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( , )
VudVub*
*
VtdVtb
* *
| VcdVcb | | VcdVcb |
g
( 0 ,0 ) (1,0)
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)
2+g/2f1+f3 with B0 →D(*)+p-/D(*)-p+ and others
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 1
Determining g in B±→D(*)0K(*)±
Interference Favored (T) Color suppressed (C)
between
A1 3 A2 3(2+2) e-ig eid
Interference if same D0 and D0 final states: Atot=A1+A2
¹ + ¡ 0
F GLW met hod: D 0 ; D 0 ! K + K ¡ ; ¼ ¼ ; K 0 ¼ ; K 0 ! ; K 0 Á
S s s
F A D S met hod: D ¡ ¹ ¡
0 ! K + ¼ ( suppr .) , D 0 ! K + ¼ ( f av.)
¹ + ¡
F GGSZ [D al i t z] met hod: D 0 ; D 0 ! K 0 ¼ ¼
S
Theoretically clean (no penguins) FCS [0.2,0.6]
0,360.04 (0.3 for B0→ D0 p0)
3 parameters rB , g and d ¯ ¯ p
¯A ( B ¡ ¹0
! D K ¡
)¯
C r i t i cal p ar am et er r B = ¯A ( B ¡ ! D0K ¡ )
¹2
¯= ´ 2 + ½ £ F C S
¹
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 2
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
B( B ¡ ! D 0 K ¡ ) ¡ B( B + !
§ D0 K + )
§ B( B + ! D 0 K + ) + B( B ¡ ! D 0 K ¡ )
§ §
A CP§ = RCP§ =
B( B ¡ ! D 0 K ¡ ) + B( B + !
§ D0 K + )
§ B( B + ! D 0 K + ) + B( B ¡ ! D 0 K ¡ )
§ 2r B si n( ±) si n( ° ) 2
= 1 + r B § 2r B cos( ±) cos( ° )
=
RCP§
8 fold ambiguity on g
ACP
RCP
ACP- g=60o g=60o RCP+ g=30o
rB=0.1
g=30o RCP+ + RCP¡
2
2
= 1 + rB
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 3
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 4
¹
232 £ 106 B B
BaBar GLW results
PRD 73, 051105(R) (2006) PRD 72 (2005) 071103
B→D0K B→D0K* B+ CP+
131 CP+
B- CP+ 37.6 B CP+
D0K D0p
B+ CP-
148 CP-
B- CP- 14.8 B CP-
RCP+ = 0:90 § 0:12 § 0:04 R C P + = 1:96 § 0:40 § 0:11
RCP¡ = 0:86 § 0:10 § 0:05 R C P ¡ = 0:65 § 0:26 § 0:08
ACP+ = + 0:35 § 0:13 § 0:04 A C P + = ¡ 0:08 § 0:19 § 0:08
ACP¡ = ¡ 0:06 § 0:13 § 0:04 A C P ¡ = ¡ 0:26 § 0:40 § 0:12
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 5
70.2 ± 14.7 79.2 ± 15.7
Belle GLW D 0K + D 0K -
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 § 0:08 D 0K + D 0K -
RCP¡ = 1:17 § 0:14 § 0:14 CP- CP-
ACP+ = + 0:06 § 0:14 § 0:05
ACP¡ = ¡ 0:12 § 0:14 § 0:05
B→D*0K (D*0→ D0p0)
RCP+ = 1:41 § 0:25 § 0:06 43.9 ± 10.2 32.7 ± 10.0
RCP¡ = 1:15 § 0:31 § 0:12
D*0K D*0K
ACP+ = ¡ 0:20 § 0:22 § 0:04
ACP¡ = + 0:13 § 0:30 § 0:08 CP+ CP-
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 6
RCP and ACP World Averages
CP+
CP+
D0K
CP-
CP-
CP- CP+
CP- CP+ CP- CP+
D*0K
CP- CP+
D0K*
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 7
g/f3 with the ADS method
Combine dominant b→c transition with DCS D0 decay
A1
dB dD
A2
A (B-→[K+p-]DK-) rBei(dB-g)+r e-idD
D
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 8
B-→D(*)0[K+p-]K(*)- ADS ¹
232 £ 106 B B
Suppressed channel not visible in D(*)0K PRD 72 (2005) 032004
R ¤ ¼; D 0 ¼0 < 0:023 R ¤ ¼; D 0 ° < 0:045
K
R K ¼ < 0:029 K
B→ D*0K B→ D*0K(D*0→D0g)
B→ D0K (D*0 → D0p0)
B→ D0K* R ¤ ¼; D 0 ¼0 + R ¤ ¼; D 0 °
K K
4.2 2.8 ev ¡ r D = r B 2 Bondar & Gershon
2 ¤
PRD70,091503(2004)
2
r*B2<(0.16)2 @ 90% C.L.
