1. 1/4/2008 LHCb Tuesday Meeting 1 Global fits to γ and the impact of CLEO-c Jim Libby and Guy Wilkinson (University of Oxford)

2. 1/4/2008LHCb Tuesday Meeting2 Outline Motivation for the global fit Motivation for the global fit The LHCb inputs to the fit The LHCb inputs to the fit Strategy and validation of the fit Strategy and validation of the fit Adding additional information beyond the original individual mode DC04 studies Adding additional information beyond the original individual mode DC04 studies –New constraint on δ D Kπ from CLEO-c An aside on CP conventions An aside on CP conventions –Non-resonant B 0 →DKπ –The CLEO-c measurements of the coherence factor and average strong phase of D→K3π Global fit results for several different scenarios Global fit results for several different scenarios –Precision on γ at tree level including time-dependent measurements Outlook Outlook

3. 1/4/2008LHCb Tuesday Meeting3 Motivation We are now using several different D final states to measure γ with B + →DK + and B 0 →DK *0 : We are now using several different D final states to measure γ with B + →DK + and B 0 →DK *0 : –D→Kπ and D→hh –D→K3π –D→K 0 ππ γ is not the only common parameter: γ is not the only common parameter: –there is r B (ratio of colour/CKM favoured amplitude to the suppressed amplitude) and –δ B (strong phase between these amplitudes)

4. 1/4/2008LHCb Tuesday Meeting4 Motivation cont. It has been seen that the greater the number of constraints on the ADS fit, in particular r B, the more stable the results It has been seen that the greater the number of constraints on the ADS fit, in particular r B, the more stable the results –Will give us ultimate precision expected on γ Therefore, combining all modes in a global fit to data will provide this Therefore, combining all modes in a global fit to data will provide this –Also include the coherence factor constraints from CLEO-c –The values and estimates of uncertainties on c i and s i not yet available so will use Bondar and Poluektov estimates Why not just combine the results via the correlation matrices? Why not just combine the results via the correlation matrices? –Some non-Gaussian behaviour has been observed –Somewhat easier (for me) to implement a global fit in the first instance

5. 1/4/2008LHCb Tuesday Meeting5 Input from the selection studies – 2 fb −1 ModeSignalBkgNoteAuthors B + →D(K + π − )K + 28k17.5k2006-066 M. Patel B + →D(K − π + )K + 0-500780 B + →D(h + h − )K + 4k7.2k B 0 →D(K + π − )K *0 1.7k8502007-050 K. Akiba & M.Gandelman B 0 →D(K − π + )K *0 300850 B 0 →D(h + h − )K *0 500500 B + →D(K + 3π)K + 30.5k46k2007-004 A. Powell B + →D(K − 3π)K + 0-6001.2k B + →D(K 0 π + π − )K + 5k 1.2k- 4.7k 2007-041 V. Gibson, C. Lazzeroni & JL

6. 1/4/2008LHCb Tuesday Meeting6 Global fit strategy Toy experiments with combined individual χ 2 from the different ADS/GLW rates and Dalitz bins Toy experiments with combined individual χ 2 from the different ADS/GLW rates and Dalitz bins –Use relative efficiencies and branching fractions to relate normalisation factors Include constraints from CLEO-c Include constraints from CLEO-c Can include or remove measurements to see their global impact Can include or remove measurements to see their global impact

7. 1/4/2008LHCb Tuesday Meeting7 2-body charged fit validation Code an extension of the model-independent Dalitz fit Code an extension of the model-independent Dalitz fit First reproduce Mitesh’s sensitivity studies as presented in his recent LHCb note to validate ADS/GLW method First reproduce Mitesh’s sensitivity studies as presented in his recent LHCb note to validate ADS/GLW method –r B =0.077, γ =60° and  B =130° –Constraint of σ(cos  D ) = 0.2 –1000 experiments with 2 fb −1 –Uncertainty on error ~0.3 to 0.4°  D (°) -25-16.6-8.308.316.625   (°) global 9.69.69.48.78.49.39.2   (°) Mitesh9.68.88.58.29.19.29.2

