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

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

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>0.99995 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

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

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).

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

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

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-

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.

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

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

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

Time distribution for Bd→π+π-

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-:

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

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

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.

Thanks

Bias in pulls using just statistical uncertainties

Example Asymmetry fits