S
R K ¼ = 0:046 § 0:031 § 0:008 Constraints on rB
from D*0K
PRD 72 (2005) 071104
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 9
BaBar constraints on rB
2 2
R K ¼ = r B + r D + 2r B r D cos( ° ) cos( ±) D0K*+
g [0,p] & (dD+dB)[0,2p]
GLW
D0 K
1-CL
ADS
1s combination
48o<g<73o
R K ¼ < 0:029 2s
3s
rSB
For maximum mixing (g/φ3=0, δ=180°): rSB=
rB<0.23 @ 90% C.L.
DK*, GLW+ADS combined
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 10
B-→D0[Kp]K- ADS(Belle)
hep-ex/0508048
Despite larger statistics, suppressed
channel not visible either: 386 106 B Bbar pairs
D0K
R K ¼ < 13:9 £ 10¡ 3 maximum mixing (φ3=0, δ=180°):
rB<0.18 @ 90% C.L.
Here too, more statistics will help!
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 11
Dalitz Analysis of B- D(*)0[KSp+p-]K-
A.Giri, Y.Grossman,A.Soffer & J.Zupan, Phys.Rev. D68, 054018 (2003)
A1 = A(B-→D0K-) A2 = rB e-igeid |A(B-→D0K-)|
AD(m2Ksp-,m2Ksp+ ) AD(m2Ksp+ ,m2Ksp-)
- rB if D*0→D0g
• Get rB, g, d from simultaneous Sensitivity
fit of the Ksp+p- dalitz plot density of B- and B+ data to g is here!
ds(m-,m+) |AD(m-,m+)|2 + rB2 |AD(m+,m-)|2
B-→B+ + 2 rB Re [ AD(m-,m+)AD*(m+,m-)ei (-g+d) ]
m- m+ and –g → +g
Some model
• Need precise knowledge of AD(m-2,m+2) uncertainty in the
g/f3 measurement
• 2 fold ambiguity on g: ( g, d ) →( g+p , d+p)
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 12
Sensitivity to g
Sensitivity to g varies across the dalitz plot:
g=75,d=180,rB=0.125 w1/(d2L/dg2)
Interference of
B-→ D0K-, D0
→K0S0
with
B-→D0K-,D0→K0S0
DCS
K*(1430) (770) GLW like
Interference of
B-→D0K-, D0 →K*+p-
DCS K*(892) (suppressed) with
B-→D0K,D0→K*+p-
ADS like
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 13
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)
• BaBar: 16 resonances (3 WS
DCS) + 1 NR component
• Belle: 15 resonances (4WS
DCS) + 1 NR component
DCS
K*(892)
(770)
Â2=d:o:f : = 1:27
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 14
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(dg)) y = Im (rBei(dg))
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
R C P + (1 ¨ A C P + ) ¡ R C P ¡ (1 ¨ A C P ¡ )
x§ =
4
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 15
B-→D(*)0K(*)- Data sample (BaBar)
PRL 95 (2005) 121802 & hep-ex/0507101 227 106 B Bbar
m-2 (GeV2/c4)
D*0K (D0p0)
(GeV2/c4)
D 0K D 0K D 0K
m+2
28220 9011
B- B+
m-2 (GeV2/c4) m+2 (GeV2/c4)
D*0K (D0g) D0K*
448 428
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 16
Belle data sample
357 fb-1 ~ 392 106 B Bbar
New! Preliminary!
