Max Baak, NIKHEF on behalf of the BABAR and BELLE Collaborations Measurements of  at BABAR and BELLE Max Baak, NIKHEF on behalf of the BABAR and BELLE Collaborations Beauty 2005, Assisi

Outline Measurements of  using BD(*)K(*) GLW Method ADS Method D0 Dalitz Method (GGSZ) Measurements of sin(2+) using B0D(*)  / Outlook  

 in the Unitarity Triangle (,) CKM Unitarity Triangle (0,0) (1,0) Expect  ≈ (60 ± 6)° from SM fit to: sin2, |Vub/Vcb|, md, ms, k Most challenging angle to measure experimentally: Low branching fractions Low reconstruction efficiencies Small interferences The only solution with  is statistics

 from B-  D(*) K- K– D0 B– D0 B– K– Access  via interference between B-  D(*)0 K- and B-  D(*)0 K-. Color-allowed b c amplitude Color-suppressed b u amplitude u u K– D0  f Vus* s Vcs* W – b c b c amplitude ratio rB relative weak phase  and strong phase B W – Vub s B– D0  f B– K– Vcb u u Reconstruct D in final state f accessible both to D0 and D0. Will discuss 3 methods with different final states f in this talk: GLW Gronau – London – Wyler 2. ADS Atwood – Dunietz – Soni 3. GGSZ Giri – Grossman – Soffer – Zupan Belle collaboration Critical parameter rB~ 0.1 for sensitivity to  ! In order to determine rB, , B simultaneously, need to measure as many D(*)0 modes as possible.

Preface: Analysis Techniques 1. B-meson identification 2. Combinatoric e+e–  qq bkg suppression mES E = EB*–E*beam data MC E Event topological variables combined in Neural Network or Fisher discriminant 3. K/ separation (Cherenkov angle / TOF) 4. Time-dependent measurements (only B0/B0) – K– BaBar Excellent separation between 1.5 and 4 GeV/c D0 B0 KS tag side e+ e+ B0 lepton Coherent B0B0 production from (4S) boost  ≈ 0.55/0.42 allows t measurement

GLW Method Reconstruct D meson in CP-eigenstates (accessible to D0 and D0) Theoretically very clean (“golden mode”) to determine  Relatively large BFs (10-5), small CP asymmetry  3 Independent measurements (A+R+ = -A-R-) and 3 unknowns (rB, , B) CP even modes: K+K-, +- CP odd modes: KS0, KS, KS, KS Phys. Lett. B253, 483 (1991); Phys. Lett. B265, 172 (1991); Phys. Lett. B557, 198 (2003)

GLW Method Results PRL92,202002, 214M BB B-CONF-0443, 275M BB 95  15 events 76  13 events 114  21 events 167  21 events B-CONF-0443, 275M BB

GLW Results Combined D0CP K− BaBar Belle Average (HFAG) RCP+ 0.87 ± 0.14 ± 0.06 0.98 ± 0.18 ± 0.10 0.91 ± 0.12 RCP− 0.80 ± 0.14 ± 0.08 1.29 ± 0.16 ± 0.08 1.02 ± 0.12 ACP+ +0.40 ± 0.15 ± 0.08 +0.07 ± 0.14 ± 0.06 +0.22 ± 0.11 ACP− +0.21 ± 0.17 ± 0.07 –0.11 ± 0.14 ± 0.05 +0.02 ± 0.12 PRL92,202002, 214M BB B-CONF-0443, 275M BB D*0CP K− (D*D0CP0) BaBar Belle Average (HFAG) RCP+ +1.06 ± 0.26 + 0.10 1.43 ± 0.28 ± 0.06 1.24 ± 0.20 RCP− 0.94 ± 0.28 ± 0.06 0.94 ± 0.29 ACP+ –0.10 ± 0.23 + 0.03 –0.27 ± 0.25 ± 0.04 –0.18 ± 0.17 ACP− +0.26 ± 0.26 ± 0.03 +0.26 ± 0.26 PRD71,031102, 123 M BB B-CONF-0443, 275M BB − 0.09 − 0.04 No useful constraints on  yet due to small branching ratios and limited statistics. D0CP K*− (K*-  KS−) BaBar Average (HFAG) RCP+ 1.77 ± 0.37 ± 0.12 1.77 ± 0.39 RCP− 0.76 ± 0.29 ± 0.06 + 0.04 (*) Belle 0.76 + 0.30 ACP+ –0.09 ± 0.20 ± 0.06 –0.02 ± 0.33 ± 0.07 –0.07 ± 0.18 ACP− –0.33 ± 0.34 ± 0.10 ± (*) 0.19 ± 0.50 ± 0.04 –0.16 ± 0.29 hep-ex/0408069, 227M BB hep-ex/0307074, 96M BB − 0.14 − 0.33 (0.15±0.10) x (ACP--ACP+) (*) CP-even pollution in the CP-odd channels

