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f 3 measurements at superKEKB

f 3 measurements at superKEKB. Pavel Krokovny KEK. Introduction Methods Summary. World average (UTfit). UTfit averages including all results available today. γ/φ 3 = 88±16 °. The total Belle+Babar luminosity used in this average is about 1ab -1 .

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f 3 measurements at superKEKB

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  1. f3 measurements at superKEKB Pavel Krokovny KEK Introduction Methods Summary

  2. World average (UTfit) UTfit averages including all results available today γ/φ3=88±16° The total Belle+Babar luminosity used in this average is about 1ab-1. Naively we can expect f3 error of 70(20) for 5ab-1 (50ab-1)

  3. Unitarity Triangle Fit (50/ab)

  4. Atwood-Dunietz-Soni method D. Atwood, I. Dunietz and A. Soni, PRL 78, 3357 (1997); PRD 63, 036005 (2001) Enhancement of СР-violationdue to use ofCabibbo-suppressedD decays B–D0K–- color allowed D0K+π– - doublyCabibbo-suppressed B–D0K–- color suppressed D0K+π– - Cabibbo-allowed Interfering amplitudes are comparable 

  5. 4 equations (3 independent: ), 3 unknowns Gronau-London-Wyler method [Phys. Lett. B 253 (1991) 483] [Phys. Lett. B 265 (1991) 172] СР eigenstateofD-meson is used (DCP). CP-even : D1K+K–, π+ π– CP-odd : D2 KS π0, KS ω, KS φ, KSη… СР-asymmetry: forD1  A1,2have opposite signs forD2 Additional constraint:

  6. ADS method (Belle) Belle collaboration, 657M BB pairs [arXiv: 0804:2063, submitted to PRD(RC)] B−→[K+π−]D K− (suppressed) and B−→[K–π+]D K− (favored) modes are selected. B→DfavK B→DsuppK CP asymmetry: rB<0.19 at 90% CL (with the conservative assumption cos φ3 cos δ = –1)

  7. GLW method (BaBar) BaBar collaboration, 382M BB pairs [arXiv: 0802:4052] CP-even modes: DCP+→K+K–, π+ π– CP-odd modes : DCP−→KS π0, KS ω The same result expressed in Cartesian variables: x± precision comparable to Dalitz analysis

  8. Both methods are theoretical clean and have no model uncertainty. The f3 precision is limited by statistics only. Current f3 error is in order of 300 The expected f3 accuracy is 150 with 5ab-1 and 50 with 50 ab-1 ADS+GLW

  9. Measure B+/B- asymmetry across Dalitz plot Dalitz analysis method Mirror symmetry between D0 and D0 Dalitz plots Sensitivity to φ3 in interference term Determine f in flavor-tagged D*+D0π+ decays Current statistical accuracy is about 150 The model uncertainty is in order of 5-100

  10. HFAG averages for x± = rB cos( δ± f3 ) , y± = rB sin( δ± f3 ) Belle/Babar measurements in good agreement Note: σ(f3) depends significantly on the value of rB 2f3 rB Belle/Babar model-dependent results Contours do not include Dalitz model errors Contours do not include Dalitz model errors

  11. -i i Binned analysis:DCP [A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003)] Number of events in D0-plot: Number of events in B-plot Free parameters where DCPKSπ+π–: ψ(3770)(KSπ+π–)D (KSπ+π–)D :

  12. rB=0.2 Binned analysis:DCP [A. Bondar, A.Poluektov, Eur. Phys. J. C47 347-353 (2006), hep-ph/0510246] • ci , si can be obtained from B data only • ci from DCP, si from B data • si constrained as  Very poor sensitivity  Poor sensitivity for y  Bias if bin size is large 50 ab-1 (50000 ev.) at SuperB should be enough for model-indep. φ3 measurement with accuracy 2-3° ~10 fb-1 (10000 ev.) at ψ(3770) needed to accompany this measurement. Nearest future: ~1000 DCP events at CLEO. Bin size should be large  bias due to

  13. Binned analysis:(KSπ+π–)2 2 correlated Dalitz plots, 4 dimensions: (6) Can use maximum likelihood technique: (7) with ci and si as free parameters. For the same binning as in DCP, number of bins is N2 (instead of N), but the number of unknowns is the same. With Poisson PDF, it’s OK to have Nij<1. Can obtain both ci and si. It’s convenient to use combined likelihood of (Ksp+p-)2 and B datato account for errors in ci and si.

  14. Binned analysis:(KSπ+π–)2 [A. Bondar, A.Poluektov,hep-ph/0703267, arXiv:0711.1509] • Can use the same binning as in DCP • ci ,simeasured independently  no model uncertainty due to constraint • Only 4-fold ambiguity: ci -c-i or si -s-i.reduces to 2-fold if DCP data are used with the same binning. • Stat. sensitivity comparable to DCP ci ,si measured in toy MC (points) and calculated (crosses) for ΔδD-binning

  15. The binned Dalitz analysis has almost the same statistical power that the unbind. But the model uncertainty can by eliminated by using the CP tagged DCP events form charm factories. The expected f3 accuracy is 70 with 5ab-1 and 2.50 degrees with 50 ab-1. This measurement will require 103 (104) CP tagged DCP from charm factory, CLEOc/BES Model-independent Dalitz analysis

  16. Conclusion • Several methods can be used to measure f3 with superKEKB. • GLW+ADS are theoretical clean. Accuracy depends on statistics only. The expected error is 150 (50) with 5ab-1 (50ab-1) • The Dalitz analysis method will be limited by model uncertainty. • The model independent Dalitz method can be used. The information form charm factories are required. The expected f3 error is 70 (2.50) with 5ab-1 (50ab-1) • Combining together ADS, GLW and Dalitz methods, we can reach accuracy of 60 (20) with 5ab-1 (50ab-1)

  17. Other possibilities: D0π+π–π0 (BaBar) [BaBar collaboration, hep-ex/0703037] Modified likelihood to account for Br difference of B+ and B–: No significant constraint on γ yet. DKsK+K–: more promising?

  18. Other possibilities: B0D0K*0 (BaBar) [V. Sordini, talk at CKM2006; hep-ph/0703292] Both amplitudes are color-suppressed, rB larger: Self-tagging decay: K*0K+π– Estimated signal yield with 350 fb-1: 45 events. With that low statistics, toy MC shows significant bias in (x,y).

  19. Satisfy simultaneously for binning with Binned analysis: DCP [A. Bondar, A.Poluektov, hep-ph/0703267] • To use the limited CLEO-c data: • Find binning with optimal sensitivity • Get rid of bias due to • Good approximation: uniform binning in ΔδD: But the optimal binning depends on D0 model.  bias if it differs from actual one (same ~10°). causes unavoidable model sensitivity. Reduces as data increases (by applying finer binning).

  20. MC simulation of the bias in f3 measurement Model dependence for 2x8 bins in (Ksp+p-)2 case: No bias when changing the model, but stat. errordegrades. Model dependence for 2x8 bins in Dcp case:

  21. Summary of stat. sensitivity Errors corresponding to 1000 events in B, DCP and (Kππ)2 samples Expected charm data contribution for 750 fb-1 at CLEO-c: (1000 DCP and 2000 (Kππ)2) σx=0.003, σy=0.007 σ(φ3)~5° with rB=0.1

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