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Global fits to γ and the impact of CLEO-c

Global fits to γ and the impact of CLEO-c. Jim Libby and Guy Wilkinson (University of Oxford). Outline. Motivation for the global fit The LHCb inputs to the fit Strategy and validation of the fit Adding additional information beyond the original individual mode DC04 studies

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Global fits to γ and the impact of CLEO-c

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

  2. Outline • Motivation for the global fit • The LHCb inputs to the fit • Strategy and validation of the fit • Adding additional information beyond the original individual mode DC04 studies • New constraint on δDKπfrom CLEO-c • An aside on CP conventions • Non-resonantB0→DKπ • The CLEO-c measurements of the coherence factor and average strong phase ofD→K3π • Global fit results for several different scenarios • Precision on γat tree level including time-dependent measurements • Outlook LHCb Tuesday Meeting

  3. Motivation • We are now using several different D final states to measure γwithB+→DK+ andB0→DK*0: • D→Kπ and D→hh • D→K3π • D→K0ππ • γis not the only common parameter: • there is rB (ratio of colour/CKM favoured amplitude to the suppressed amplitude) and • δB (strong phase between these amplitudes) LHCb Tuesday Meeting

  4. Motivation cont. • It has been seen that the greater the number of constraints on the ADS fit, in particular rB, 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 • Also include the coherence factor constraints from CLEO-c • The values and estimates of uncertainties on ci and si not yet available so will use Bondar and Poluektov estimates • 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 LHCb Tuesday Meeting

  5. Input from the selection studies – 2 fb−1 LHCb Tuesday Meeting

  6. Global fit strategy • Toy experiments with combined individual χ2 from the different ADS/GLW rates and Dalitz bins • Use relative efficiencies and branching fractions to relate normalisation factors • Include constraints fromCLEO-c • Can include or remove measurements to see their global impact LHCb Tuesday Meeting

  7. 2-body charged fit validation • 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 • rB=0.077, γ=60° and B=130° • Constraint ofσ(cosD) = 0.2 • 1000 experiments with 2 fb−1 • Uncertainty on error ~0.3 to 0.4° LHCb Tuesday Meeting

  8. Kπ and hh toy experiments δKπ=16.6 Mitesh Note rB δB() δKπ() γ() LHCb Tuesday Meeting

  9. 2-body neutral fit validation • Also reproduced Kazu and Miriam’s sensitivity studies as presented in LHCb-2007-050 • rB=0.4, γ=60° and D=3° • Constraint ofσ(cosD) = 0.1 • 1000 experiments with 2 fb−1 • Uncertainty on error ~0.3 to 0.4° Some points have non-Gaussian behaviour LHCb Tuesday Meeting

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

  11. CP formalism • Why does this matter? • The parameters rDKπandDKπare defined as: • However, we use the ratios of D0 and D0 to the same final state in the CLEO-c coherence and LHCb ADS analyses which are different in the two CP formalisms LHCb Tuesday Meeting

  12. Nature is cruel • Therefore we need to subtract 180° from the measured value of D before inputting it to the ADS analysis Old A few degrees worse Smaller asymmetry between suppressed B+ and B− modes New LHCb Tuesday Meeting

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

  14. CLEO-c 4-body constraints <RK3p cos(d K3p)> = -0.60 ± 0.19 ± 0.24 3 4 1 (RK3p )2 = -0.20 ± 0.23 ± 0.09 2 RK3p cos( d Kp – d K3p) = 0.00± 0.16 ± 0.07 d Kp =(158+14-16)° • 4 points in RK3π-K3π space considered • RK3π= 0.2 and K3π= 144° • RK3π= 0.4 and K3π= 130° • RK3π= 0.2 and K3π= 250° • RK3π= 0.0 and K3π= 180° • (phase doesn’t matter) Applied as four individual constraints given non-Gaussian behaviour of combination LHCb Tuesday Meeting

  15. Charged ADS two and four body • Baseline assumptions • Input values of rB=0.1, γ=60°and B=130° • rD=0.616 (PDG 2007) • Four-body coherence factor central values * Non-Gaussian so RMS quoted LHCb Tuesday Meeting

  16. Why incoherence is still useful? • No dependence on rB when RK3π=0 • The better determination of rB improves the 2-body dominated determination of γ Add 4-body + CLEO-c LHCb Tuesday Meeting

  17. Varying RK3πand K3π LHCb Tuesday Meeting

  18. Neutral ADS/GLW estimated impact of 4 body • No selection for B0→D(K3π)K*0 • Assume background and signal scale in the same way asB+→D(K3π)K+ to begin with LHCb Tuesday Meeting

  19. Combine and include Dalitz • Combine the ADS/GLW • No B0→D(K3π)K*0 given the limited impact • Add Dalitz with the largest background considered in DC04 studies • Effective uncertainty is 9-10° in global fit • Standalone uncertainty 13° LHCb Tuesday Meeting

  20. Systematic uncertainties LHCb Tuesday Meeting

  21. Dalitz systematic uncertainties • Really need to take measured uncertainties on ci and si from CLEO-c • will be available soon • In the meantime perform fit without Dalitz information • Benchmark point RK3π=0.35 • σ(γ)=7.6° without Dalitz (σ(γ)=5.5° with Dalitz) • Effectiveσ(γ) from Dalitz 8.0° (cf Dalitz alone 12.2°) • Global fit working as more than sum of parts • Add 5° in quadrature to effective statistical uncertainty forψ(3770) data related uncertainty • This is the latest Bondar and Poluektov number arXiv:0801.0840 • Need to check this myself • Recombine  σ(γ)=5.9° including Dalitz error - 10% degradation LHCb Tuesday Meeting

  22. Addition of uncorrelated measurements LHCb Tuesday Meeting

  23. 0.5 fb-1 and 10 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 • σ(γ)=2.1° No Dalitz systematic error • σ(γ)=2.8° with Dalitz systematic error LHCb Tuesday Meeting

  24. Outlook LHCb Tuesday Meeting

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