G-Fact Mass Fitting

Validation of signal fraction fitter (Lars)

To validate the signal fraction fitter (aka mass fitter) a series of data sets were generated with different mixes of signals and combinatoric background were generated. Each data set has approximately 1000 toy data sets with 100k events each. All data sets are located in /data/lhcb01/eklund/B2hhToyData/, in sub-directories as given below.

Event mix: Bd -> π π, Bd -> K π and combinatoric background

Directory: BdMix _561pipi_103Kpi/, 1000 data sets, 100k events each

Event mix: Bd -> π π, Bd -> K π, Bs -> K K and combinatoric background

Directory: Mix_Bd2pipiKpiNBs2KK/ , 940 data sets, 100k events each

Event mix: Bd -> π π, Bd -> K π, Bs -> K K, Bs -> K π and combinatoric background

Directory: Mix_BdNBs2pipiKpiKK/ , 860 data sets, 100k events each

Event mix: Bd -> π π, Bd -> K π, Bs -> K K, Bs -> K π, Bd -> π π π and combinatoric background

Directory: fullMFMixAug2010/ , 1000 data sets, 100k events each

Sensitivity to number of events

A series of fits to the data set Mix_Bd2pipiKpiNBs2KK (above) was done using a decreasing number of events, from 100 000 to 100 events. The initial values and fit configuration was identical to the fit described above. The results are summarised in the following graphs.

• The error from the fit as reported by MINUIT versus number of events is show in this graph. As expected, the statistical error from the fit follows well the 1/sqrt(N) law. The unit here is % signal fraction, hence 1% error means that the signal fraction Bd -> pi pi is estimated to be 24 +/- 1 %.
• The mean of the pull distribution is shown in this graph. The mean is less that 0.1 apart from the fits with the largest number of events. Since the statistical error is very small (<2*10^-3 for 100k evt) even the smallest bias is seen. At 100k event the observed absolute bias is < 4*10^-4.
• The bias in absolute numbers is shown in this graph. This is calculated as the statistical error of the fit times the mean of the pull distribution. Hence this gives the bias in absoulte units. The bias is less than 0.1 % if more than 1000 events are used, below that number a measurable bias is seen.
• The sigma of the pull distribution is seen in this graph. Seems to be pretty independent of the number of events.

Paul's study with the signal fraction fitting

Just start typing here paul....This is a link.

-- AlisonBates - 2010-08-06