1. Measurement of the CKM-angle g at BABAR and Belle
J.P.Lees, LAPP-Annecy (IN2P3-CNRS),
for the BaBar and Belle collaborations
g/f3 with B±→D(*)0K(*)± (GLW, ADS, GGSZ)
2b+g/2f1+f3 with B0 →D(*)+p-/D(*)-p+ and others
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

2. Determining g in B±→D(*)0K(*)±
Color suppressed (C)
Favored (T)
A1 3
A2 3(2+2) e-ig eid
Interference
between
Interference if same D0 and D0 final states: Atot=A1+A2 F G L W m e t h o d : D ; ! K + S s Á A ( u p r . ) , f a v Z [ l i z ]
FCS [0.2,0.6]
(0.3 for B0→ D0 p0)
Theoretically clean (no penguins)
0,360.04
3 parameters rB , g and d C r i t c a l p m e B = A ( ! D K ) 2 + F S
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

3. 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 A C P = B ( ! D K ) + R C P = B ( + ! D K ) = 2 r B s i n ( ) R C P = 1 + r 2 B c o s ( )
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)
Strong phase d (radians)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

4. Measurement techniques
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 →D0K
B →D0p
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

5. J-P Lees, Measurement of the CKM-angle g
BaBar GLW results 2 3 1 6 B
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+ R C P + = : 9 1 2 4 8 6 5 A 3
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

6. J-P Lees, Measurement of the CKM-angle g
70.2 ± 14.7
79.2 ± 15.7
Belle GLW results
D0K+
D0K-
CP+
CP+
PRD 73, (R) (2006)
275x106 B Bbar pairs
149.5 ± 19.0 CP- evts
B→D0K
D0K+
D0K- R C P + = 1 : 3 6 8 7 4 A 5 2
CP-
CP-
B→D*0K (D*0→ D0p0) 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-
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

7. RCP and ACP World Averages J-P Lees, Measurement of the CKM-angle g
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!
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

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:
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

9. B-→D(*)0[K+p-]K(*)- ADS2 3 1 6 B
PRD 72 (2005)
Suppressed channel not visible in D(*)0K R K ; D
< : 4 5 R K ; D
< : 2 3 R K
< : 2 9
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 R S K = : 4 6 3 1 8
PRD 72 (2005)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

10. BaBar constraints on rB J-P Lees, Measurement of the CKM-angle g
D0K*+ 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 2s R K
< : 2 9 3s
rSB
rSB=
For maximum mixing (g/φ3=0, δ=180°):
90% C.L.
DK*, GLW+ADS combined
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

11. B-→D0[Kp]K- ADS(Belle) J-P Lees, Measurement of the CKM-angle g
hep-ex/
386  106 B Bbar pairs
Despite larger statistics, suppressed channel not visible either:
D0K R K
< 1 3 : 9
maximum mixing (φ3=0, δ=180°):
90% C.L.
Here too, more statistics will help!
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

12. Dalitz Analysis of B- D(*)0[KSp+p-]K-
A.Giri, Y.Grossman,A.Soffer & J.Zupan, Phys.Rev. D68, (2003)
A1 = A(B-→D0K-)
AD(m2Ksp-,m2Ksp+ )
A2 = rB e-igeid |A(B-→D0K-)|
AD(m2Ksp+ ,m2Ksp-)
- rB if D*0→D0g
Get rB, g, d from simultaneous fit of the Ksp+p- dalitz plot density of B- and B+ data
Sensitivity to g is here!
ds(m-,m+)  |AD(m-,m+)|2 + rB2 |AD(m+,m-)|2
B-→B+ 
m-  m+ and –g → +g
+ 2 rB Re [ AD(m-,m+)AD*(m+,m-)ei (-g+d) ]
Some model uncertainty in the g/f3 measurement
Need precise knowledge of AD(m-2,m+2)
2 fold ambiguity on g: ( g, d ) →( g+p , d+p)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

13. J-P Lees, Measurement of the CKM-angle g
Sensitivity to g
Sensitivity to g varies across the dalitz plot:
w1/(d2L/dg2)
g=75,d=180,rB=0.125
Interference of
B-→ D0K-, D0 →K0Sr0
with
B-→D0K-,D0→K0Sr0
 GLW like
DCS
K*(1430)
r(770)
Interference of
B-→D0K-, D0 →K*+p-
(suppressed) with
B-→D0K,D0→K*+p-
 ADS like
DCS K*(892)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