ADS Method B–  D0 K– B–  D0 K– K+– K+– Reconstruct D in final state K - small BF (10-6) Amplitude:  Amplitudes comparable in size  large CP violation Count B candidates with opposite sign kaons! Phys. Rev. Lett. 78, 3257 (1997) suppressed favored B–  D0 K– B–  D0 K– K+– K+– interference favored suppressed PDG, Phys.Lett. B592, 1 (2004) D : D decay strong phase unknown. Scan over all values. 2 observables vs 3 unknowns: rB, , B

ADS Method Results BABAR: 227M BB BELLE: 275M BB −3.2 −5.3 −0.009 preliminary 275 M BB PRL 94, 091601 B+ D0K+ B+ D0K+ N = 4.7 +4.0 N = 8.5 +6.0 (2.3) −3.2 −5.3 RADS = 0.013 +0.011 RADS = 0.023 +0.016 ± 0.001 −0.009 −0.014 AADS = +0.88 +0.77 ± 0.06 –0.62 preliminary B+  [D00]D* K+ BELLE: 275M BB N = −0.2 +1.3 −0.8 RADS = −0.002 +0.010 −0.006 No signal observed! B+  [D0]D* K+ preliminary N = 1.2 +2.1 −1.4 RADS = 0.011 +0.018 −0.013 hep-ex/0408028 -0.1 0.1 E (GeV)

The smallness of rB makes the extraction of  with GLW/ADS difficult! ADS Method Results 0 < D < 2 rd ± 1 48° <  < 73° same, any  RADS # Events 227 M BB hep-ex/0408028 Belle (90% CL) B+ D0K+ RADS = 0.013 +0.011 −0.009 275 M BB PRL 94, 091601 BaBar (90% CL) B+ D0K+ RADS = 0.023 +0.016 ± 0.001 −0.014 DK: rB < 0.23 D*K: r*B2 < (0.16)2 DK: rB < 0.27 @ 90% C.L. @ 90% C.L. BaBar RADS  1 The smallness of rB makes the extraction of  with GLW/ADS difficult!

GGSZ Method K– D0 B– B– K– D0 Phys. Rev. D68, 054018 (2003) Color-allowed b c amplitude Color-suppressed b u amplitude KS u u K– D0 Vus* + s Vcs* - W – b c b c KS interference W – Vub s B– B– K– Vcb D0 + u - u Reconstruct D in final state: KS +- (not a CP-eigenstate) Employs K-K mixing (“cheap” decay-mode: high BF ~2.2x10-5 ) Final state accessible through many intermediate non-CP states. Need Dalitz analysis to separate resonance interferences!

GGSZ Method 2 ± = D0 D0 - + KS KS + - D decay amplitude f consists of sum of many resonances (more on next slide). Amplitude f parameterized in terms of Dalitz variables m+2 and m-2 Decay rates  of B+ and B- written as: u u - + d d W W c s c s KS KS D0 D0 + - u u 2 ± = Simultaneous fit to D  KS +- Dalitz planes of B+ and B- to extract rB, , and 

Isobar formalism, no D mixing, no CPV in D decays D0  KS + - Dalitz Model To extract rB and  need high-precision D decay model f (m+2, m-2) Obtain f (m+2, m-2) using fit to “tagged” D0 sample:  Use large D*+ D0+ sample. Charge of the pion gives flavor of D. Isobar formalism, no D mixing, no CPV in D decays D*+ D0+, 81.5k events from 91 fb-1, purity 97% hep-ex/0504039 2 = 3824/ 3054 =1.25 K*(892) DCS K*(892) 0(770) 0(770) DCS K*(892) 13 resonances (2 ), 3 DCS partners, 1 non-resonant component

D0  KS + - Dalitz Model Belle: indentical approach hep-ex/0411049 Belle: indentical approach Include two more DCS resonances: K*+(1410) - , K*+(1680)- 13 resonances (2 ), 5 DCS partners, 1 non-resonant component D*+ D0+, 186.9k events, purity 97% K*(892) DCS K*(892) m+2 (GeV2/c4) m-2 (GeV2/c4) 0(770) m-2 (GeV2/c4) 2 =2543/1106 =2.30 m2 (GeV2/c4) m+2 (GeV2/c4)

Dalitz sensitivity scan to  CA: Cabibbo Allowed DCS: Doubly-Cabibbo Suppressed CS: Color Suppressed Sensitivity to  (MC) =75°, =180°, rB =0.125 d2 ln L/d2 CA: D0K(892)*-+ CS: D0KS0(770) DCS: K0(1430)*+ - DCS: D0K(892)*+- D0 CA: K0(1430)*+ -

GGSZ Method Results The two plots would be the same without CP violation. Are they?

