## **D->hh Mass and Time Fitting**

The intention of this analysis is to measure the average lifetime of the D0 in the channels D0->Kπ and D0->KK in order to measure y_CP. The first step in this is to determinte the relative fractions of signal and backgrounds; this done using a standard unbinned maximum likelihood fit to the mass distribution in G-Fact. The fitted signal fractions then feed into the second step: the lifetime fit. This uses the method of fitting with an unparameterised time of flight PDF for the combinatorial background, which was developed by Maro Gersabeck, and is described in detail in chapter 4 of his thesis.

## **Toy Studies**

Using create_toy_data_D2hh.py 1000 datasets of 10K candidates were generated. Currently only the signal and one background class are generated, with 80% of candidates produced as signal. The PDFs used for the generation are:

- Signal:
- Mass: A Gaussian with mean 1864.84 MeV and sigma 8.5 MeV
- Time of flight: An exponential with mean 0.4101 ps convoluted with a Gaussian with mean 0 and sigma 40 fs for the proper time resolution

- Background:
- Mass: A linear distribution with minimum 1815 MeV, maximum 1915 MeV and gradient -6.67924e-05 /MeV
- Time of flight: Same as for signal, but with a mean of 1 ps for the exponential

The acceptance functions for the time of flight distributions are taken to be equal to 1 for all times just now.

### Results of the mass fit:

The width of the fitted signal fractions and the mean of the errors on them agree, and the pull distribution has mean consistent with 0 and width consistent with 1, so one can conclude that the fit is unbiased.

### Results of the time fit:

Again the sigma of the fitted lifetimes and the mean of their errors agree, and the pull plot has mean consistent with 0 and sigma consistent with 1, so the fit is unbiased.

## Next Steps

- Run on data with the unbiased fitter for the region t > 1.1 ps
- Add acceptance function to the toy data and test the fitter again
- Obtain the acceptance function for the offline selection and implement this in the fit

-- MichaelAlexander - 2010-08-12