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J. Albert Caltech October 7, 2004

Measurement of and. 2b+g. g. (or φ 3 and 2 φ 1 + φ 3 ). J. Albert Caltech October 7, 2004. The Angle  of the Unitarity Triangle. We expect  to be approximately (57 ±9)º , if the Standard Model is consistent . But how to directly measure it….

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J. Albert Caltech October 7, 2004

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  1. Measurement of and 2b+g g (or φ3 and 2φ1+φ3) J. Albert Caltech October 7, 2004

  2. The Angle  of the Unitarity Triangle • We expect  to be approximately (57±9)º, if the Standard Model is consistent. • But how to directly measure it… We have several ways of directly measuring .No single one of them is a “silver bullet”: D(*)0CPK(*)+(Gronau-London-Wyler) D0(Kπ)h+(Atwood-Dunietz-Soni) D(*)0(D03-body)K+(Dalitz, GGSZ) sin(2β+) from D(*)π/D(*)ρ 4a)assisted by Ds(*)π/Ds(*)ρ sin(2β+) from D(*)0K(*)0 The dark horse: D(s)(*)D(*) combined fit (D-L-A) FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 2

  3. Measurement of  from Direct CPV (i.e. GLW, ADS, GGSZ/Dalitz) Secret to Success: interference between color-allowed D0K and color-suppressed D0K amplitudes. Decay-time-independent! * Vus Vub Vcb * Vcs • The D0K and D0K amplitudes have a relative weak phase of .  • But need 2 more pieces of information!: • Relative magnitude • Strong phase difference δB The bigger the better! Larger rB larger interference term  better constraints on . From B  D0K GLW analysis: rB < 0.22 (90% CL) hep-ex/0402024 rB = 0.26+0.10±0.03±0.04 hep-ex/0406067 -0.14 FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 3

  4. How to Reconstruct a B0 DK Event Continuum e+e-  q+q- rejection obtained via event topology. Topological variables combined in a Fisher discriminant or a Neural Net ΔE = E*B-E*beam • DK/Dπ separation obtained via ΔE and from particle ID (e.g. BaBar DIRC) ΔE (GeV) FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 4

  5. The Gronau-London-Wyler Method • B- D0CPK(*)-, where D0CP is a CP-eigenstate decay (CP+: D0 π+π-, K+K- CP-: D0 Ksπ0) • We have the following observables: • 4 observables (RCP+, RCP-,ACP+, ACP-)  determine 3 unknowns (rB,δB,) Normalized to flavor state BF(B  DK) ~ 10 -4, BF(D fCP) ~ 10 -2 Small…  strongly statistics limited FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 5

  6. B- D0CPK(*)- yields from B- CP+ B+ CP- B- CP- B+ CP+ CP+ (p+p-,K+K-) NBB=214 106 D0CP K - CP- (KSp0) D0p background D0CP K* - (K* - KSp -) Adding KSf, KSw NBB=227 106 FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 6

  7. B- D(*)0CPK- yields from B+ D1*0π+ B+ D1*0 K+ B+ D10 K+ B+ D2*0π+ B+ D2*0 K+ B+ D20 K+ FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 7

  8. Gronau-London-Wyler Method Results: From DCPK* Loose bound on rB D0CP K - D0CP K* - (K*- KSp -) NBB=227 106 NBB=214 106 Additional systematic error on ACP- ( CP even background) D*0 (D0CPp0)K - NBB=123 106 More CP eigenstate final states still to be added… More statistics needed to constrain g FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 8

  9. Gronau-London-Wyler Method Results: B+ D1*0K+ statistical significance 5.6 σ Acp=0.07±0.14±0.06 Acp=-0.27±0.25 ±0.04 Acp=-0.11±0.14 ±0.05 B+ D*02K+ statistical significance 4.5 σ Acp=0.26±0.26±0.03 250 fb-1 FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 9

  10. The Atwood-Dunietz-Soni Method D decay into flavor state dB dD Count B candidates with opposite sign kaons Input: Phys.Rev.Lett.91:171801,2003 D decay strong phase dDunknown FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 10

  11. B- D(*)0ADS(K+π-)K- at D*0(D0g)K D0K D*0(D0p0)K NBB=227 106 D D*(Dπ) D*(D) No significant signal in current dataset FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 11

  12. B- D(*)0ADS(K+π-)K- at K Yields from ΔE fits 30.7 ± 8.8 10178 ± 104 K K 17.8-3.1 = 14.7±7.6 events (3.1 evts. peaking B background) Yields from ΔE fits 17.8 ± 7.1 535.0 ± 25.9 FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 12