BaBar GGSZ Method Results hep-ex/0504039 DK D*0(D00)K D*0(D0)K Mode Signal (events) B+D0K+ 282 ± 20 B+D*0K+ (D*0D00) 90 ± 11 B+D*0K+ (D*0D0) 44 ± 8 m-2 B+ B+ B+ m+2 m-2 BABAR: 227M BB m+2 m-2 B– B– m-2 DCS K*(892) B– m+2 m+2

Belle GGSZ Method Results hep-ex/0411049 DCS K*(892) - thick black line: with interference - thin grey line: without interference BELLE: 275M BB Mode Signal (events) Bkg.frac. (%) BD0K− 209 ± 16 25 ± 2 BD*0K− 58 ± 8 13 ± 2 BD0K*− 36 ± 7 27 ± 5 hep-ex/0504013

BaBar GGSZ Method Results 68% 95% Frequentist CLs BABAR: 227M BB DK hep-ex/0504039 preliminary Frequentist CLs DK : rB = 0.118 ± 0.079 ± 0.034 +0.036 –0.034 B = ( 104 ± 45 )° +17 +16 –21 –24 D*K : rB* = 0.169 ± 0.096 +0.030 +0.029 –0.028 –0.026 D*K B* = ( 296 ± 41 ± 15 )° +14 –12  = ( 70 ± 31 ) ° +12 +14 –10 –11 stat. syst. Dalitz

Belle GGSZ Method Results rB hep-ex/0411049 BELLE: 275M BB DK hep-ex/0504013 B (deg) Frequentist CLs DK : DK rB = 0.21 ± 0.08 ± 0.03 ± 0.04 B = ( 157 ± 19 ± 11 ± 21 )°  = ( 64 ± 19 ± 13 ± 11 )° rB[D*] D*K D*K : B[D*] (deg) rB* = 0.12 +0.16 ± 0.02 ± 0.04 -0.11 B* = ( 321 ± 57 ± 11 ± 21 )° D*K Promising results!  = ( 75 ± 57 ± 11 ± 11 )° DK* : rB(K*) = 0.25 +0.17 ±0.09 ±0.04 ±0.08 (*) -0.18 rB[K*] DK* B(K*) = ( 353 ±35 ±8 ±21 ±49 )° B[K*] (deg) (*)  = ( 112 ±35 ±9 ±11 ±8)° (*) DK* Combined result of DK and D*K:  = ( 68 +14  13  11 ) ° -15 stat. syst. Dalitz (*) Possible bias caused by a contribution from non-resonant B–→ DKS–.  (degrees)  (degrees)

rB(*) World Average BaBar ADS limit pushing rB down. 0 < D < 2 rd ± 1 48° <  < 73° same, any  [ no improved constraint when adding  from CKM fit ] RADS Frequentist CLs Belle ADS (90% CL) BaBar ADS (90% CL) Belle Dalitz BaBar Dalitz Using GLW, ADS, GGSZ results Bayesian CLs rB [BDK] 68% 95% BaBar ADS limit pushing rB down. Belle Dalitz value (0.21) relatively large. 0.10  0.04 0.09  0.04

CP violation in B0  D(*) / CP violation through B0-B0 mixing and interference of amplitudes:  CP violation proportional to ratio r of amplitudes Small: r  |V*ubVcd / VcbV*ud|  0.020  Large BF’s, at level of 1%  No penguin pollution  theoretically clean Relative weak phase  from bu transition Relative strong phase  Suppressed amplitude through b  u transition Favored amplitude u,c,t u,c,t Strong phase difference CKM Unitarity Triangle  g

sin(2+) from B0  D(*) / Time evolution for B0 decays and B0 decays (Rmix) to D(*)/: CP asymmetry: small sine terms  Need S+ and S- together to give (2+) and  From D(*)/ sine coefficients, 4 ambiguities in (2+) Express result as |sin(2+)| SM: sin(2+) ~ 1 Factorization theory:  is small SMALL sine terms

sin(2+) Caveat: determination of r(*) Simultaneous determination of sin(2+) and r(*) from time-evolution not possible with current statistics  need r(*) as external inputs ! Estimate r(*) from B0  Ds(*)+-/- using SU(3) symmetry [1] Using:  [1] I. Dunietz, Phys. Lett. B 427, 179 (1998) SU(3) [2] Inputs used in CKMFitter/ UTFit : r(D) = 0.019 ± 0.004 r(D*) = 0.015 ± 0.006 r(D) = 0.003 ± 0.006 We add 30% theoretical errors to account for: Unknown SU(3) breaking uncertainty Missing W-exchange diagrams in calculation Missing rescattering diagrams (Can be estimated with B0Ds(*)+K-) no theoretical errors included [2] fD : decay constants

