1. 1 Approval Presentation, 17.08.11 LHCb-ANA- 2011-062

2. Motivation for Measurement The final state D s - K + is accessible by both B s and B s : 2 Both diagrams are similar in magnitude, hence large interference between them is possible. Using flavour tagging, we can measure four decay rates – B s or B s to D s + K - or D s - K + From these rates, γ can be extracted in an unambiguous and theoretically clean way. A review of the γ extraction can be found in e.g. LHCb note 2007-041.

3. Branching Ratio Strategy A reliable extraction of γ requires a considerable amount of data – Aim is to present first γ measurement from B s →D s K at Moriond 2012. First step towards measuring γ is to observe B s →D s K in our data, and measure its branching ratio (BR) relative to B s →D s π. – Most systematics cancel in the ratio – Main differences between the modes are the bachelor PID requirements and the smaller B s →D s K yield. Analysis strategy for the relative BR measurement follows that used for the hadronic f d /f s measurement from 2010 data. Independently, the hadronic and semileptonic f d /f s measurements from 2010 data can be combined to extract BR(B s →D s π). This is then used to measure BR(B s →D s K) absolutely. 3

4. Current Experimental Status: D s K PDG value is BR(B s →D s K) = (3.0 ± 0.7)*10 -4 (23% relative error) – Calculated by rescaling Belle (*) measurement: BR(B s →D s K)= (2.4 +1.2/- 1.0(stat)± 0.3(syst) ± 0.3(f s ) )*10 -4. This uses 7±3 signal events. – In addition, CDF (**) measures BR(B s →D s K)/BR(B s →D s π) = 0.097 ± 0.018 ± 0.009 with ~100 D s K candidates, using a combined mass-PID fit. 4 B s →D s π B s →D s K (**) PRL 103 191802 (*) PRL 102 021801 CDF Belle

5. Current Experimental Status: D s π BR(B s →D s π) = (3.2 ± 0.5)*10 -3 (16% relative error), from combining – Belle (*) : (3.67 ± 0.34(stat)± 0.43(syst) ± 0.49(f s ) )*10 -3 with 160 events – CDF (**) : (3.03 ± 0.21(stat)± 0.45(syst) ± 0.46(f d /f s ) )*10 -4 with 500 events 5 (*) PRL 102 021801 (**) PRL 98 061802, rescaled to new BR(B d →Dπ) CDF Belle

6. What about LHCb? Today we are requesting approval of preliminary results for BR(B s →D s K)/BR(B s →D s π), BR(B s →D s π) and BR(B s →D s K). We plan to write a paper in the very near future. Plots for approval are marked with 6 For Approval

7. Data Sample and Trigger/Stripping The analysis uses ~336pb -1 of 2011 data. Trigger requirements are – L0: Hadron TOS or Global TIS – HLT: HLT1Track and HLT2 Topo BBDT TOS (2,3 or 4 body) Stripping lines from B2DX module (with D2hhh) – No PID is used, to allow inclusive selection of all the relevant modes Relative efficiency of reconstruction, trigger and stripping is checked on MC that has been reprocessed with a 2011 TCK (0x006d0032) – Results on later slides 7

8. Offline Selection: BDTG For the 2010 f d /f s analysis, TMVA was used to check the performance of different provide classifiers as an offline selection, using kinematic and geometrical variables – Role of the MVA is to minimise combinatorics (not physics backgrounds) The best performing MVA was the Boosted Decision Tree with Gradient boosting (BDTG). 8 In the current analysis, the 2010 BDTG is retained, but optimal cut is re-evaluated – Optimal working point need not be the same, as the trigger has changed Re-optimisation for 2011 is performed using 10% of the B s →D s π data (uniformly distributed in time)

9. BDTG (Re-)Optimisation Figure of merit is 9 Here, B refers to combinatoric bkg only, and 1/14 is the expected Cabibbo suppression factor between B s →D s π and B s →D s K. Choose start of significance plateau (BDTG>0.1) as our working point. This cut loses 6% of signal, for a background reduction of 45%.