B→ D0K B→ D*0K 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 17
Belle: New! Preliminary!
357 fb-1 ~ 392 106 B Bbar Dalitz (x,y) fit results
D0K D*0K D 0K *
2g
BaBar: PRL 95 (2005) 121802 & hep-ex/0507101 227 106 B Bbar
D 0K B- D*0K B+ B+ D 0K *
B+
d = 2 rB|sin g| B-
size of direct CPV B- 2.5s
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 18
Summary of x and y measurements
HFAG
uncorrelated
averages
(Dalitz Only)
B-
B+
x- y-
x+ y+
x=rB cos(dB g) y=rB sin(dB g)
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 19
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 = 0.12±0.08±0.03±0.04 DK • pdf shapes (mES, …)
rb* = 0.17±0.10±0.03±0.03 D*K • Dalitz structure of background
rs < 0.19 @ 90% CL DK* • efficiency in the dalitz plot
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 20
Constraints on rB and g (Belle)
New! Preliminary!
+19 +23
φ3=66-20 °(stat) φ3=86+37°(stat)
-93 φ3=11-57°(stat)
Combined for 3 modes: φ3=53°+15 3° (syst)9° (model)
-18
8°<φ3<111° (2σ interval)
rDK =0.159-0.050 0.012(syst)0.049(model)
+0.054
CPV significance: 78% rD*K=0.175+0.108 0.013(syst)0.049(model)
-0.099
rDK*=0.564+0.216 0.041(syst)0.084(model)
-0.155
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 21
Exploit mixing
and interference
sin(2+g) in B0D(*)p,D
between b c (favored) b u (Doubly-Cabibbo suppressed)
1
d + Vcd
d ( )
V*ud h 3 (2+2) e-ig D* -
2 V u e-i V*ub c
cb u,c,t
h+
(*) -
B0 b c D B0 B0 b u
d u,c,t d
e-i
A1 Vcb V*ud A2 e-i(2)Vcd V*ub
= r A1 e-i(2+g) ei(d)
Favored decay has “large”
d= strong phase difference
branching fraction (~0.3-0.8%)
¯ ¯
But…. ¯A ( B 0 ! D ( ¤) + h¡
r = ¯ ¹0
¯
¯
r estimated from
¯A ( B ! D ( ¤) + h¡ ¯ 2 (0.02) Bf(B0→ Ds+ p-)
+ SU(3) flavor
small CP asymmetry symmetry
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 22
Experimental technique
B0 Time dependent analysis
K K+
K+
Tag B p-
sz ~ 160 mm Reco B
sz ~ 80 mm p-
e- e+ D
-
Partial or
(4s)
p+ Full
g = 0.56 Dz reconstruction
Unmixed D- p+
r = 0.02
Mixed D- p+ d=0
sin(2+g) = 1
Unmixed D+ p- r=0 w=0
D p+
*-
Mixed D+ p- mixed
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 23
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
lepton Tags Slept 2 r (sin(2+g d)
Kaon Tags SK 2 r (sin(2+g d)
+ 2 r’(sin(2+g d’)
Rewrite as S = (a c) + b
a = 2r sin(2+g) cos (d) free of tag-side CPV
c= cos(2+g) [2r sin(d)+2r’sin(d’)]
Lepton tags free of tag-side CPV
b = 2r’ sin(2+g) cos (d’)
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 24
B0D*p partially reconstructed
232 10 B B (BaBar)
6
bar
Increase the statistics by
reconstructing only the two pions
- 18710 D*p events tagged with a
lepton (purity = 54%)
- 70580 D*p events tagged with a
kaon (purity 31%) Most precise measurement to date
D *p
a -0.034 0.014( stat.) 0.009( syst.)
D *p
c lep -0.025 0.020( stat.) 0.013( syst.)