BaBar: Inclusive B0  D*  BABAR: 227M BB Using a,b,c parametrization: D* partial reconstruction: fast Tag side interference: r’, ’ are the ratio and phase difference between the bu and bc amplitudes in the Btag decay. r’0 in lepton tags. PRD68, 034010 lepton tags - High statistics! - Large backgrounds preliminary hep-ex/0504035 preliminary lepton tags peaking D* kaon tags combinatoric BB other peaking BB continuum 18710 ± 270 lepton tags 70580 ± 660 kaon tags

Belle: Inclusive B0  D*  hep-ex/0408106 preliminary BELLE: 152M BB Belle: only uses lepton tags (no tag-side interference) sum signal bkg. Same Flavor: mixed events Opposite Flavor: unmixed events 8322 signal lepton tags

BaBar: Exclusive B0  D(*) / BABAR: 110M BB Phys.Rev.Lett. 92:251801(2004), 88 M BB Exclusive reconstruction of channels: - B  D  - B  D*  - B  D     - Full reco.: ~10x less efficient; far lower backgrounds - Same sensitivity to sin(2+) as inclusive approach lepton tags hep-ex/0408059 preliminary

Belle: Exclusive B0  D(*)  PRL 93 (2004) 031802; Erratum-ibid. 93 (2004) 059901 BELLE: 152M BB Exclusive reconstruction of channels: - B  D  - B  D*  Uses B  D*l as control sample for tag-side interference   cleanest tags (*) After tagging and vertexing

No clear CP violation yet! HFAG on |sin(2+)| HFAG Averages: No clear CP violation yet!

Combined Limit on |sin(2+)| Bayesian CLs www.utfit.org 68% 95% Combined limit on |sin(2+)| : Assuming 30% error on r(*) for SU(3) breaking: CKMFitter: |sin(2+)| > 0.53 @ 68% C.L. UTFit: |sin(2+)| > 0.74 @ 68% C.L. Frequentist CLs

Outlook Many approaches to measure  have been investigated by BaBar and Belle. GLW and ADS methods don't provide strong constraints on  when considered alone. Current experimental results favour small values of rB. GGSZ results are promising! GLW+ADS+GGSZ: CKMFitter:  = [ 63 +15 ]°+ n UTFit:  = [ 64  18 ]°+ n sin(2+) from D(*)/: CKMFitter: |sin(2+)| > 0.53 @ 68% C.L. UTFit: |sin(2+)| > 0.74 @ 68% C.L. GLW+ADS+GGSZ+sin(2+): CKMFitter:  = [ 70 +12 ]°+ n All results are in good agreement with the global CKM fit ( = [ 60  6 ]°) All decay modes can use lots more statistics! High statistics expected in next years may allow BaBar and Belle to measure  to < 10°. -13 Using GLW, ADS, GGSZ results  (deg)  = 64 ± 18 ([30,100] @ 95% CL) -14

B A C K U P slides ...

BaBar: Removing the Imaginary (?) 

Belle GGSZ: Systematic Errors

B  D*-+ time-dependent evolution a) unmixed B0(t) D*-+ B0 Initial state Flavor eigenstate b) mixed B0 With bu transition No bu transition B0(t) B0 Initial state Flavor eigenstate D*-+ b) a) b) a) B  D*-+ pure cosine: r = 0 - plus sine term, 5x the expected size in data r = 0.1,  = 0 sin(2+) = 1 B  D*-+ - pure cosine: r = 0 CP asymmetry: small additional sine term Smallness of amplitude ratio r greatly reduces sensitivity to sin(2+)

() Dependency on rB BaBar and Belle show quite different sensitivities to  Both find quite different values for rB (BaBar: ~0.12, Belle: ~0.21) Different sensitivity to  caused by dependency on rB . Toy MC Studies Comparing only results of BDK stat. Sensitivity to  very dependent on critical parameter rB (~0.1)! BaBar Belle rB [DK]