10. PID Calibration Correctly calibrating the PID cut efficiencies is crucial for this analysis. Extensive use is made of the tools developed by the RICH group. The D* (for K and π) and Λ (for proton) calibration samples are binned in momentum and p T, and the resulting efficiency map is used to weight signal events. 10 Magnet Up and Magnet Down data are calibrated separately – PID performance is not constant in time, as RICH calibration needs to be propagated to the more recent data Separation between K and π is poor above 100GeV, hence apply a cut of p<100GeV on the bachelor. Example: DLL(K- π)>5 (1D binning for visualisation) K eff π misID

11. PID Cuts: D Daughters For the moment, only the D s →KKπ mode is considered – Other modes could be added in the future To obtain clean samples of B s →D s h, PID cuts need to be applied to the D daughters to suppress B d →D + h and Λ b → Λ c h. Hence on the D s + → K - K + π + candidate we require: – DLL(K- π) > 0 for the K - and DLL(K- π) < 5 for the π + (to suppress combinatorics) – DLL(K- π) > 5 for the K + (to suppress D + →K - π + π + ) – DLL(p-K) < 0 for the K + (to suppress Λ c + →K - p π + ) – K + failing DLL(p-K) < 0 are retained if Kpπ mass is outside the Λ c mass window Applying these cuts and a mass window of [1944,1990]MeV gives: – Efficiency of 78% for B s →D s π (using momentum distributions from MC), – MisID of 1.2% for B d →D + π (using momentum distributions from data), – MisID of 1.7% for Λ b → Λ c π (using momentum distributions from MC). 11

12. B s →D s π Purity after PID Cuts After these cuts, the B s →D s π peak is rather pure 12

13. PID Cuts: Bachelor 13 For the D s π fit, a cut of DLL(K-π)<0 is applied, to eliminate any residual contamination from D s K. A hard cut of DLL(K-π)>5 is applied before doing the D s K fit, to suppress the favoured D s π mode. As a cross-check, D s K fit is also done with a loose cut of DLL(K-π)>0, and a very tight cut of DLL(K-π)>10. The efficiencies of these cuts, applied after the p<100GeV cut, are:

14. Efficiency Ratios from MC Ratio of generator level efficiencies is found to be 1.027±0.010. Until the reasons for this are understood, the 1.027 is used as a correction factor, and a systematic of 2.7% is applied. 14 Ratio of efficiencies for reconstruction, trigger, BDT cut and upper momentum cut on the bachelor is 1.03±0.01. This correction factor is applied, and the associated systematic is conservatively set to 3%.

15. Signal Lineshapes 15 The B mass uses the D (s) mass constraint (improves resolution). Different shapes are tested on the MC signal samples. Deafult shape is double Crystal Ball, with common mean & sigma Radiative tail is smaller for modes with bachelor K than bachelor π. B s →D s π B s →D s K

16. MisID Background Shapes The physics bkgs to the different modes often involve misidentified hadrons. So getting the misID’d mass shapes correct is important. Example: the shape for D s π bkg to D s K is obtained as follows: Firstly, a clean sample of D s π is extracted from the D s h data by applying DLL(K-π)<0 on the bachelor This cut biases the bachelor momentum, however the original momentum distribution can be recovered from the whole D s h sample – This works because the D s π and D s K bachelor momenta are very similar Then the mass is recomputed under the D s K hypothesis Next, the shape is weighted according to the momentum spectrum of the misidentified bachelors – This from the original momentum distribution and the misID rate as a function of momentum 16

17. MisID Background Shapes The shapes for D s π and Dπ under the D s K are sufficiently similar that in the fit only the D s π shape is used 17 The shape for Dπ bkg to D s π is obtained in a similar way, changing D daughter mass hypothesis instead of the bachelor. The shape for the DK bkg to D s K should be the same as the Dπ bkg to D s π. Under the D s K mass hypothesis

18. An Incidental Discovery… A bump was seen in the D s K fit at around 5500MeV, that was not described by the misidentified D s π shape. The bump was investigated, and it turned out to be Λ b → D s p! 18 A peak is seen at the Λ b mass after switching to the D s p mass hypothesis, applying extremely tight PID cuts (DLL(p-π)>10 and DLL(p-K)>15) on the bachelor, and tightening the BDT cut. In the future a measurement will be made of the BR of this mode, but for now… A peak is also seen at lower mass, compatible with Λ b → D s * p