CP asymmetry
PRD 71, 112003[2005]
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 25
sin(2+g) from B0D(*)p,D
Results from B0→ D(*)p, D Combine partial and fully reco results
full reco : for the a and clep parameters and use
the r parameters from SU(3)
hep-ex/0602049 symmetry r(Dp) = 0.019 ± 0.004
* r(D p) = 0.015 ± 0.006
15038 evts, purity 87%
D +p - r(D) = 0.003 ± 0.006
D*p 14002 evts purity 87% 30% theoretical error on rf
D* 8736 evts purity 82% |sin(2+g)| > 0.64 @ 68 % C.L.
|sin(2+g)| > 0.42 @ 90 % C.L.
aDp = -0.010 0.023 0.007
Frequentist
aD*p = -0.040 0.023 0.010 confidence level
aD = -0.024 0.031 0.009
68% CL
cDp = -0.033 0.042 0.012
cD*p = +0.049 0.042 0.015 90% CL
cD = -0.098 0.055 0.018
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 26
New! Preliminary!
hep-ex/0604013
357 fb-1 ~ 392 106 B Bbar
sin(2φ1+φ3) (Belle)
B 0 ( B 0 ) D (*)p - full reconstruction
B 0 ( B 0 ) D*p D* D 0p D*π partial rec
(only lepton tags)
D*π full rec
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 27
New! hep-ex/0604013 submitted to PRD
1s
S
2R
(-1) L sin( 21 + 3 d ),
sin(2φ1+φ3) 2s
1 + R2 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 + Full-rec
CPV significance (S++S-)
: partial-rec
2.5σ [D*p], 2.2s [Dp]
S+ S+
B 0 ( B 0 ) D*p
|sin(2φ1+φ3)|>0.46 (0.13)
Using RD*p = 0.0210.007 0.006
B 0 ( B 0 ) D p
|sin(2φ1+φ3)|>0.48 (0.07)
at 68% (95%) CL
Using RDp = 0.0210.004 0.006 1s
2s
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 3s 28
HFAG averages a and c parameters
a = 2r sin(2+g) cos (d) a = (-1)l(S++S-)/2 [belle]
clept = 2 r cos(2+g) sin(d)
More statistics will help! Individualdmeasurements
c small Dp and dD*p small?
of a close to the 3s statistical significance!
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 29
p)
s
Bf(B0 → Ds(*) New!
c
( )
D S* +
hep-ex/0604012, submitted to PRL b u
B0 p - -
/
230 106 B Bbar
d
+ ¡
B( B 0 ! D s ¼ ) = ( 1:3 § 0:3 § 0:2) £ 10¡ 5 Ds→ fp, K0SK+, K*0K+
¤ ¡
B( B 0 ! D s + ¼ ) = ( 2:8 § 0:6 § 0:5) £ 10¡ 5
N(Ds+p-)=48
Measure also
+
B( B 0 ! D s K ¡ ) = ( 2:5 § 0:4 § 0:4) £ 10¡ 5
¤
B( B 0 ! D s + K ¡ ) = ( 2:0 § 0:5 § 0:4) £ 10¡ 5
W-exchange diagrams are small
N(Ds*+p-) = 42
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 30
Theory papers:
Other (crazy?)
ideas
B0→D(s)(*)+a-0(2) Phys.Lett.B 517,125 (2001)
JHEP 0106:067 (2001
PRD 67, 014011 (2003)
b c amplitude ~ suppressed in B0→D(*)+a-0(2)
Potentially large CP-asymmetry
bc d bu d ( )
pa +
+
+ D* -
fa0(2)<<fp u 0(2) W c
b c d b u
B 0 +
( )
D* - B0 B0 pa +
+
W 0(2)
d b d
Test B of the suppressed decay using the
SU(3) related mode: Ds(*)
B0→Ds(*)+a-0(2) a0(2)
( Vf
AD AD
B a D 0
0
cd
Vf
(*)
B a
+-
(*)
s 0
2
()
+
0
-
(*)
)
2
( ) ( ) fD= decay constant
cs(*)
D s
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 31
B0->Ds(*)+a-0(2)
232 106 B Bbar
hep-ex/0512031 (2005)
Submitted to PRD
Theory prediction:
•No evidence for signal
•Upper limits for BF are
smaller than theoretical
expectation.
