Measurement of the CKMangle g at BABAR and Belle

1
Measurement of the CKM-angle g at BABAR and
Belle

• J.P.Lees, LAPP-Annecy (IN2P3-CNRS),
• for the BaBar and Belle collaborations

2
Determining g in B?D()0K()
Interference if same D0 and ?D0 final states
AtotA1A2
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
3
The GLW Method observables
Clean but statistically limited Bf(B-?D0K-) ?
Bf(D0 ? cp) ? 10-6
Ratio of Bf for CP/non CP
Asymmetry B-/B for CP1/-1
8 fold ambiguity on g
ACP
RCP
RCP
g60o
ACP-
g60o
g30o
rB0.1
g30o
RCP-
g90o
g90o
ACP
Weak sensitivity to rB
Strong phase d (radians)
Strong phase d (radians)
4
Measurement techniques

• Reconstruct B??D0h? with D0?Kp NON CP, D0 ?
  KK-,pp- 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
5
BaBar GLW results
6
B?D0K
70.2 14.7
79.2 15.7
Belle GLW results
D0K
D0K-
CP
CP
PRD 73, 051106(R) (2006) 275x106 B Bbar pairs
149.5 19.0 CP- evts
D0K
D0K-
CP-
CP-
B?D0K (D0? D0p0)
43.9 10.2
32.7 10.0
D0K?
D0K?
CP
CP-
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RCP and ACP World Averages
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!
8
g/f3 with the ADS method
A (B-?Kp-DK-) ? rBei(dB-g)rDe-idD
Small BF(10-7), but A2 O(A1) expect large CPV
Observables
Measure Kp-K- and K-pK- rates
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B-?D()0Kp-K()- ADS
PRD 72 (2005) 032004
Suppressed channel not visible in D()0K
B? D0K(D0?D0g)
B? D0K(D0 ? D0p0)
B? D0K
B? D0K
Bondar Gershon PRD70,091503(2004)
4.2 ? 2.8 ev
? rB2lt(0.16)2 _at_ 90 C.L.
Constraints on rB from D0K
PRD 72 (2005) 071104
10
BaBar constraints on rB
D0K
g? 0,p (dDdB)?0,2p
D0 K
1-CL
1s
2s
3s
rSB
DK, GLWADS combined
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B-?D0KpK- ADS(Belle)
hep-ex/0508048 386 ? 106 B Bbar pairs
Despite larger statistics, suppressed channel not
visible either
D0K
maximum mixing (f30, d180) rBlt0.18 _at_ 90 C.L.
Here too, more statistics will help!
12
Dalitz Analysis of B-? D()0KSpp-K-
A.Giri, Y.Grossman,A.Soffer J.Zupan, Phys.Rev.
D68, 054018 (2003)
A1 A(B-?D0K-) ?AD(m2Ksp-,m2Ksp )
A2 rB e-igeid A(B-?D0K-) ?AD(m2Ksp
,m2Ksp-)
- rB if D0?D0g

• Get rB, g, d from simultaneous
  fit of the
  Kspp- 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
2 rB Re AD(m-,m)AD(m,m-)ei (-gd)
B-?B ? m- ? m and g ? g
Some model uncertainty in the g/f3 measurement

• Need precise knowledge of AD(m-2,m2)

• 2 fold ambiguity on g ( g, d ) ?( gp , dp)

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Sensitivity to g
Sensitivity to g varies across the dalitz plot
w?1/(d2L/dg2)

• g75,d180,rB0.125

• Interference of
• B-? D0K-, D0 ?K0Sr0
• with
• B-??D0K-,?D0?K0Sr0
• ? GLW like

DCS K(1430)
r(770)
Interference of B-?D0K-, D0 ?Kp- (suppressed)
with B-??D0K,?D0?Kp- ? ADS like
DCS K(892)
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D0 Dalitz model for A(m-2,m2)
extract A(m-2,m2) from high purity tagged
D?D0p , D0?K0pp- sample
use isobar model ( ? coherent sum of Breit-Wigner
(BW) amplitudes)

• BaBar 16 resonances (3 WS DCS) 1 NR
  component
• Belle 15 resonances (4WS DCS) 1 NR component

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Cartesian coordinates
From previous studies, parameters (rB, g, d)
badly behave statistically

