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ISSN - 01689002, Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2007, vol. 579, p. 1096-1116

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

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

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. © 2007 Elsevier B.V. All rights reserved.