Mixing with Semileptonic Events

I'm using RooFitTools to write a macro for fitting the oscillation frequency of B0-B0bar. This is an outline of what the macro uses and produces.

Macro inputs - 5 input data files

File containing D*-D0 mass difference over range 0.139-0.170 GeV
File containing deltat and mixing status from signal region
File containing deltat and mixing status from sideband (0.148-0.158 GeV)
File containing deltat and mixing status from fake lepton sample
File containing deltat and mixing status from flip lepton sample

In the future these will be consolidated to a single root output file with several TTree members (signal, fake and flip)

Macro operation - The macro breaks the fitting down into several steps which pin down various quantities needed for the final fitting. The more parameters you can measure and fix before the final fitting, the better.

1) Fit for the combinatoric background. This uses a slightly modified function from RooFitTools/examples. The deltam.cc macro fits the D*-D0 difference to a single guassian for signal and D*-D0 background and yields the background fraction in the signal region.

2) Fit for time structure of combinatoric background. This uses the sideband data as an input. The background is modeled as:

A B lifetime component with and without mixing. B0 lifetime is used for this pdf.
A B lifetime component with no mixing. Charged B lifetime is used for this pdf.
A prompt component - zero lifetime.

These components are added together and convoluted with a double guassian resolution function. The final pdf is my generic "sideband" pdf. The choice for the resolution function is still open, another possibility is a G*(1 + E).

Currently, during the fit, all resolution function parameters are allowed to float and the fitted values are saved for the final fit. The mistag rate and oscillation frequency for the background are also allowed to float and saved for the final fit.

3) Continue this procedure for the other samples. The same generic sideband pdf is used to fit for parameters in the fake lepton and flip lepton samples. The same set of parameters are allowed to float and are individually saved for later. This means that each sample for each tagging category will have its own set of resolution parameters, mistag rate and background oscillation frequency.

4) The ccbar background is modeled as having only a prompt component. This is reasonable to do since one c quark will hadronize to a D* while the other will probably provide the >1.2 GeV lepton candidate. Because of vertexing constraints, the D*l vertex can't be very far from the Y4S decay, thus it appears to have ~zero lifetime.

5) Some quantities must be measured ahead of time.

Lepton fake rates from Electron and Muon ID groups
CCbar fraction, measured from offpeak data and scaled up by luminosity.
Fraction of B0 to B+ in signal region, from MC. This is used in the generic sideband pdf to fix the relative amounts of B0-like vs ChargedB-like backgrounds.
Flip lepton fraction, measured in data and probably corrected with a scale factor from MC

The lepton fake rate, CCbar and Flip lepton fractions are multiplied by (1-comb. fraction) since the combinatoric fit has already subtracted some of these contributions away.

6) Add the background and signal pdfs and do final fit. At this time, all the background parameters have been measured and fixed. The only free parameter in the final fit are dm, mistag rate and resolution parameters for the signal pdf.

Current performance. I haven't had much time to cross check many things, the first thing I did was run the macro over signal MC from Osaka. The fitted value of dm was .463 ps-1 +/- .040 ps-1. The MC value for dm from DECAY.DEC is .464 ps-1. This is a nice first check, I need to verify that the mistag rates and resolution parameters come out with reasonable values next.

Future improvements. I am still adding in some features from David Kirkby's newest tag for RooFitTools which addresses some problems associated with the background pdf's and mixing status. I also plan to make the macro more modular and add it to the package RooFitMacros. Work also needs to be done on seeing if we really need different resolution, mistag rates for each background in each tagging category.