sichtermann, E. P. Solodov, M. Sossong, A. Steinmetz, L. Sulak, C. Timmermans, A. Trofimov, D. Urner, P. von Walter, D. Warburton, D. Winn, A. Yamamoto, D. Zimmerman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In the muon (g - 2) experiment at Brookhaven National Laboratory, the spin precession frequency ωa is obtained from a standard χ2 minimization fit applied to the time distribution of decay electrons. The unusually high accuracy (∼ 0.5 ppm) of the experiment puts stringent requirements on the quality of the fit and the level of understanding of the statistical properties of the fitted parameters. We discuss the properties of the fits and their implications on the derived value for ωa, including estimates of the effect of an imperfect fit function, methods of including additional external information to reduce the error, the effects of splitting the data into many smaller subsets of data, applying different weighting methods to the data using energy information, and various tests of data suitability.

Original languageEnglish
Pages (from-to)1096-1116
Number of pages21
JournalNuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
Issue number3
Publication statusPublished - 11 Sept 2007
Externally publishedYes


This work is partially supported by the Russian Foundation for Basic Research, Grants 06-02-16156, 06-02-16445 and the U.S. National Science Foundation.

FundersFunder number
National Science Foundation
Russian Foundation for Basic Research06-02-16445, 06-02-16156


    • Bias of fit parameters
    • Correlations
    • Set-subset variance
    • Statistical errors
    • Systematic errors
    • χ minimization fit


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