  13. ADS Constraints on rB from and D0K RADS RADS RADS can be translated to rB< 0.28 (90% CL) However, not easy to directly determine g FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 13

  14. The D(*)0(D03-body)K+ Dalitz Method Sensitivity to g If bothD0andD0decay into the same final state,B+ D0K+ and B+ D0K+ amplitudes interfere. Mixed state is produced: Phase θ is a sum of strong and weak phases: for B±  D0K± Use 3-body final state, identical for D0and D0: Ksπ+π-. Dalitz plot density: (r, , δ) can be obtained with simultaneous fit of B+ and B- data. Isobar model for f(m2+ ,m2- ) can fix phase variationδD across Dalitz plot. Only two-fold ambiguity in g extraction FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 14

  15. D0(Ksππ)K+Dalitz Fit from CA K*(892) Plot of mpipi r(770) DCS K*(892) Assumes no D-mixing, no CP violation in D decays! Belle’s is similar: FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 15

  16. D(*)0(Ksππ)K+yields from and 40 8 83 11 261 19 209 16 D0K Mbc(GeV) 58 8 D*0(D0p0)K Mbc(GeV) • Fit theD0 Dalitz plots using unbinned maximum likelihood fit. • D0 model fixed. • Free parameters (r, φ3, δ) D*0(D0g)K FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 16

  17. Dalitz Method Constraints on  from 180 A posteriori rB with uniform a priori: g 0 D0K- D0K- 68% 95% -180 0. 0.3 0.3 rB D0 modes alone = (73±45±10±10)º As for the D* modes: There is a phase shift between D* D0π and D* D0γas noted in hep-ph/0409281. The error on  decreases significantly when this is accounted for! FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 17

  18. Dalitz Method Constraints on  from Errors using toy MC experiments and frequentist approach FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 18

  19. Sin(2β+) from D(*)π/D(*)ρ Time dependent analysis ~l2 ~l4 favored bc amplitude suppressed bu amplitude time-dependent CP violation arises from interference of mixing and decay: Asymmetry parameters Lepton tag Exclusive reconstruction of D-p+, D*-p+,D-r+ D*r Combinatoric BB Peaking BB Continuum Partial reconstruction of D*-p+ FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 19

  20. D(*)π sin(2β+) results from Kaon tag Lepton tag D*r Combinatoric BB Peaking BB Continuum • Two experimental methods: • exclusive reconstruction of D-p+ and D*-p+ - higher signal purity, lower efficiency • partial reconstruction of D*-p+ - high efficiency, more background • results with exclusive reco.: [hep-ex/0408059] • results with partial reco.: [hep-ex/0408038] • constraints on sin(2b+g) (partial reco): • |sin(2b+g)| > 0.75 at 68% CL • |sin(2b+g)| > 0.58 at 90% CL FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 20

  21. D(*)π sin(2β+) results from sin(2φ1 + φ3) from B0 D*-π+ full reconstruction results: [PRL 93 (2004) 031802, erratum: ibid 93 (2004) 059901] Partial reconstruction results: [hep-ex/0408106] Lepton tag Assuming δ = 0 or π (factorisation), Belle obtains : FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 21

  22. D(*)0K(*)0 results from NBB=124 106 Sensitivity given by Search for b  u transition (self tagging mode) Eventually TD analysis… FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 22

  23. D(*)0K(*)0 results from +6.4 19.2 events 3.2 σ -5.8 B(B0 D0K0)= (3.72±0.65±0.37)x10-5 +1.25 B =( 3.18 ±0.32) x10-5 -1.12 +7.5 B(B0 D0K*0)= (3.08±0.56±0.31)x10-5 12.3 events 2.1 σ -5.8 B < 4.8 x 10-5 90% CL B < 0.4 x 10-5 90% CL B < 1.9 x 10-5 90% CL B0 D0K*0 &B0 D*0K*0 upper limits (Vub suppressed): +3.6 0.4 events +7.5 3.3 events -3.1 -2.1 r <0.39 D0K*0 (equvalent to rB but for neutral B) FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 23

  24. A Different Approach:Using B  D(s)(*)D(*) NEW! • Datta and London present a method for extracting gamma from measurements of D(s)(*)D(*), using a combination of branching fraction and CP asymmetry information. hep-ph/0310252 (Phys.Lett.B 584 81 (2004)) • The CP asymmetry from the tree amplitude measures sin2β, so where does  come in? •  comes from the u- and t-penguin terms:  from penguins!! • 3 observables, 5 unknowns: • Use information from 2 other sources: • β from charmonium sin2β • DsD decays for Actamplitude! solution for  (in V-V and P-P modes)  where: A slightly more complex solution for the vector-pseudoscalar modes! FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 24