19. Λ b → D s (*) p Shape Under D s K Cutting on DLL(p-K) would lose too much signal, so we must live with this background, and model its shape. The shape is taken from simulated events, after reweighting for the efficiency of the DLL(K-π)>5 cut as a function of momentum. The Λ b → D s * p shape is obtained by shifting the Λ b → D s p shape down by 200MeV. As a baseline, the relative amount of Λ b → D s p and Λ b → D s * p is assumed to be the same. 19 Λ b → D s p plus Λ b → D s * p The amount of Λ b → D s p in the D s K fit is estimated by taking the 24 events from the previous slide, and correcting for the efficiency of the tight PID cuts and the BDTG cut. – This gives an expectation of ~150 events (Λ b → D s p + Λ b → D s * p)

20. Partially Reconstructed (and other) Bkgs For partially reconstructed physics bkgs, the shapes are taken from MC, with data-driven momentum reweighting applied where a misidentification is involved. PDFs are made using RooKeysPDF. 20 One final type of physics background needs to be considered: charmless modes such as B s →K*KK These can appear if no cut is applied on the flight distance of the D from the B vertex – They can peak under the signal To remove such backgrounds, a soft cut of FDχ 2 (D from B) > 2 is applied. This will have the same efficiency for B s →D s π and B s →D s π, so will not affect the ratio of BR’s.

21. Combinatoric Background Shape The slope of the combinatoric background can floated in the D s π fit. However it must be fixed in the D s K fit, due to the low statistics and the presence of the misidentified B s →D s π in the right-hand sideband. Fitting to wrong-sign (same-sign D and bachelor) events passing the D s K selection and PID cuts, the slope is compatible with being flat. 21 As a cross-check, the wrong-sign events passing the D s π selection are also fitted, and the slope agrees well with that found in the D s π signal fit. D s K wrong-sign

22. Splitting by Magnet Polarity Since the PID efficiencies vary slightly between MagUp and MagDown, the misID background shapes change. In addition, the signal mean is found to shift by ~1MeV between MagUp and MagDown. So we split the data by polarity, and fit the two subsamples independently. About 55% (45%) of the data is MagDown (MagUp). In the following slides, the MagDown fit is on the left, and the MagUp on the right. 22

23. Recipe for Dπ Fit This fit is needed to estimate the amount of background Dπ to D s π, and to check the mean and sigma of the signal shape with high statistics. The tails of the signal mass shape are fixed from the MC fit, but the mean and sigma are floated – Mean and sigma are allowed to be different for MagUp and MagDown The yields of all components are left free. The slope of the combinatoric background is also floated in the fit. 23

24. Fits: Dπ with PIDK<0 24

25. Recipe for D s π Fit 25 The expected number of misID B d →Dπ is calculated using the fitted Dπ yield, a mass window factor (from MC), and misID from the PID calibration tools. – It is constrained to be within 10% of this estimate The misID B d →Dπ shape is also reweighted to take misID curve vs momentum into account. The signal width is fixed to that found in the B d →Dπ fit, scaled by the ratio of widths for B s →D s π and B d →Dπ in the MC Signal mean and comb background slope are floating. A Λ b → Λ c π component was allowed in the fit, but got fitted to zero. Some B d →D s π can also be seen – re-use B s →D s π mass shape, and constrain yield to {known BR ratio*f d /f s } = 1/35 relative to B s →D s π yield.

26. Fits: D s π with PIDK<0 26 For Approval

27. Recipe for D s K Fits The amount of misID B s →D s π background is floated – Provides x-check on misID rate estimate – Any B d →Dπ should be taken care of by the B s →D s π shape Treatment of signal shape is the same as for B s →D s π Comb background slope is fixed to be flat (from wrong-sign) 27 Amount of B d →DK is constrained from the B d →Dπ under D s π, using the B d →DK/B d →Dπ BR ratio Relative yields of PartReco backgrounds are constrained using – Relative reconstruction efficiencies (from MC) when e.g. a charged track or soft pion/photon is missed – B s branching ratios from B d branching ratios, using SU(3) symmetry – The yields can ove by 33% from these estimates The B d →D s K yield is floated. The B s →D s K and B d →D s K shapes are the same. Amount of Λ b → D s (*) p is constrained as detailed earlier.

