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Measuring the Angle γ of the Unitarity Triangle: Approaches and Results

This presentation by J. Albert at Caltech discusses the measurement of the angle γ of the Unitarity Triangle, essential for understanding CP violation in the Standard Model. Various methods for direct measurement of γ are explored, including the Gronau-London-Wyler approach and analyses using D0K and D0K* decays. The significance of interference effects and the need for additional data in ensuring accurate determinations of the strong phase difference are highlighted. Key results and statistical constraints are presented along with future prospects for improving measurements.

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Measuring the Angle γ of the Unitarity Triangle: Approaches and Results

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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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