Measurements of gamma & future projections Marco Zito CEA-Saclay, Dapnia-SPP On behalf of the BaBar and Belle Collaborations Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Why measuring  is difficult ? VtdVtb * In the Wolfenstein phase convention,  is the angle between Vub and Vcb. The ratio Vub/Vcb enters all interference terms sensitive to  : small asymmetry or few events ! VudVub * a/f2 g/f3 b/f1 VcdVcb * Strategies : γ : B->DK : (GLW) Small asymmetry : many modes B->DK (ADS) Large asymmetry : few events B->DK Dalitz plot analysis (previous talk) BD(*) Small asymmetry : partial + full reconstruction Other methods for measuring sin(2 β+γ)  (2 β+γ) Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Suppressed amplitude: g with B- D0K- decays B+ b u c s K+ D0 g s Suppressed amplitude: b  u transition Color suppression u K+ Favored amplitude b c B+ D0 u u Interference (and direct CP violation) may occur if D° and D° decay in the same final state f : f can be CP eigenstate (+-, K+K-, Ks° …) Gronau, London, Wyler (GWL) method f =DCSD for D° (K+-) and CFD for D° (K+-) Atwood, Dunietz, Soni (ADS) or f=3 body final state : Dalitz plot analysis (Giri, Grossman, Soffer, Zupan) (previous talk) DCSD : Doubly Cabibbo Suppressed Decay CFD : Cabibbo Favoured Decay Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

The GLW Method & observables Clean but statistically limited: Bf(B-→D0K-)  Bf(D0 → cp)  10-6 Asymmetry B-/B+ for CP=+1/-1 Ratio of Bf for CP/non CP 8 fold ambiguity on g ACP ACP- g=60o RCP RCP+ g=60o g=30o rB=0.1 g=30o R C P + ¡ 2 = 1 r B RCP- ACP+ g=90o g=90o Weak sensitivity to rB Strong phase d (radians) Beauty 06, Oxford, 27 Sept. 2006 Marco Zito Strong phase d (radians)

Measurement techniques (B- D0K-) For D(*)0K use Cancellation of many systematics Reconstruct B→D0h with D0→Kp [NON CP], D0 → K+K-,p+p- [CP+] and D0 → K0sp0 (K0sw,K0sf) [CP-] Eliminate background from qqbar/ccbar events using Neural Net or Fisher discriminants based on event shape variables Fit of R(K/p) based on kinematic variables (DE) and PID (for each mode / charge) B →D0p B →D0K Excellent π-K separation thanks to Dirc! Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

BaBar GLW results B→D0K* B→D0K B+ CP+ B- CP+ B+ CP- B- CP- 232 106 BB̿ D0K D0p 148 CP- PRD 73, 051105(R) (2006) B→D0K 131 CP+ A C P ¡ = : 2 6 § 4 1 + 8 9 R 5 B→D0K* PRD 72 (2005) 071103 B+ CP+ B- CP+ B+ CP- B- CP- 14.8 B CP- 37.6 B CP+ RCP+ = 0.90±0.12±0.04 RCP- = 0.86±0.10±0.05 ACP+ = 0.35±0.13±0.04 ACP- = -0.06±0.13±0.04 RCP+ = 1.96±0.40±0.11 RCP- = 0.65±0.26±0.08 ACP+ = -0.08±0.19±0.08 ACP- = -0.26±0.40±0.12 Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

RCP and ACP World Averages D0K D*0K D0K* CP+ CP+ CP- CP- CP+ CP+ CP- CP- CP+ CP+ CP- CP- GLW measurements alone do not constraint g/f3. Information on g and rB from combination with other methods. More statistics will help! Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Combine dominant b→c transition with DCS D0 decay g/f3 with the ADS method dB dD A1 A2 Combine dominant b→c transition with DCS D0 decay A (B-→[K+p-]DK-)  rBei(dB-g)+rDe-idD Small BF(~10-7), but A2 = O(A1): expect large CPV Observables: Measure [K+p-]K- and [K-p+]K- rates Large sensitivity to rB input: Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