28. Fits: D s K with PIDK>5 (default) 28 For Approval

29. Fits: D s K with PIDK>10 (cross-check) 29 For Approval

30. Fits: D s K with PIDK>0 (cross-check) 30 For Approval

31. Remark on B d →D s K While this component is clearly visible in the D s K fits, the amount of background underneath it makes a reliable fit to its yield very difficult, at least with the current dataset. Hence we cannot make a competitive measurement of its BR (error in PDG is ~13%). 31

32. Systematics Menu for BR Ratio Ratio of trigger/stripping/(non-PID) selection efficiencies from MC Fit model systematics will be evaluated using a large number of toy fits (as was done for f d /f s analysis). But for the moment, we simply apply cross-checks on the data, and assign conservative systematics. For the PID, take systematic on efficiency curves quoted by the RICH group, evaluated at our cut values PID systematic can enter in three different ways: – Final PID efficiency correction to obtain BR(D s K)/BR(D s π) – Shape of misID bkgs after reweighting – Expected number of Dπ/K under D s π/K (constrained in the fit) 32

33. Systematics Budget for BR Ratio The fit model systematic for D s K is the most involved part of the systematics calculation. The main contributions to this part are: – The slope of the combinatoric is fixed to half of the D s π slope. This reduces the signal yield by 3%. – The constraints on the partially reconstructed backgrounds are all varied by a factor of two. This changes the signal yield by ±4%. – Also, the ratio of the Λ b → D s * p component to the Λ b → D s p component was varied by a factor of two. The change to the signal yield is <0.5%. 33

34. Results: BR(B s →D s K)/BR(B s →D s π) 34 Averaging MagUp and MagDown, we get N(DsK) = 406±26, N(Dsπ) = 6038±105 ε PID (DsK) = 83.4±0.2%, ε PID (Dsπ) = 85.0±0.2% ε sel (Dsπ)/ ε sel (DsK) = 0.945± 0.014 We obtain

35. Extraction of BR(B s →D s π) Basically we turn the 2010 fd/fs combination on its head, by combining the ratio of yields of B s →D s π and B d →Dπ from the hadronic analysis, and the fd/fs value from the semileptonic analysis 35 Output: Input:

36. Results: BR(B s →D s K) Combining these two results, we obtain 36 This agrees with the Belle result, but is significantly below the CDF result.

37. Conclusions Using 2010 data we measure With 336pb -1 of 2011 data we measure These are combined to yield These are all World’s Best measurements. Last but not least, we would like to thank our referees, Stefania Vecchi and Stephane Monteil, for their quick work which has been very helpful in improving our analysis! 37

38. Backups 38

39. Extracting γ from D s K 39 Strong phase difference

40. BDT Training (2010) 40 The MVA was trained for the f d /f s analysis using a small (2pb -1 ) subsample of the 2010 data Several MVAs were tried, the Boosted Decision Tree with Gradient boosting (BDTG) was found to have the best performance

41. CDF Measurement 41 PID variable (uses de/dx)

42. Bachelor Momentum in MC 42

43. PID Eff Curve for DLLK<0 43

44. PID Efficiencies from Calib Tools 44 These are for the bachelor momentum spectrum, after the p<100GeV has been applied.

45. Results of Signal Fit in MC 45

46. Example of PartReco Bkg 46 Shape for B d →D *- π + from 2010 MC, under pion (left) and kaon (right) mass hypothesis for the bachelor

47. Shape of Dπ bkg to D s π (from MC) 47

48. Wrong Sign Fit for D s π 48

49. Comparison to Theoretical Expectation As a side-product of the 2010 f d /f s analysis, we measured: 49 Whereas we now measure : B d →DK Has only one tree diagram, while the B s →D s K has two So our result suggests that the two different tree diagrams contributing to the D s K final state interfere destructively