8. 1/4/2008LHCb Tuesday Meeting8 Kπ and hh toy experiments Mitesh Note δ Kπ =16.6  rBrB δB()δB() δKπ()δKπ() γ()γ()

9. 1/4/2008LHCb Tuesday Meeting9 2-body neutral fit validation Also reproduced Kazu and Miriam’s sensitivity studies as presented in LHCb-2007-050 Also reproduced Kazu and Miriam’s sensitivity studies as presented in LHCb-2007-050 –r B =0.4, γ =60° and  D =3° –Constraint of σ(cos  D ) = 0.1 –1000 experiments with 2 fb −1 –Uncertainty on error ~0.3 to 0.4°  B (°) 01020306090120180   (°) global 8.28.29.010.2 11.3 (RMS) 13.2(RMS)9.45.8   (°) 2007-0508.78.88.99.9---6.4 Some points have non-Gaussian behaviour

10. 1/4/2008LHCb Tuesday Meeting10 New things to be added CLEO-c measure  D Kπ with double-tagged events in a manner similar to the coherence analysis CLEO-c measure  D Kπ with double-tagged events in a manner similar to the coherence analysis –Also constrain D-mixing The recent measurement arXiv:0802.2264 [hep-ex]: The recent measurement arXiv:0802.2264 [hep-ex]: – However, the analysis uses a different CP convention to the ADS framework: However, the analysis uses a different CP convention to the ADS framework:

11. 1/4/2008LHCb Tuesday Meeting11 CP formalism Why does this matter? Why does this matter? –The parameters r D K π and  D K π are defined as : –However, we use the ratios of D 0 and D 0 to the same final state in the CLEO-c coherence and LHCb ADS analyses which are different in the two CP formalisms

12. 1/4/2008LHCb Tuesday Meeting12 Nature is cruel Therefore we need to subtract 180° from the measured value of  D before inputting it to the ADS analysis Therefore we need to subtract 180° from the measured value of  D before inputting it to the ADS analysis  D (°) -25-16.6-8.308.316.625   (°) 9.49.59.58.78.79.19.4  D (°) -190-174-158-144-130   (°) 12.710.813.812.610.8 A few degrees worse Smaller asymmetry between suppressed B + and B − modes Old New

13. 1/4/2008LHCb Tuesday Meeting13 B → DK * Coherence effects exist in modes with a K* from contributions from non- resonant K π Coherence effects exist in modes with a K* from contributions from non- resonant K π Example from Pruvot et al. (hep-ph/0703292) Example from Pruvot et al. (hep-ph/0703292) Considers B Dalitz plot and model in K* region Considers B Dalitz plot and model in K* region –For r S =0.4, k=1 in the absence of pollution find r S from 0.3 to 0.45 and k=0.95±0.03 Systematic effect Systematic effect p refers to position in DKπ phase space

14. 1/4/2008LHCb Tuesday Meeting14 CLEO-c 4-body constraints (R K3  ) 2 = -0.20 ± 0.23 ± 0.09 = -0.60 ± 0.19 ± 0.24 R K3  cos(  K  –   ) = 0.00 ± 0.16 ± 0.07  K      ° 4 points in R K3 π -  K3 π space considered 1.R K3 π = 0.2 and  K3 π = 144° 2.R K3 π = 0.4 and  K3 π = 130° 3.R K3 π = 0.2 and  K3 π = 250° 4.R K3 π = 0.0 and  K3 π = 180° (phase doesn’t matter) 1 2 3 4 Applied as four individual constraints given non-Gaussian behaviour of combination

15. 1/4/2008LHCb Tuesday Meeting15 Charged ADS two and four body Baseline assumptions Baseline assumptions –Input values of r B =0.1, γ =60° and  B =130° –r D =0.616 (PDG 2007) –Four-body coherence factor central values  D (°) -190-174-158-144-130   (°) 2-body no CLEO 12.9*12.0*10.010.010.0   (°) + CLEO 10.3*9.4*10.010.09.3   (°) + 4-body but no CLEO K3 π 10.4*10.4*9.99.28.1   (°) + CLEO K3 π 8.69.38.07.36.7 * Non-Gaussian so RMS quoted

