1. 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

2. 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

3. 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

4. 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)

5. 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

6. BaBar GLW results B→D0K* B→D0K B+ CP+ B- CP+ B+ CP- B- CP-
BB̿
D0K
D0p
148 CP-
PRD 73, (R) (2006)
B→D0K
131 CP+ A C P = : 2 6 4 1 + 8 9 R 5
B→D0K*
PRD 72 (2005)
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

7. 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

8. 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

9. BD(*)0K(*), DCS D0K+ - decays
232 *106 BB pairs
D(*)0K: PRD 72,
D0K*: PRD 72,
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

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

11. 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 - 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

12. 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

13. 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

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

15. 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/
r(D) = ± 0.004
r(D*) = ± 0.006
r(D) = ± 0.006
D+p evts,
D*p evts
30% theoretical error on rf
D*r evts
|sin(2+)| > 68 % C.L.
|sin(2+)| > 90 % C.L.
aDp =   0.007
aD*p =   0.010
aDr =   0.009
90% CL
68% CL
Frequentist
confidence level
cDp =   0.012
cD*p =   0.015
cDr =   0.018
Beauty 06, Oxford, 27 Sept. 2006
Marco Zito

16. 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 (2006)
- full reconstruction
D*π partial rec
(only lepton tags)
D*π full rec
Beauty 06, Oxford, 27 Sept. 2006
Marco Zito

17. 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

18. 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

19. Bf(B0 → Ds(*) p) W-exchange diagrams are small
hep-ex/ , 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

20. 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, (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

21. B0->Ds(*)+a-0(2) No evidence for signal
232  106 B Bbar
hep-ex/ (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

22. 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

23. 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, (2003)
Beauty 06, Oxford, 27 Sept. 2006
Marco Zito

24. 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, 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 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

25. 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, (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

26. 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

27. 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

28. 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

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

30. BaBar constraints on rB D0K*+
RKπ= r2B +r2D + 2rB rD cos(γ) cos(δB+ δD) R K = 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°):
90% C.L.
rSB=
Beauty 06, Oxford, 27 Sept. 2006
Marco Zito
DK*, GLW+ADS combined