B( B ! D s a¡ ) < 1:5 £ 10¡
+
0
5 Mode not usable to measure
B( B ! D s a¡ ) < 19 £ 10¡
+ 5 sin (2β+γ)
2
B( B ! D s a¡ ) < 3:6 £ 10¡
+
0
5
B( B ! D s a¡ ) < 20 £ 10¡
+
0
5
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 32
sin(2+g) with B0 /B0 → D(*)0K(*)0
3 (2+2) e-ig
2 •Vub and Vcb mediated
amplitudes both color
suppressed:
1
•Expect large
asymmetries
•But smaller branching
A1VcbVus A2= rB A1e-igeid fractions than for Dp
Critical parameter: ¯ ¯
¯Vu bVc¤ ¯
=¯ s¯
¯V V ¤ ¯ ' 0:4 ?
cb u s
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 33
D 0K 0 10414 D*0K0 175 D(*)0K(*)0
232 106 B Bbar
To be submitted to PRD
No signal in the
D0K*0 7712 D0K*0 suppressed mode
•rB value smaller than
theo. expectation
B( B ! D 0 K 0 ) = ( 5:3 § 0:7 § 0:3) £ 10¡ 5
•Not useful to
B( B ! D ¤0 K 0 ) = ( 3:6 § 1:2 § 0:3) £ 10¡ 5 measure g value yet!
¹ ¹ Equivalent Belle result on
B( B 0 ! D 0 K ¤0 ) = ( 4:0 § 0:7 § 0:3) £ 10¡ 5
86M BB
¹ ¹ ¹
B( B 0 ! D 0 K ¤0 ) < 1:1 £ 10¡ 5 PRL 90, 141802 (2003)
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 34
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, rB2(D*0K)<0.162 @ 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 CPV @3s is within reach….
– 2+g with D(*)p/: 232 (386) million B’s
• Difficult and challenging analysis
• Observation of CPV @ 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 35
Backup Slides
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 36
Numeric results of the daliz (x,y) fit
babar belle
x–= 0.025+0.072
-0.080
y–= 0.170+0.093
-0.117
x+= –0.135+0.069
-0.070
+0.090
y+= –0.085-0.086
x-= –0.128+0.167
-0.146
+0.172
y-= –0.339-0.158
x+= 0.032+0.120
-0.116
+0.137
y+= 0.008-0.136
PRL 95 (2005) 121802
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 37
Time dependent distribution for B0 Dp
Mistag probability Resolution function
- -
+ +
-
+1
+
- oscillation frequency
-
+
+
- d) 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
d=0
sin(2+g) = 1
w=0
Dt (ps)
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 38
B0→ D(*)p, D full reco (BaBar)
Lepton tags, D*p final state
Babar full reco 232 106 B Bbar D*-p+, mixed
hep-ex/0602049 D*+p-, mixed
D+p-
15038 evts
purity 87%
D*p
14002 evts
background Dt (ps) Dt (ps)
purity 87%
aDp = -0.010 0.023 0.007
D*p aD*p = -0.040 0.023 0.010
8736 evt
aD = -0.024 0.031 0.009
purity 82%
cDp = -0.033 0.042 0.012
cD*p = +0.049 0.042 0.015
cD = -0.098 0.055 0.018
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 39
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 40
Determination of rf f = Dp, D*p, D
a f 2rf sin( 2 + g ) cos d f 2 observables for 3 unknowns
c f ,lep 2rf cos(2 + g ) sin d f need to know r to determine 2+g
We currently use SU(3) to estimate rf:
s d ( )
D* +
(*) +
DS
c SU(3) c
b u b u
B 0 p / - -
B0 p -/ -
d d
BR( B 0 Ds(*)+p - / - ) Vcd f D(*) Note: New Babar measurement of
r
BR( B 0 D (*)-p + / + ) Vcs f D(*) Bf(B→Ds(*)p) : see next
s
We add theoretical uncertainty - SU(3) may not hold
on rf 30-100% -Exchange diagrams
(under discussion among theorists) neglected
Vancouver, April 9, 2006 J-P Lees, Measurement of the CKM-angle g 41