BD(*)0K(*), DCS D0K+ - decays 232 *106 BB pairs D(*)0K: PRD 72, 032004 D0K*: PRD 72, 071104 BD(*)0K(*), DCS D0K+ - decays ~no signal  no constrain on  (alone), only limits on RADS and rB (using |cos(B+D)cos|<1) mES (GeV/c2) Events RADS rB D0K <0.029 90% C.L. <0.23 D*0K <0.023 (D*0D00) <0.045 (D*0D0) <0.16 D0K* 0.046±0.032 1 0.20±0.14 Already presented at EPS05 Published during last year Similar relations for D*0 Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

B-→D0[Kp]K- ADS(Belle) hep-ex/0508048 386  106 B Bbar pairs Despite larger statistics, suppressed channel not visible either: D0K RADS=(0.0+8.4 -7.9±1.0)x10-3 maximum mixing (φ3=0, δ=180°): rB<0.18 @ 90% C.L. Here too, more statistics will help! Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

BD0K, DCS D0K+ - 0 ( ) R NEW! 226 *106 BB pairs BABAR-CONF-06/007 NEW! BD0K, DCS D0K+ - 0 Similar to previous analysis with f= K+p- p0. Complication for  extraction from |AD|,D variation across the D0 Dalitz plane: ( ) g cos 2 ] [ D B ADS r K f R + = ® G º - C C unknown, |C|≤1 rD2  (D0K+p-p0)/ (D0K-p+ p0)| = (0.214±0.011)% (BaBar, preliminary) Compared to f=K+p- :: more background but smaller rD  similar sensitivity to rB2 (limit from RADS using | Ccos | ≤ 1) Signal yield from fit RADS<0.039 (95% C.L.) Experimental RADS likelihood rB<0.185 (95% C.L.) Bayesian L(rB) (flat rB and |Ccos| prior PDFs) Also expression for CP asymmetry is slightly modified. Not reported here since it is not measured yet. Rads deve essere colorato come rB Fare una slide di backup su Incorporazione sistematiche in L(Rads) Determinazione L(rB) Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Measurement of sin(2b+g) in B0D(*)p Suppressed amplitude through b  u transition Favored amplitude Strong phase difference CP violation from interference of mixing (weak phase= 2b) and decay (weak phase )  interference terms measures sin(2b+g) Theoretically clean : no penguin contribution, strong phase measurable Small time dependent asymmetry (o(4%)) r is an external input CKM angle B0 mixing f B0 Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Experimental technique (4s) bg = 0.56 Tag B sz ~ 160 mm Reco B sz ~ 80 mm Dz K D- K+ + - e- e+ B0  Time dependent analysis Partial or Full reconstruction Unmixed D- p+ r = 0.02  = 0 sin(2+) = 1 w=0 Mixed D- p+ r = 0 Unmixed D+ p- D*-p+ mixed Mixed D+ p- S = (a  c) + b Beauty 06, Oxford, 27 Sept. 2006 Tag side CP violation effect Marco Zito

Most precise measurement to date 232  106 B Bbar B0D* partially reconstructed (BaBar) Increase the statistics by reconstructing only the two pions - 18710 D* events tagged with a lepton - 70580 D* events tagged with a kaon Most precise measurement to date CP asymmetry PRD 71, 112003[2005] Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

sin(2+) from B0D(*),D 232  106 B Bbar sin(2+) from B0D(*),D Results from B0→ D(*)p, Dr full reco : Combine partial and fully reco results for the a and clep parameters and use the r parameters from SU(3) symmetry hep-ex/0602049 r(D) = 0.019 ± 0.004 r(D*) = 0.015 ± 0.006 r(D) = 0.003 ± 0.006 D+p- 15038 evts, D*p 14002 evts 30% theoretical error on rf D*r 8736 evts |sin(2+)| > 0.64 @ 68 % C.L. |sin(2+)| > 0.42 @ 90 % C.L. aDp = -0.010  0.023  0.007 aD*p = -0.040  0.023  0.010 aDr = -0.024  0.031  0.009 90% CL 68% CL Frequentist confidence level cDp = -0.033  0.042  0.012 cD*p = +0.049  0.042  0.015 cDr = -0.098  0.055  0.018 Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

sin(2φ1+φ3) (Belle) D*π partial rec D*π full rec - full reconstruction 357 fb-1 ~ 392  106 B Bbar sin(2φ1+φ3) (Belle) PRD 73 092003 (2006) - full reconstruction D*π partial rec (only lepton tags) D*π full rec Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

sin(2φ1+φ3) S +(D*π)=0.049±0.020±0.011 S –(D*π)=0.031±0.019±0.011 Full-rec + partial-rec Full-rec CPV significance (S++S-): 2.5σ [D*p], 2.2s [Dp] S+ S+ |sin(2φ1+φ3)|>0.46 (0.13) Using RD*p = 0.0210.007  0.006 |sin(2φ1+φ3)|>0.48 (0.07) at 68% (95%) CL 1s 2s 3s Using RDp = 0.0210.004  0.006 Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

