Extract Signals by Fitting $\chi^2$ Distribution of the Kinematic Fit

Abstract

In measuring the $\psip$ radiative decays at BESII, contribution of the background is serious in most of the final states. To extract the number of signal events, a fit to the $\chi^2$ distribution of kinematic fit using signal and background components is proposed. Extensive Monte-Carlo simulations (MCS) are performed, and the results show that the shape of $\chi^2$ distribution of the signal channel looks different from those of the background channels, thus it provides us by fitting the $\chi^2$ distribution of the data to extract the number of signal events. An input-output test is performed using MCS, and the uncertainty of the fit method is found to be less than 2%.