1. Paul Sail, Lars Eklund and Alison Bates
Status of the Glasgow B→hh analysis CP Working group γ from loops 15th October 2010
Paul Sail, Lars Eklund and Alison Bates

2. Overview Data selection
Introduce Glasgow’s newly developed fitting package called G-Fact.
Signal fraction fit results on toy data including sensitivity study on the number of events.
Asymmetry fitter using the mass fitter signal fractions as input.
Summary and outlook

3. Data selection
Run on X pb-1 from Real Data + Reco06-Stripping10-Merged
List of selection cuts:
min(piplus_MINIPCHI2, piminus_MINIPCHI2)>30
max(piplus_MINIPCHI2, piminus_MINIPCHI2)>100
min(piplus_PT, piminus_PT)>1500
max(piplus_PT, piminus_PT)>3000
max(piplus_TRACK_CHI2NDOF,piminus_TRACK_CHI2NDOF)<4
B0_PT>2000
B0_IPCHI2_OWNPV<8 && B0_DIRA_OWNPV>
B0_FDCHI2_OWNPV>625
B0_OWNPV_CHI2/B0_OWNPV_NDOF<1.6
PID Cuts
piplus_PIDmu<5 && piminus_PIDmu<5 && piplus_PIDe<2.5 && piminus_PIDe<2.5 && piplus_PIDp<-1 && piminus_PIDp<0
piplus_PIDK<0
piminus_PIDK<0
piplus_PIDK>0
piminus_PIDK>0

4. Bd→Kπ
B→hh
Bd→K+π-
Bd→K-π+
Bd→π+π-
Bs→K+K-

5. G-Fact
Glasgow has developed a stand alone fitting package called G-Fact (Glasgow Fitter of ACp and Time) which can
Fit for the signal fraction
Then either fit for
lifetimes or
Adir,mix(B(d,s)→hh).

6. Fit for signal fractions
The signal fractions are fitted for by maximising this total likelihood to find P(class)
The signal probability used in subsequent fits is
Total likliehood
PDF for each class
Prob for each class
Mass distribution for each class
Prob. of a particular event being in each decay class
Total mass PDF

7. Signal fractions
Use a toy data sample with 1000 data sets, 100k events each data set
Decay
True s/f [%]
Initial value [%]
Mean fit value [%]
Sigma fit value [%]
Pull mean*
Pull sigma
Bd→π+π-
8.47 10
8.45
0.13
-0.13±0.03
1.02±0.02
Bd→K+π-
17.82 15
17.84
0.14
0.12±0.03
0.99±0.03
Bd→K-π+
14.58
-0.02±0.03
1.01±0.03
Bs→K+K-
0.10
0.01±0.03
1.02±0.03
Bs→K+π-
1.62 1
0.07
-0.03±0.04
0.96±0.03
Bs→K-π+
0.72
0.71
0.05
-0.32±0.03
1.01±0.02
Bd→π+π-π0
15.0
14.98
0.16
-0.11±0.03
Combinatoric
33.32 38
35.02
*the pull means are showing a slight bias but this is not a true bias, as will be discussed in the next slide

8. Sensitivity to number of events
The mean of the pull distribution for the fitted s/f seems to show a bias for large data samples
However, the bias in absolute numbers is shown below
absolute bias = pull mean * statistical error of fit
The bias in absolute numbers is less than 0.1 % if more than 1000 events are used, below that number a measurable bias is seen.
Bd→π+π-
Bd→K+π-
Bd→π+K-
Bs→K+K-

9. Sensitivity to number of events… continued
Bd→π+π-
Bd→K+π-
Bd→π+K-
Bs→K+K-
The sigma of the pull distribution seems fairly independent of the number of events.

10. Sensitivity to initial values
A study has been performed to test how sensitive the signal fraction fitter is to the initial values given to the fit. Initial values were generated randomly in the following ranges,
Bd→π+π- [0.02,0.279]
Bd→K+π- [0.125,0.428]
Bd→K-π+ [0.099,0.354]
Bs→K+K- [0.061,0.25]
Combinatoric [0.11,0.35]
Conclusions
Statistical error is independent of initial fit input values, as expected.
Mean of the pull is distributed over ±0.1 for all signal classes and initial values for #events>1000
Bias in pull mean in absolute numbers is
Less than 0.1% if #events > 1000
Less than 0.5% if #events > 100
Sigma of the pull distribution is independent of #events and initial values

11. Asymmetry fitter
Currently implemented analytical PDFs using the following expressions for the time class models

12. Asymmetry Fits Using a toy data sample which contained
Generated s/fs of 24% Bd2pipi, 20% Bd2Kpi and 21%Bs2KK events with the rest being combinatoric background. SSB = 0.65
Fit signal fractions used in asymmetry fitter obtained from the signal fraction fitter
1000 data sets with 100k events.
Generated Asymmetry
Fit input Asymmetry
Mean fitted Asymmetry
Sigma of Fitted Asymmetry
Adir(Bd→π+π-)
0.38
0.32
0.380±0.002
0.061±0.002
Amix(Bd→π+π-)
0.61
0.69
0.604±0.002
0.048±0.001
Adir(Bs→K+K-)
0.1
0.15
0.088±0.002
0.057±0.001
Amix(Bs→K+K-)
0.25
0.3
0.194±0.002
Bd asymmetries are very well fitted
Bs asymmetries are not so well fitted since there is no proper time resolution modelled in the fitted as yet and there is a Gaussian smearing in the generation

13. Time distribution for Bd→π+π-

14. Improved Bs→K+K- asymmetry fitter
Currently the Bs→K+K- asymmetry fitter has no proper time resolution modelled. We have just completed the calculation for the analytical expression for the normalised PDF
Which results in the new PDF for Bs→K+K-:

15. New Bs→K+K- PDF New PDF Old PDF
Now need to implement this new PDF in G-Fact and run the asymmetry fitter and study the improvement in the Bs asymmetries

16. Summary Selection from data looks good
Developed new fitting package, G-Fact, for B→hh decays
Signal fractions fits are good
sensitivity on number of events and initial fit parameters studied using signal fraction fitter
Asymmetry fitter well developed and tested
Lifetime fitter exists and has been extensively tested in charm area but soon will be developed in B→hh

17. Outlook Signal fraction fitter Asymmetry fitter Lifetime fitter
Verify on MC
Run on real data
Need to study current PID PDFs which are currently extracted from MC
Need to compare mass PDFs from data and MC to extract offsets and scale factors
Implement Λb decays into background
Asymmetry fitter
Implement and test new analytical PDF for Bs decays
Re-express the 4 currently independent asymmetries in terms of d, θ and γ
Lifetime fitter
Start rigorous testing in B→hh decays.

18. Thanks

19. Bias in pulls using just statistical uncertainties

21. Example Asymmetry fits