16. 1/4/2008LHCb Tuesday Meeting16 Why incoherence is still useful? –No dependence on r B when R K3 π =0 –The better determination of r B improves the 2-body dominated determination of γ Add 4-body + CLEO-c

17. 1/4/2008LHCb Tuesday Meeting17 Varying R K3 π and  K3 π  D (°) -190-174-158-144-130 R K3 π = 0.2 and  K3 π = 144° 8.6 ° 9.3 ° 8.0 ° 7.3 ° 6.7 ° R K3 π = 0.4 and  K3 π = 130° 6.6 ° 6.4 ° 6.3 ° 6.0 ° 5.6 ° R K3 π = 0.2 and  K3 π = 250° 8.8 ° 8.9 ° 8.0 ° 7.1 ° 6.8 ° R K3 π = 0.2 and  K3 π = 180° 8.3 ° 9.1 ° 7.3 ° 6.7 °

18. 1/4/2008LHCb Tuesday Meeting18 Neutral ADS/GLW estimated impact of 4 body No selection for B 0 →D(K3π)K *0 No selection for B 0 →D(K3π)K *0 Assume background and signal scale in the same way as B + →D(K3π)K + to begin with Assume background and signal scale in the same way as B + →D(K3π)K + to begin with  B (°) 04590135180   (°) 2-body + CLEO 5.710.07.89.15.3   (°) + 4-body but no CLEO K3 π 5.810.98.59.15.2   (°) + CLEO K3 π 5.510.38.09.05.1

19. 1/4/2008LHCb Tuesday Meeting19 Combine and include Dalitz Combine the ADS/GLW Combine the ADS/GLW –No B 0 →D(K3π)K *0 given the limited impact Add Dalitz with the largest background considered in DC04 studies Add Dalitz with the largest background considered in DC04 studies –Effective uncertainty is 9-10 ° in global fit –Standalone uncertainty 13°  B (°) 04590135180 Combined B+/B0 ADS/GLW 4.6 ° 7.6 ° 6.3 ° 7.1 ° 4.6 ° + model independent Dalitz 4.2 ° 5.7 ° 5.3 ° 5.7 ° 4.2 °

20. 1/4/2008LHCb Tuesday Meeting20 Systematic uncertainties

21. 1/4/2008LHCb Tuesday Meeting21 Dalitz systematic uncertainties Really need to take measured uncertainties on c i and s i from CLEO-c Really need to take measured uncertainties on c i and s i from CLEO-c –will be available soon In the meantime perform fit without Dalitz information In the meantime perform fit without Dalitz information –Benchmark point R K3 π =0.35 –σ(γ)=7.6° without Dalitz (σ(γ)=5.5° with Dalitz ) –Effective σ(γ) from Dalitz 8.0° ( cf Dalitz alone 12.2°) Global fit working as more than sum of parts Global fit working as more than sum of parts –Add 5° in quadrature to effective statistical uncertainty for ψ(3770) data related uncertainty This is the latest Bondar and Poluektov number arXiv:0801.0840 This is the latest Bondar and Poluektov number arXiv:0801.0840 Need to check this myself Need to check this myself –Recombine  σ(γ)=5.9° including Dalitz error - 10% degradation

22. 1/4/2008LHCb Tuesday Meeting22 Addition of uncorrelated measurements

23. 1/4/2008LHCb Tuesday Meeting23 0.5 fb -1 and 10 fb -1 With 0.5 fb -1 : With 0.5 fb -1 : –σ(γ)=11.4° at my benchmark point and reasonably well behaved –Very non-Gaussian without CLEO-c constraints –No Dalitz systematic (presumably small effect with low LHCb statistics) With 10 fb -1 With 10 fb -1 –σ(γ)=2.1° No Dalitz systematic error –σ(γ)=2.8° with Dalitz systematic error

24. 1/4/2008LHCb Tuesday Meeting24 Outlook