14. D0 Dalitz model for A(m-2,m+2)
extract A(m-2,m+2) from high purity tagged D*+→D0p+ , D0→K0p+p- sample
use isobar model (  coherent sum of Breit-Wigner (BW) amplitudes)
CA K*(892)
r(770)
DCS
K*(892) Â 2 = d : o f 1 7
BaBar: 16 resonances (3 WS DCS) + 1 NR component
Belle: 15 resonances (4WS DCS) + 1 NR component
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

15. Cartesian coordinates
From previous studies, parameters (rB, g, d) badly behave statistically
No sensitivity to g for rB<0.10 (+underestimated errors on g and d)
fit biases on rB for rB ~0.1 [physical bound rB>0 + low statistics]
Fit cartesian coordinates (x, y) instead (4 parameters)
x  = Re (rBei(dg)) y = Im (rBei(dg))
Gaussian Errors on x,y (no unphysical zone)
(x+,y+), (x-,y-) uncorrelated
Unbiased results  rB
 Easier to combine different results
Note: GLW results also sensitive to x x = R C P + ( 1 A ) 4
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

16. B-→D(*)0K(*)- Data sample (BaBar)
PRL 95 (2005) & hep-ex/  106 B Bbar
D0K
D*0K (D0p0)
9011
D0K
D0K
m+2 (GeV2/c4)
28220
m-2 (GeV2/c4) B- B+
m-2 (GeV2/c4)
m+2 (GeV2/c4)
D*0K (D0g)
448
D0K*
428
 Simultaneous fit of the D0 Dalitz plots for B+ and B- data using the D0 isobar decay model previously described
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

17. J-P Lees, Measurement of the CKM-angle g
Belle data sample
357 fb-1 ~ 392  106 B Bbar
New! Preliminary!
B→ D*0K
B→ D0K*
B→ D0K
331±17 events
81±8 events
54±8 events B- B+ B- B+ B- B+
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

18. Dalitz (x,y) fit results J-P Lees, Measurement of the CKM-angle g
Belle: New! Preliminary!
Dalitz (x,y) fit results
357 fb-1 ~ 392  106 B Bbar
D0K*
D0K
D*0K 2g
BaBar: PRL 95 (2005) & hep-ex/  106 B Bbar B+
D0K*
D0K B-
D*0K B+ B+ B-
d = 2 rB|sin g| 
size of direct CPV B-
2.5s
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

19. B- B+ Summary of x and y  measurements x- y- y+ x+ x=rB cos(dB  g)
HFAG uncorrelated averages (Dalitz Only) B- B+ x- y- y+ x+
x=rB cos(dB  g)
y=rB sin(dB  g)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

20. J-P Lees, Measurement of the CKM-angle g
Constraints on rB and g
From the 12 measured parameters (x, y, x*, y*, xS, yS) build 7d confidence levels on (g, rB, d, rB*,d*,rsB, ds) through a frequentist [Neymann] approach:
 2d projections contours (1s, 2s) on rB, g
g = 67o  28o (stat)  13o (syst)  11o (Dalitz model)
rb = ±0.08±0.03± DK
rb* = ±0.10±0.03± D*K
rs < @ 90% CL DK*
pdf shapes (mES, …)
Dalitz structure of background
efficiency in the dalitz plot
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

21. Constraints on rB and g (Belle)
New! Preliminary!
BDK
BDK*
BD*K
φ3=66-20 °(stat)
φ3=86-93°(stat)
φ3=11-57°(stat)
+19
+37
+23
Combined for 3 modes: φ3=53°+15 3° (syst)9° (model)
8°<φ3<111° (2σ interval)
rDK = 0.012(syst)0.049(model)
CPV significance: 78% rD*K= 0.013(syst)0.049(model)
rDK*= 0.041(syst)0.084(model)
-18
-0.050
-0.099
-0.155
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

22. J-P Lees, Measurement of the CKM-angle g
sin(2+) in B0D(*),D
Exploit mixing and interference
between
b  c (favored)
b  u (Doubly-Cabibbo suppressed)
Vcb
V*ud
 1
 l2 l
3 (2+2) e-ig
Vcd
e-ib
V*ub
u,c,t
u,c,t
e-ib
A1 Vcb V*ud
A2  e-i(2b)Vcd V*ub
= r A1 e-i(2b+g) ei(d)
Favored decay has “large” branching fraction (~ %)
= strong phase difference
But….
r estimated from Bf(B0→ Ds+ p-)
+ SU(3) flavor symmetry
small CP asymmetry r = A ( B ! D ) + h
 l2 (0.02)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

23. 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-
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

24. 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
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

