Beauty 06, Oxford, 27 Sept Marco Zito1 Measurements of gamma using ADS, GLW and other methods & future projections Marco Zito CEA-Saclay, Dapnia-SPP On behalf of the BaBar and Belle Collaborations

Beauty 06, Oxford, 27 Sept Marco Zito2 Why measuring  is difficult ?       V td V tb * V ud V ub * V cd V cb * In the Wolfenstein phase convention,  is the angle between V ub and V cb. The ratio V ub /V cb enters all interference terms sensitive to  : small asymmetry or few events ! Strategies : 1.γ : B->DK : (GLW) Small asymmetry : many modes 2.B->DK (ADS) Large asymmetry : few events 3.B->DK Dalitz plot analysis (previous talk) 4.B  D(*)  Small asymmetry : partial + full reconstruction 5.Other methods for measuring (2 β+ γ)  (2β+γ)

Beauty 06, Oxford, 27 Sept Marco Zito3  with B   D 0 K  decays 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 -, K s  ° …) 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) B+B+ b u u u c s K+K+ D0D0  B+B+ b u c u s u D0D0 K+K+ Suppressed amplitude: b  u transition Color suppression Favored amplitude DCSD : Doubly Cabibbo Suppressed Decay CFD : Cabibbo Favoured Decay

Beauty 06, Oxford, 27 Sept Marco Zito4 The GLW Method & observables Ratio of Bf for CP/non CP Asymmetry B-/B+ for CP=+1/-1 8 fold ambiguity on  Clean but statistically limited: Bf(B - →D 0 K - )  Bf(D 0 → CP)  R + +R - =1+r B 2 4 observables, 3 unknowns (r,δ,γ) Study f=CP eigenstate Weak sensitivity to r through

Beauty 06, Oxford, 27 Sept Marco Zito5 Measurement techniques (B   D 0 K   Reconstruct B  → D 0 h  with D 0 → K  [NON CP], D 0 → K + K -,     [CP+] and D 0 → K 0 s  0 (K 0 s ,K 0 s  ) [CP-] B → D 0 K B → D 0  Eliminate background from qqbar/ccbar events using Neural Net or Fisher discriminants based on event shape variables Fit of R(K/  ) based on kinematic variables (  E) and PID For D (*)0 K use Cancellation of many systematics Excellent  -K separation thanks to Dirc!

Beauty 06, Oxford, 27 Sept Marco Zito6 BaBar GLW results D0KD0K D0D0 148 CP- PRD 73, (R) (2006) B→D 0 K 131 CP+ A CP ¡ = ¡ 0 : 26 § 0 : 40 § 0 : 12 A CP + = ¡ 0 : 08 § 0 : 19 § 0 : 08 R CP ¡ = 0 : 65 § 0 : 26 § 0 : 08 R CP + = 1 : 96 § 0 : 40 § 0 : 11 B→D 0 K* PRD 72 (2005) B + CP+ B - CP+ B + CP- B - CP B  CP B  CP+ R CP+ = 0.90±0.12±0.04 R CP- = 0.86±0.10±0.05 A CP+ = 0.35±0.13±0.04 A CP- = -0.06±0.13±0.04 R CP+ = 1.96±0.40±0.11 R CP- = 0.65±0.26±0.08 A CP+ = -0.08±0.19±0.08 A CP- = -0.26±0.40± BB̿ R and A : functions of (r,δ,γ)

Beauty 06, Oxford, 27 Sept Marco Zito7 D0KD0K D* 0 K D0K*D0K* R CP and A CP World Averages GLW measurements alone do not constraint  3. Information on  and r B from combination with other methods. More statistics will help! CP+ CP- CP+ CP - CP+

Beauty 06, Oxford, 27 Sept Marco Zito8   with the ADS method Small BF(~10 -7 ), but A 2 = O( A 1 ) : expect large CPV BB DD A1A1 A2A2 Combine dominant b → c transition with DCS D 0 decay Observables: Large sensitivity to r B A (B - → [K +  - ] D K - )  r B e i(  B -   +r D e -i  D input: Measure [K +  - ]K - and [K -  + ]K - rates

Beauty 06, Oxford, 27 Sept Marco Zito9 R ADS =( ±1.0)x10 -3 hep-ex/  10 6 B B bar pairs hep-ex/  10 6 B B bar pairs B - → D 0  K - ADS(Belle) D0KD0K maximum interference (φ3=0, δ=180°): r B 90% C.L. Despite larger statistics, suppressed channel not visible either: Here too, more statistics will help! R ADS

