1. Rob Lambert, NIKHEFNikhef 10th February 20121  m blinded analysis of stripping 13 data Rob Lambert and Thomas Bird LHCb-ANA-2011-104 https://twiki.cern.ch/twiki/bin/view/LHCbPhysics/DmsSemileptonicMixingNote

2. Result  So you’re not waiting too long: Rob Lambert, NIKHEFNikhef 10th February 20122 BLIND

3. Not discussed today  Past show stoppers  (I present the present analysis, not all the dead-ends)  MC samples used  (discussed elsewhere)  Many many Toys and full MC fits  (only useful as proof-of-principle, not used in the analysis) Rob Lambert, NIKHEFNikhef 10th February 20123

4. Introduction  We are fitting for  m s and  m d in a simultaneous fit  Why this channel?  For B s it is the dominant flavour-specific decay mode  Why simultaneous?  Topologically indistinguishable decays  Shared background sources  Fit one, get the other “for free”  Why do it at all?  There will never be good enough resolution to overcome D s   We want to eventually fit for  A fs time-dependently  It will be the same fitter, a simple change of variables Rob Lambert, NIKHEFNikhef 10th February 20124

5. Outline  Data and Selection  Mass Model  Proper-time model  k-factor  Acceptance  Resolution  Splitting into regions of B-mass  Fit results  Systematics Rob Lambert, NIKHEFNikhef 10th February 20125

6. Data and Selection  Stripping-13 dataset of (341 ± 12) pb-1  Update to 1 fb -1 is not planned, we instead want to push for  A fs  Selection strategy:  “Keep all the data”  “Simultaneous selection of B s and B d ” 1.Maximise S/  (S+B) on MC09 2.Take all physics triggers 3.Loosen  2 cuts to those suggested by tracking group 4.Tighten PID cuts to remove K->  and  ->  mis ID to <1%  All the cuts are given in the backup, and page 7 of the note Rob Lambert, NIKHEFNikhef 10th February 20126

7. Data and Selection  Selection yields millions of signal candidates  “n” is the “Normalized mass”, which will be defined later Rob Lambert, NIKHEFNikhef 10th February 20127

8. Mass Model  Investigated thoroughly with 2010 data: LHCb-INT-2011-019LHCb-INT-2011-019 Rob Lambert, NIKHEFNikhef 10th February 20128 DdDd DsDs D*(2010) 2010

9. Proper Time: General Odd: tag and final state are not consistent Even: tag and final state are consistent R(t) is a resolution function  (t) is an acceptance function  They are defined empirically by the above equation.  We take the “standard” LHCb flavour-tagging  In addition we have the missing neutrino which must be corrected for. Rob Lambert, NIKHEFNikhef 10th February 20129

10. Proper time: k  Several correction methods investigated: LHCb-INT-2011-004LHCb-INT-2011-004  k-factor is the most stable, a statistical MC-based correction Rob Lambert, NIKHEFNikhef 10th February 201210 Quartic function of “n” k is Fixed to be 1 at n=1 MC

11. Proper time: Acceptance  Many functions investigated: LHCb-INT-2011-020LHCb-INT-2011-020 Rob Lambert, NIKHEFNikhef 10th February 201211 a la LHCb hadronic modesa la CDF/D0Matches Gaussian resolution MC

12. Proper time: resolution  Resolution is a quadratic function of the proper time.  Bias and width are fitted directly from the MC  We include this dependence directly in the signal PDF Rob Lambert, NIKHEFNikhef 10th February 201212 MC

13. Final Signal PDF  No analytic integral  Post-multiplied by Gaussian acceptance Rob Lambert, NIKHEFNikhef 10th February 201213

14. Final Signal PDF  Faster wiggles die away quickly Rob Lambert, NIKHEFNikhef 10th February 201214 Example tag Asymmetry Perfect Tagging30% mistag  m = 17 ps -1  m = 30 ps -1  m = 0.5 ps -1 DEMO

15. Using more k-information?  The k-factor is the dominant issue for resolution  Missing information reduced at high (D  )-mass Rob Lambert, NIKHEFNikhef 10th February 201215 MC Event-by-event: Needs a Punzi term Needs numeric convolution Massive overkill for  A fs …

16. Splitting by B-mass  Simplest first step, use only two bins of (D  )-mass  Toy study performed to identify gains (details in note)  Split the data into two categories: gain ~25%  m s precision Rob Lambert, NIKHEFNikhef 10th February 201216 TOY Better Worse  m s gets  m d gets

17. PDF fit to full LHCb MC Rob Lambert, NIKHEFNikhef 10th February 201217  m s = (17.9 ± 0.25) ps -1 MC High mass regionLow mass region Even-tagOdd-tag

18. Blinding  To avoid fine-tuning, particularly of the resolutions   m was blinded by adding a uniform random number  ± 0.1 for  m d ~ 5   ± 1.0 for  m s ~ 3   Unfortunately some early fits were accidentally unblinded when the random number was large and positive, but that has not affected our analysis procedure and was since rectified. Rob Lambert, NIKHEFNikhef 10th February 201218

19. Fit Results: Masses Rob Lambert, NIKHEFNikhef 10th February 201219 Odd - tagEven - tag Low B-massHigh B-mass Total Signal Peaking Cheby (1) Cheby (2)