25. B0D* partially reconstructed (BaBar)
232  106 B Bbar
Increase the statistics by
reconstructing only the two pions
D* events tagged with a
lepton (purity = 54%)
D* events tagged with a
kaon (purity 31%)
Most precise measurement to date
CP asymmetry
PRD 71, [2005]
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

26. 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, purity 87%
D*p evts purity 87%
30% theoretical error on rf
D*r evts purity 82%
|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
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

27. J-P Lees, Measurement of the CKM-angle g
New! Preliminary!
New! hep-ex/
sin(2φ1+φ3) (Belle)
357 fb-1 ~ 392  106 B Bbar
- full reconstruction
D*π partial rec
(only lepton tags)
D*π full rec
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

28. J-P Lees, Measurement of the CKM-angle g
New! hep-ex/ submitted to PRD
sin(2φ1+φ3) 1s 2s 3s S- S-
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-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
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

29. J-P Lees, Measurement of the CKM-angle g
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?
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

30. J-P Lees, Measurement of the CKM-angle g
Bf(B0 → Ds(*) p)
New!
hep-ex/ , submitted to PRL
230  106 B Bbar B ( ! D + s ) = 2 : 8 6 5 1 3
Ds→ fp, K0SK+, K*0K+
N(Ds+p-)=48
N(Ds*+p-) = 42
Measure also B ( ! D + s K ) = 2 : 5 4 1 B ( ! D + s K ) = 2 : 5 4 1
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
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

31. J-P Lees, Measurement of the CKM-angle g
B0→D(s)(*)+a-0(2)
Theory papers:
Phys.Lett.B 517,125 (2001)
JHEP 0106:067 (2001
PRD 67, (2003)
Other (crazy?)
ideas
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
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

32. J-P Lees, Measurement of the CKM-angle g
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 ( ! D + s a )
< 1 : 5 2 9 3 6
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

33. 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: = V u b c s ' : 4 ?
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)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

34. D(*)0K(*)0 No signal in the suppressed mode 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! B ( ! D K ) = 5 : 3 7 1 6 2 4
<
Equivalent Belle result on 86M BB
PRL 90, (2003)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

35. J-P Lees, Measurement of the CKM-angle g
Summary
Many new or final results since last summer
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
Dalitz: 232 (386) million B’s
Most powerful method, sensitive to both rB and g
New Belle result. Good Belle vs BaBar agreement on D(*)0K x/y contours. Observation of direct is within reach….
2b+g with D(*)p/r: 232 (386) million B’s
Difficult and challenging analysis
Observation of 3s is within reach….
Good perspectives with higher statistics since the theoretical uncertainties are very low: stay tuned
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

36. J-P Lees, Measurement of the CKM-angle g
Backup Slides
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

37. Numeric results of the daliz (x,y) fit
babar
belle
x–=
y–=
x+= –
y+= –
+0.072
+0.093
+0.069
+0.090
x-= –
y-= –
x+=
y+=
+0.167
+0.172
+0.120
+0.137
PRL 95 (2005)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

38. J-P Lees, Measurement of the CKM-angle g
Time dependent distribution for B0 D + -
Mistag probability
Resolution function + - 1 d)
oscillation frequency
Warning: definition of C and S slightly different between Belle & BaBar
Ideal case
D*-p+ unmixed
D*-p+ mixed
D+-p- mixed
CP violation
Only cosine:
r = 0
r = 0.02
 = 0
sin(2+) = 1
w=0
Dt (ps)
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

39. B0→ D(*)p, Dr full reco (BaBar)
Lepton tags, D* final state
D*-p+, mixed
D*+p-, mixed
Dt (ps)
background
Babar full reco
hep-ex/
232  106 B Bbar
D+p-
15038 evts
purity 87%
D*p
14002 evts
purity 87%
aDp =   0.007
aD*p =   0.010
aDr =   0.009
cDp =   0.012
cD*p =   0.015
cDr =   0.018
D*p
8736 evt
purity 82%
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

40. J-P Lees, Measurement of the CKM-angle g
HFAG averages : D*+ p-
More statistics will help! Individual measurements of a close to the 3s statistical significance!
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g

41. Determination of rf We currently use SU(3) to estimate rf:
f = Dp, D*p, Dr
2 observables for 3 unknowns
 need to know r to determine 2+
We currently use SU(3) to estimate rf:
SU(3)
Note: New Babar measurement of Bf(B→Ds(*)p) : see next
We add theoretical uncertainty
on rf  %
(under discussion among theorists)
SU(3) may not hold
Exchange diagrams neglected
Vancouver, April 9, 2006
J-P Lees, Measurement of the CKM-angle g