HFAG averages a and c parameters a = 2r sin(2b+g) cos (d) clept = 2 r cos(2b+g) sin(d) a = (-1)l(S++S-)/2 [belle] More statistics will help! Individual measurements of a close to the 3s statistical significance! c small  dDp and dD*p small? Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Bf(B0 → Ds(*) p) W-exchange diagrams are small hep-ex/0604012, submitted to PRL 230  106 B Bbar Ds→ fp, K0SK+, K*0K+ B(B°→Dsπ) = (1.3±0.3 ±0.2)x10-5 B(B°→D*sπ) = (2.8±0.6 ±0.5)x10-5 N(Ds+p-)=48 N(Ds*+p-) = 42 Measure also B(B°→DsK) = (2.5±0.4 ±0.4)x10-5 B(B°→D*sK) = (2.0±0.5 ±0.4)x10-5 W-exchange diagrams are small SU(3) r(Dp) = (1.3  0.2  0.1 ) 10-2 r(D*p) = (1.9  0.2  0.2 ) 10-2 Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

B0→D(s)(*)+a-0(2) b  c amplitude ~ suppressed in B0→D(*)+a-0(2) Theory papers: Phys.Lett.B 517,125 (2001) JHEP 0106:067 (2001 PRD 67, 014011 (2003) Other new ideas B0→D(s)(*)+a-0(2) b  c amplitude ~ suppressed in B0→D(*)+a-0(2) Potentially large CP-asymmetry b  c a0(2) l b  u fa0(2)<<fp a0(2) Test B of the suppressed decay using the SU(3) related mode: Ds(*) B0→Ds(*)+a-0(2) a0(2) fD= decay constant Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

B0->Ds(*)+a-0(2) No evidence for signal 232  106 B Bbar hep-ex/0512031 (2005) Submitted to PRD B0->Ds(*)+a-0(2) Theory prediction: No evidence for signal Upper limits for BF are smaller than theoretical expectation. New Mode not usable to measure sin (2β+γ) B(B°→Dsa0) = 1.9x10-5 B(B°→ Ds a2 ) = 19x10-5 B(B°→ D*s a0) = 3.6x10-5 B(B°→ D*s a2) = 20x10-5 Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

sin(2b+g) with B0 /B0 → D(*)0K(*)0 3 (2+2) e-ig l2 Vub and Vcb mediated amplitudes both color suppressed: Expect large asymmetries But smaller branching fractions than for Dp l ~ 1 A1VcbVus A2= rB A1e-igeid Critical parameter: ? Measure the different D(*)0K(*)0 Bf Measure rB in self-tagging final state D0K*0 (assuming that rB for DK*  same as rB for DK0) Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

No signal in the suppressed mode Equivalent Belle result on 86M BB D(*)0K(*)0 7712 D0K*0 D0K*0 D0K0 10414 D*0K0 175 232  106 B Bbar To be submitted to PRD No signal in the suppressed mode rB value smaller than theo. expectation Not useful to measure  value yet! Equivalent Belle result on 86M BB PRL 90, 141802 (2003) Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Conclusions Many new or updated results GLW: BaBar (Belle) with 232 (275) million B’s Clean but statistically limited. Best precision is in the D0K channel ADS: 232 (386) million B’s rB is small: rB(D0K)<0.18, rB2(D*0K)<0.162 @ 90% CL Hints of larger rB in the DK* channel need confirmation 2b+g with D(*)p/r: 232 (386) million B’s Challenging analysis but good agreement between experiments Observation of CPV @ 3s is within reach…. Most results statistically limited: Future large luminosity data set will help Premium on coherent global analysis of world data set Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Belle GLW results R = 1 : 3 § 6 8 7 4 A 5 2 R = 1 : 4 § 2 5 6 3 A 8 70.2 ± 14.7 79.2 ± 15.7 D0K+ D0K- Belle GLW results CP+ CP+ PRD 73, 051106(R) (2006) 275x106 B Bbar pairs 149.5 ± 19.0 CP- evts B→D0K RCP+ = 1.13±0.16±0.05 RCP- = 1.17±0.14±0.14 ACP+ = 0.06±0.14±0.05 ACP- = -0.12±0.14±0.05 D0K+ D0K- R C P + = 1 : 3 § 6 8 ¡ 7 4 A 5 2 CP- CP- B→D*0K (D*0→ D0p0) RCP+ = 1.41±0.25±0.06 RCP- = 1.15±0.31±0.12 ACP+ = -0.20±0.22±0.04 ACP- = 0.13±0.30±0.08 R C P + = 1 : 4 § 2 5 6 ¡ 3 A 8 43.9 ± 10.2 32.7 ± 10.0 D*0K D*0K CP+ CP- Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