20. Fit Results: Time Rob Lambert, NIKHEFNikhef 10th February 201220 Total Signal Peaking Cheby (1) Cheby (2)

21. Fit Results: Asymmetry Rob Lambert, NIKHEFNikhef 10th February 201221 Combined, both mass regionsProjection in high-mass region  There are some tens of asymmetry plots in the analysis note  All of them seem well-behaved as above

22. Fit Results: correlation Rob Lambert, NIKHEFNikhef 10th February 201222 Too Many Parameters to discuss… All are listed in the backup  m only correlates with mistag (-20%)

23. Sources of Systematics 1.k-factor model dependence 2.Proper time scale (Velo 0.1%, momentum 0.1%, from D s  ) 3.Resolution worse in Data than MC? 4.Acceptance some parameters fixed from MC  was fixed in the fit Rob Lambert, NIKHEFNikhef 10th February 201223

24. k-factor systematic  Exhaustive toy study performed in: LHCb-INT-2011-020LHCb-INT-2011-020  How bad could it possibly be? Rob Lambert, NIKHEFNikhef 10th February 201224 Fit to population +/- 1 standard deviation Central value fit to mean k-factor +/- 1 fit error on all polynomial params MC Different MC Versions? B s and B d differences? Different proportions of D** states?

25. k-factor systematic  Exhaustive toy study performed in: LHCb-INT-2011-020LHCb-INT-2011-020  Generate with a biased k-factor, fit with nominal k-factor  Use 0.3% relative systematic uncertainty Rob Lambert, NIKHEFNikhef 10th February 201225 Within 0.3% Within 1.2% … but completely unphysical! TOY

26. Cross-check fits  For resolution, acceptance, , all completely consistent Rob Lambert, NIKHEFNikhef 10th February 201226

27. Systematic Uncertainties  We reach:  Systematic error on  m = 0.33 %  Still very much statistically limited Rob Lambert, NIKHEFNikhef 10th February 201227 BLIND

28. More cross-checks..  We were asked to take a look at some other features:  https://twiki.cern.ch/twiki/bin/view/LHCbPhysics/DmsSemileptonicMixingNote#Comments_and_responses https://twiki.cern.ch/twiki/bin/view/LHCbPhysics/DmsSemileptonicMixingNote#Comments_and_responses  Stephanie Hansmann-Menzemer has volunteered to be our internal reviewer … already got quite a few interesting comments…  There are a lot more issues to double-check and so unblinding might take a while longer yet. Rob Lambert, NIKHEFNikhef 10th February 201228

29. E.g. Rob Lambert, NIKHEFNikhef 10th February 201229  Notice anything?? 60 variables here …

30. E.g. Rob Lambert, NIKHEFNikhef 10th February 201230  Notice anything?? 60 variables here … Stephie did!

31. Summary  A very complicated analysis to see a simple wiggle!  We aim to quickly move on to measuring  A fs with 1 fb -1  In our analysis note we also report a determination of the fraction of B d -> D s  X  LHCb-ANA-2011-104 LHCb-ANA-2011-104  All comments, questions, suggestions very welcome! Rob Lambert, NIKHEFNikhef 10th February 201231 BLIND

32. Backup slides Rob Lambert, NIKHEFNikhef 10th February 201232

33. Future work 1.MC improvement of k-factor,  Biased  m, ~1.5  can occur in different B-mass regions.  Investigate: the k-factor method needs improvement  Event-by-event k-factor?  Completely different fitter would be required!  Needed to correctly calibrate/optimize the tagger? 2.Studies in D s  show the real data resolution is worse  Optimizing the tagger needs correct resolution  Create a fake k-factor in the real data  B d -> D 3 , fully reconstructed,  Discard two pions (treat like, ,  0 )  Reconstruct a fake k-factor and compare with the MC Rob Lambert, NIKHEFNikhef 10th February 201233

34. Split fit results Rob Lambert, NIKHEFNikhef 10th February 201234

35. Shared Fit Params Rob Lambert, NIKHEFNikhef 10th February 201235 BLIND

36. MC Data vs Old Fit Rob Lambert, NIKHEFNikhef 10th February 201236 MC Old fit with one overall resolution, Doesn’t work at all!! OLD

37. Convolution  Convolution is the smearing of one fixed distribution with another fixed distribution  We are doing:  Which is no longer a convolution, so none of the usual convolution identities apply  From now on I will try to say “smearing” Rob Lambert, NIKHEFNikhef 10th February 201237

38. Convolution  I could still define it as a convolution if I can translate or rotate t and  to obtain the original formula  But the Gaussian become quartic in t, no simple rotation Rob Lambert, NIKHEFNikhef 10th February 201238

39. Event-by-event?  An event-by-event proper time resolution is a transformation  If  t is an external independent observable, this can be broken down into component PDFs (punzi), but not true in our case!  In our case we could instead do:  Re-write our PDF completely with momenta and lengths…  Then we have two punzi effects and two unknown background distributions…  Too complicated for such a simple measurement… Rob Lambert, NIKHEFNikhef 10th February 201239

40. Pseudo event-by-event  Selects the resolution function at t, then knowing…  But we now suffer from the frequentist fallacy “A single measured quantity is a good estimator of the true quantity”  So we must show it works at least in the full MC … Rob Lambert, NIKHEFNikhef 10th February 201240

41. Selection cuts (all) Rob Lambert, NIKHEFNikhef 10th February 201241