## Abstract

In the muon (g - 2) experiment at Brookhaven National Laboratory, the spin precession frequency ω_{a} is obtained from a standard χ^{2} 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 ω_{a}, 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 language | English |
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Pages (from-to) | 1096-1116 |

Number of pages | 21 |

Journal | Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment |

Volume | 579 |

Issue number | 3 |

DOIs | |

Publication status | Published - 11 Sept 2007 |

Externally published | Yes |

### Funding

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.

Funders | Funder number |
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National Science Foundation | |

Russian Foundation for Basic Research | 06-02-16445, 06-02-16156 |

## Keywords

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