B0D(*)p :partial reconstruction Use only the fast and soft pion tracks : no D° reconstruction ! B0 D*- +f D0 -s X F E(F)~.5 mB Combine the fast pion (2.1<p<2.4 GeV/c) with a slow pion (p<250 MeV). Compute the mass Mmiss of the recoiling object (r.m.s. 3 MeV) 1 rad S P(s-)<250 MeV D0 The unreconstructed D0 complicates vertexing and tagging Most of the D0 decay product inside this cone Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

B0D(*)p :the BaBar event sample B invariant mass Exclusive reconstruction(ER) : N(D)=5200 N(D*)=4700 BaBar Based on a 81 fb-1 sample Partial reconstruction(PR) : N(D*)=6400 (lepton tag) N(D*)=25100 (kaon tag) Lepton tagged Kaon tagged signal combinatoric BaBar Continuum Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

CP violation on tag side - Potential competing CP violating effects from b → u transitions on the tag side if a Kaon is used to tag the B Slept 2 r (sin(2b+g  d) lepton Tags Kaon Tags SK 2 r (sin(2b+g  d) + 2 r’(sin(2b+g  d’) Rewrite as S = (a  c) + b a = 2r sin(2b+g) cos (d) c= cos(2b+g) [2r sin(d)+2r’sin(d’)] b = 2r’ sin(2b+g) cos (d’) free of tag-side CPV Lepton tags free of tag-side CPV BaBar: fit CP observables a and clepton (free of tag-side CPV). Belle: Fit S+ and S- (partial reco: only lepton tags) Full reco: use all tags but measure tag side CPV parameters S+’ and S-’ from a sample of D*ln evts [only tag side cpv) a = (S++S-)/2 c = (S+-S-)/2 Beauty 06, Oxford, 27 Sept. 2006 Marco Zito

Constraints on rB from D*0K B-→D(*)0[K+p-]K(*)- ADS 232 106 BB̿ PRD 72 (2005) 032004 Suppressed channel not visible in D(*)0K RADS < 0.045 RADS < 0.023 R ¤ K ¼ ; D ° < : 4 5 RADS < 0.029 R K ¼ < : 2 9 R ¤ K ¼ ; D < : 2 3 B→ D*0K(D*0→D0g) B→ D*0K (D*0 → D0p0) B→ D0K B→ D0K* R ¤ K ¼ ; D + ° 2 ¡ r = B Bondar & Gershon PRD70,091503(2004) 4.2  2.8 ev  r*B2<(0.16)2 @ 90% C.L. Constraints on rB from D*0K RADS=0.046±0.031±0.008 R S K ¼ = : 4 6 § 3 1 8 Beauty 06, Oxford, 27 Sept. 2006 PRD 72 (2005) 071104 Marco Zito

BaBar constraints on rB D0K*+ RKπ= r2B +r2D + 2rB rD cos(γ) cos(δB+ δD) R K ¼ = r 2 B + D c o s ( ° ) ± g [0,p] & (dD+dB)[0,2p] D0 K GLW ADS combination 1-CL 1s 48o<g<73o RKπ<0.029 2s 3s rSB For maximum mixing (g/φ3=0, δ=180°): rB<0.23 @ 90% C.L. rSB= Beauty 06, Oxford, 27 Sept. 2006 Marco Zito DK*, GLW+ADS combined