Beauty 06, Oxford, 27 Sept Marco Zito10 B  D (*)0 K (*), DCS D 0  K +   decays 232 *10 6 BB pairs D (*)0 K: PRD 72, D 0 K * : PRD 72, m ES (GeV/c 2 ) Events ~no signal  no constrain on  (alone), only limits on R ADS and r B (using |cos(  B +  D )cos  |<1) R ADS rBrB D0KD0K < % C.L. < % C.L. D *0 K <0.023 (D *0  D 0  0 ) <0.045 (D *0  D 0  ) 90% C.L. < % C.L. D0K*D0K* 0.046±  0.20±  rSB=rSB= DK*, GLW+ADS combined

Beauty 06, Oxford, 27 Sept Marco Zito11 B  D 0 K, DCS D 0  K +     226 *10 6 BB pairs BABAR-CONF-06/007 Similar to previous analysis with f= K +    . Complication for  extraction from |A D |,  D variation across the D 0 Dalitz plane:   cos2 )][()][( )][()][( 220 DBDBADS rrrr KfDBKfDB KfDBKfDB KDB R        C Compared to f=K +   : more background but smaller r D  similar sensitivity to r B 2 (limit from R ADS using | Ccos  | ≤ 1) C unknown, |C|≤1 r D 2   (D 0  K      )/  (D 0  K      )| = (0.214±0.011)% (BaBar, preliminary) Signal yield from fit R ADS <0.039 (95% C.L.) Experimental R ADS likelihood r B <0.185 (95% C.L.) Bayesian L(r B ) (flat r B and |Ccos  | prior PDFs)

Beauty 06, Oxford, 27 Sept Marco Zito12 Measurement of sin(2  +  ) in B 0  D (*)  CP violation from interference of mixing (weak phase= 2  and decay (weak phase  )  interference terms measures sin(2  +  ) Theoretically clean : no penguin contribution, strong phase measurable Small time dependent asymmetry (o(4%)) r is an external input Suppressed amplitude through b  u transition Favored amplitude Strong phase difference CKM angle B0B0 B0B0 f mixing

Beauty 06, Oxford, 27 Sept Marco Zito13 Experimental technique (4s)  = 0.56 Tag B  z ~ 160 m Reco B  z ~ 80 m zz K D-D- K+K+ ++ K+K+ -- -- e- e+ B 0  Time dependent analysis Partial or Full reconstruction D *-  + mixed r = 0 r = 0.02  = 0 sin(2  +  ) = 1 w=0 Unmixed D-  + Mixed D-  + Tag side CP violation effect

Beauty 06, Oxford, 27 Sept Marco Zito14 sin(2  +  ) from B 0  D (*) ,D  a D  =   a D*  =   a D  =   c D  =   c D*  =   c D  =   Results from B 0 → D (*) , D  full reco : D +    evts, D*  evts D*  evts 232  10 6 B B bar PRD

Beauty 06, Oxford, 27 Sept Marco Zito15 Increase the statistics by reconstructing only the two pions PRD 71, [2005] D*  events tagged with a lepton D*  events tagged with a kaon CP asymmetry Most precise measurement to date 232  10 6 B B bar B0  D*  partially reconstructed (BaBar)

Beauty 06, Oxford, 27 Sept Marco Zito16 sin(2φ 1 +φ 3 ) (Belle) - full reconstruction D * π full rec 357 fb -1 ~ 392  10 6 B B bar PRD (2006) S + (D*π)=0.049±0.020±0.011 S – (D*π)=0.031±0.019±0.011 S + (Dπ)=0.031±0.030±0.012 S – (Dπ)=0.068±0.029±0.012 Full+part-rec Full-rec CPV significance (S + +S - ) : 2.5σ [D*  ], 2.2  [D  ] S+ S- Full+part-rec

Beauty 06, Oxford, 27 Sept Marco Zito17 HFAG averages a and c parameters a = 2r sin(2  ) cos (  ) c lept = 2 r cos(2  ) sin(  ) a = 2r sin(2  ) cos (  ) c lept = 2 r cos(2  ) sin(  ) a = (-1) l (S + +S - )/2 [belle] c small   D   and  D*  small? More statistics will help! Individual measurements of a close to the 3  statistical significance!