  25. Constraints on gamma from D(s)(*)D(*) • One can determine constraints on  from fits to already-published data on D(s)(*)D(*). See J.A., Datta, & London, hep-ph/0410015 (submitted to Phys. Lett. B) Input measurements from… Constraints from vector-vector modes: Constraints from vector-pseudoscalar modes: (weak) Combined constraints: Constraints will improve greatly with upcoming data!… FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 25

  26. Conclusions r δ φ3 (°) φ3 (°) • Many different approaches to measuring . Information from GLW, ADS, Dalitz, sin(2β+) measurements, and D(s)(*)D(*)decays are all useful (and the future may hold new approaches…). • Incredible progress in analysis and technique development from both Belle and BaBar. • Statistics are the only thing holding us back! Many paths to … “In the world there are many different roads but the destination is the same. There are a hundred deliberations but the result is one.” --- Confucianism, I Ching Belle D0K Dalitz Combined BaBar+Belle D(s)(*)D(*) BaBar GLW+ADS+D0K Dalitz 68 %C.L. 95 % C.L. FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 26

  27. Backup Slides

  28. D0(Ksππ)K+Dalitz Fit from M (GeV 2 ) Ksπ – 2 Assumes no D-mixing, no CP violation in D decays FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 15

  29. D0(Ksππ)K+yields from and K*(892) bands B- D0K- B+ D0K+ 73 events 73 events 40 8 83 11 B+ D*0K+ B- D*0K- 19 events 20 events 261 19 D0K Mbc(GeV) D*0(D0p0)K Mbc(GeV) • Fit theD0 Dalitz plots using unbinned maximum likelihood fit. • D0 model fixed. • Free parameters (r, φ3, δ) D*0(D0g)K FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 16

  30. Dalitz Method Constraints on  from r (φ3, δ) and (φ3+π, δ+π) ambiguity δ (°) φ3 (°) φ3 (°) Errors using toy MC experiments and frequentist approach B+ D*0K+: B+ D0K+: +0.19 +0.10 -0.17 r=0.20 ± 0.02(syst) ± 0.04(model), φ3=51±46°±12°(syst) ±11°(model), δ=302±46°±11°(syst) ±21°(model) CP violation significance: 23% r=0.26 ± 0.03(syst) ± 0.04(model), φ3=86±23°±13°(syst) ±11°(model), δ=168±23°±11°(syst) ±21°(model) CP violation significance: 97% -0.14 +17° Combined:φ3=77±13°(syst) ±11°(model), rB = 0.26± ± 0.03(syst) ± 0.04(model), 95% CL interval: 26°<φ3<126° (incl. systematic error) CP violation significance: 95% -19° 11 15 FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 18

  31. D(*)π sin(2β+) results from sin(2φ1 + φ3) from B0 D*-π+ partial reconstruction Lepton tag To extract S+ and S- we fix τB and Δm at their world average values, after constrainnig wrong tag fraction w± obtained from previous fit.. Fit result S+ = 0.035 ± 0.041 ± 0.018 S- = 0.026 ± 0.040 ± 0.018 Assuming δ = 0 or π (factorisation), Belle obtains : FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 21

  32. A Different Approach:Using B  D(s)(*)D(*) • Datta and London present a method for extracting gamma from measurements of D(s)(*)D(*), using a combination of branching fraction and CP asymmetry information. hep-ph/0310252 (Phys.Lett.B 584 81 (2004)) • The CP asymmetry from the tree amplitude measures sin2β, so where does  come in? •  comes from the u- and t-penguin terms: FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 25

  33. How can D(s)(*)D(*)decays measure gamma? • For a given B D(*)D(*)decay, there are 3 observables: a branching fraction, a direct CP asymmetry, and a time-dependent CP asymmetry (3 of each – one for each helicity state – in the case of D*+D*-): • This is 3 equations in 5 unknowns. More information required… • The additional information can be obtained by inputting two things: 1) beta, as determined from charmonium decays, and 2) branching fractions of B Ds(*)D(*)decays. • SU(3)-breaking in the relation between D(*)D(*)and Ds(*)D(*)can be parameterized by the ratio of decay constants Δ= fDs(*)/fD(*) FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 26

  34. Extracting gamma from D(s)(*)D(*)decays • The 3 equations in 3 unknowns can be solved into a single equation for : • For D*D (vector-pseudoscalar), things are a little more complicated. Six coupled equations to solve: where: FPCP-2004Oct. 7, 2004Measurement ofand 2β+J. Albert 27

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