Results for muon channel - Update

Fit with Poisson Likelihood

• r_bb = 1.013 ± 0.027
• r_cc = 0.81 ± 0.33
• r_gg = 0.98 ± 0.32

With the likelihood method contributions from a finite Monte Carlo sample are not considered.

Generating pseudo-experiments of the data assuming the data is poisson distributed yields pull distributions of gaussian shape with mean O(10^-2) and rms ~1.

Fit with Chi2

• r_bb = 1.012 ± 0.033
• r_cc = 0.84 ± 0.41
• r_gg = 0.95 ± 0.39

In this case, statistical fluctuations arising from the finite MC sample are taken into account. The poisson to gaussian approximation is only valid if the number of events in the bin is larger than 5.  We then considered in the fit only bins with at least 7 entries in the data.

To check that this method is valid and consistent with the likelihood method, pseudo-experiments of the data and the MC were generated and the pull distributions of the fit parameters were calculated considering that the "true" value of the parameters are the ones obtained in the likelihood.

The mean (rms) of the pull distributions are 1.0 (-0.08) , 0.99 (-0.08) and 1.0 (-0.16) for r_bb, r_cc and r_gg, respectively. Notice that r_gg is slightly biased.

In order to estimate the contribution of the finite MC sample to the error of the fit, the pull distributions of the fit parameters were obtained using pseudo-experiments generated for the MC only. The pull distributions are then gaussians with width less than one. That is the fraction of the fit error that is purely due to the MC statistical fluctuations. We obtained widths of 0.6 for the three parameters. Splitting the error contributions from the data and from the MC we obtained:

• r_bb = 1.012 ± 0.027 (data) ± 0.020 (MC)
• r_cc = 0.84 ± 0.34 (data) ± 0.25 (MC)
• r_gg = 0.95 ± 0.31 (data) ± 0.23 (MC)