Beauty 06, Oxford, 27 Sept Marco Zito18 Bf(B 0 → D s (*)  230  10 6 B B bar N(D s +  - )=48 N(D s *+  - ) = 42 Measure also D s → , K 0 S K+, K *0 K + r(D  ) = (1.3  0.2  0.1 )  r(D*  ) = (1.9  0.2  0.2 )  W-exchange diagrams are small hep-ex/ , submitted to PRL SU(3) B(B° →D s π) = (1.3±0.3 ±0.2)x10 -5 B(B° →D* s π) = (2.8±0.6 ±0.5)x10 -5 B(B° →D s K) = (2.5±0.4 ±0.4)x10 -5 B(B° →D* s K) = (2.0±0.5 ±0.4)x10 -5

Beauty 06, Oxford, 27 Sept Marco Zito19 Constraints in the ρ-η plane Combine Babar and Belle, partial and fully reco results for the a and c lep parameters and use the r parameters from SU(3) symmetry r(D  )= ± r(D *  )= ± r(D  )= ± 0.006

Beauty 06, Oxford, 27 Sept Marco Zito20 b  c amplitude ~ suppressed in B 0 →D (*)+ a - 0(2) Potentially large CP-asymmetry f D = decay constant B 0 → D (s) (*)+ a - 0(2) Test B of the suppressed decay using the SU(3) related mode: Theory papers: Phys.Lett.B 517,125 (2001) JHEP 0106:067 (2001 PRD 67, (2003) f a 0(2) << f  Other new ideas a 0(2) b  c a 0(2) b  u a 0(2) D s (*) B 0 → D s (*)+ a - 0(2)

Beauty 06, Oxford, 27 Sept Marco Zito21 B 0 ->D s (*)+ a - 0(2) No evidence for signal Upper limits for BF are smaller than theoretical expectation. New Mode not usable to measure sin (2β+ γ ) 232  10 6 B B bar hep-ex/ (2005) Submitted to PRD 232  10 6 B B bar hep-ex/ (2005) Submitted to PRD Theory prediction: B(B° →D s a 0 ) < 1.9x10 -5 B(B° → D s a 2 ) < 19x10 -5 B(B° → D* s a 0 ) < 3.6x10 -5 B(B° → D* s a 2 ) < 20x10 -5

Beauty 06, Oxford, 27 Sept Marco Zito22 V ub and V cb mediated amplitudes both color suppressed: Expect large asymmetries But smaller branching fractions than for D  sin(2  ) with B 0 /  B 0 → D (*)0 K (*)0 Critical parameter:  3  (  2 +  2 ) e -i  A 1  V cb V us A 2 = r B A 1 e -i  e i    Measure the different D (*)0 K (*)0 Bf  Measure r B in self-tagging final state D 0 K* 0 (assuming that r B for DK*  same as r B for DK 0 ) ?

Beauty 06, Oxford, 27 Sept Marco Zito23 77  12 D0K*0D0K*0 D0K*0D0K*0 D0K0D0K0 104  14 D* 0 K 0 17  5 D (*)0 K (*)0 232  10 6 B B bar To be submitted to PRD 232  10 6 B B bar To be submitted to PRD No signal in the suppressed mode r B value smaller than theo. expectation Not useful to measure  value yet! Equivalent Belle result on 86M BB PRL 90, (2003)

Beauty 06, Oxford, 27 Sept Marco Zito24 Prospects Most results statistically limited Effect of adding GLW and ADS to Dalitz : Reasonable decrease in error Dalitz still dominant for measuring γ sin(2  +  ) from B 0  D (*)  : 3.2 σ effect in partial reconstruction (1 ab-1) Analysis of B 0  D * ρ will help reduce syst. Error on  with B+ r B =0.1

Beauty 06, Oxford, 27 Sept Marco Zito25 Conclusions Many new or updated results 232 GLW: BaBar (Belle) with 232 (275) million B’s Clean but statistically limited. Best precision is in the D 0 K channel ADS: 232 (386) million B’s r B is small: r B (D 0 K)<  with D   : 232 (386) million B’s Challenging analysis but good agreement between experiments Interesting constraints on 2  have been obtained Observation of 3  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 Marco Zito26 B→D0KB→D0K 70.2 ± ± ± 19.0 CP- evts R CP + = 1 : 13 § 0 : 16 § 0 : 08 R CP ¡ = 1 : 17 § 0 : 14 § 0 : 14 A CP + = + 0 : 06 § 0 : 14 § 0 : 05 A CP ¡ = ¡ 0 : 12 § 0 : 14 § 0 : 05 PRD 73, (R) (2006) 275x10 6 B B bar pairs PRD 73, (R) (2006) 275x10 6 B B bar pairs Belle GLW results B → D* 0 K (D *0 → D 0  0 ) R CP + = 1 : 41 § 0 : 25 § 0 : 06 R CP ¡ = 1 : 15 § 0 : 31 § 0 : 12 A CP + = ¡ 0 : 20 § 0 : 22 § 0 : 04 A CP ¡ = + 0 : 13 § 0 : 30 § 0 : ± 10.2 D0K+D0K+ D0K+D0K+ D0K-D0K- D0K-D0K- CP+ CP ± 10.0 D* 0 K  CP+ D* 0 K  CP- R CP+ = 1.13±0.16±0.05 R CP- = 1.17±0.14±0.14 A CP+ = 0.06±0.14±0.05 A CP- = -0.12±0.14±0.05 R CP+ = 1.41±0.25±0.06 R CP- = 1.15±0.31±0.12 A CP+ = -0.20±0.22±0.04 A CP- = 0.13±0.30±0.08

Beauty 06, Oxford, 27 Sept Marco Zito27 B 0  D (*)  :partial reconstruction Use only the fast and soft pion tracks : no D° reconstruction ! 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) FF D0D0 Most of the D 0 decay product inside this cone P(  s - )<250 MeV E(  F )~.5 m B The unreconstructed D 0 complicates vertexing and tagging 1 rad SS B0B0 D *-  + f  D 0  - s X

Beauty 06, Oxford, 27 Sept Marco Zito28 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 S K   2 r (sin(2    ) + 2 r’(sin(2   ’) Rewrite as S  = (a  c) + b a = 2r sin(2  ) cos (  ) c= cos(2  ) [2r sin(  )+2r’sin(  ’)] b = 2r’ sin(2  ) cos (  ’) S lept   2 r (sin(2    ) lepton Tags Kaon Tags BaBar: fit CP observables a and c lepton (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*l evts [only tag side cpv) a = (S + +S - )/2c = (S + -S - )/2 free of tag-side CPV Lepton tags free of tag-side CPV

Beauty 06, Oxford, 27 Sept Marco Zito29 PRD 72 (2005) B - → D (*)0      K (*)- ADS Suppressed channel not visible in D (*)0 K B → D 0 K B → D *0 K (D *0 → D 0  0 ) B → D *0 K(D *0 → D 0  ) R K ¼ < 0 : 029 R ¤ K ¼ ; D 0 ¼ 0 < 0 : 023 R ¤ K ¼ ; D 0 ° < 0 : 045  r* B 2 <(0.16) 90% C.L. Bondar & Gershon PRD70,091503(2004) R ¤ K ¼ ; D 0 ¼ 0 + R ¤ K ¼ ; D 0 ° 2 ¡ r 2 D = r ¤ B 2 B → D 0 K* R S K ¼ = 0 : 046 § 0 : 031 § 0 :  2.8 ev PRD 72 (2005) Constraints on r B from D* 0 K R ADS < R ADS < R ADS < R ADS =0.046±0.031± BB̿

Beauty 06, Oxford, 27 Sept Marco Zito30 BaBar constraints on r B D 0 K 48 o <  <73 o For maximum mixing (  /φ 3 =0, δ=180°): r B 90% C.L. R K ¼ = r 2 B + r 2 D + 2 r B r D cos ( ° ) cos ( ± ) 1-CL GLW ADS combination 11 22 33 rSBrSB  [0,  ] & (  D +  B )  [0,2  ] D 0 K* + rSB=rSB= DK*, GLW+ADS combined R Kπ <0.029 R Kπ = r 2 B +r 2 D + 2r B r D cos(γ) cos(δ B + δ D )

Beauty 06, Oxford, 27 Sept Marco Zito31 sin(2φ 1 +φ 3 ) (Belle) - full reconstruction D * π full rec D * π partial rec (only lepton tags) 357 fb -1 ~ 392  10 6 B B bar PRD (2006)