• No sensitivity to g for rBlt0.10 (underestimated
  errors on g and d)
• fit biases on rB for rB 0.1 physical bound
  rBgt0 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?
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B-?D()0K()- Data sample (BaBar)
PRL 95 (2005) 121802 hep-ex/0507101 227 ?
106 B Bbar
D0K
D0K
D0K
m2 (GeV2/c4)
m-2 (GeV2/c4)
282?20
B-
B
m2 (GeV2/c4)
m-2 (GeV2/c4)
? Simultaneous fit of the D0 Dalitz plots for B
and B- data using the D0 isobar decay model
previously described
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Belle data sample
357 fb-1 392 ? 106 B Bbar
New! Preliminary!
B? D0K
B? D0K
B? D0K
818 events
548 events
33117 events
B-
B
B-
B-
B
B
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Belle New! Preliminary!
Dalitz (x,y) fit results
357 fb-1 392 ? 106 B Bbar
D0K
D0K
D0K
2g
BaBar PRL 95 (2005) 121802 hep-ex/0507101 227
? 106 B Bbar
D0K
B
D0K
D0K
B-
B
B
B-
d 2 rBsin g ? size of direct CPV
B-
2.5s
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Summary of x? and y ? measurements
HFAG uncorrelated averages (Dalitz Only)
B- B
x-
y-
y
x
x?rB cos(dB ? g)
y?rB sin(dB ? g)
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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 0.120.080.030.04 DK rb
0.170.100.030.03 DK rs lt 0.19 _at_ 90
CL DK

• pdf shapes (mES, )
• Dalitz structure of background
• efficiency in the dalitz plot

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Constraints on rB and g (Belle)
New! Preliminary!
B??DK?
B??DK?
B??DK?
f386-93(stat)
f311-57(stat)
f366-20 (stat)
23
37
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Combined for 3 modes f35315 ?3 (syst)?9
(model)
8ltf3lt111 (2s interval)
rDK 0.1590.054
?0.012(syst)?0.049(model) CPV significance 78
rDK0.1750.108 ?0.013(syst)?0.049(model)
rDK0.5640.216
?0.041(syst)?0.084(model)
-18
-0.050
-0.099
-0.155
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sin(2??) in B0?D()?,D?
Exploit mixing and interference between
b ? u (Doubly-Cabibbo suppressed)
b ? c (favored)
l
Vcd
?3 ?(?2?2) e-ig
e-ib
Vub
u,c,t
u,c,t
e-ib
A1? Vcb Vud
A2 ? e-i(2b)Vcd Vub r A1 e-i(2bg) ei(d)
Favored decay has large branching fraction
(0.3-0.8)
? strong phase difference
But.
r estimated from Bf(B0? Ds p-) SU(3) flavor
symmetry
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Experimental technique
Unmixed D- p
r 0.02 ? 0 sin(2??) 1 w0
Mixed D- p
r 0
Unmixed D p-
D-p mixed
Mixed D p-
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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(2bg ? d)
lepton Tags
SK? ?2 r (sin(2bg ? d) 2 r(sin(2bg ?
d)
Kaon Tags
Rewrite as S? (a ? c) b a 2r sin(2bg)
cos (d) c cos(2bg) 2r sin(d)2rsin(d)
b 2r sin(2bg) 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 Dln evts only tag side cpv)
a (SS-)/2
c (S-S-)/2
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B0?D? partially reconstructed (BaBar)
232 ? 106 B Bbar
Increase the statistics by reconstructing only
the two pions
- 18710 D? events tagged with a lepton
(purity 54) - 70580 D? events tagged with a
kaon (purity 31)
Most precise measurement to date
CP asymmetry
PRD 71, 1120032005
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sin(2??) from B0?D()?,D?
Combine partial and fully reco results for the a
and clep parameters and use the r parameters from
SU(3) symmetry
Results from B0? D()p, Dr full reco
hep-ex/0602049
r(D?) 0.019 0.004 r(D?) 0.015
0.006 r(D?) 0.003 0.006
Dp- 15038 evts, purity 87
Dp 14002 evts purity 87
30 theoretical error on rf
Dr 8736 evts purity 82
sin(2??) gt 0.64 _at_ 68 C.L. sin(2??) gt 0.42
_at_ 90 C.L.
aDp -0.010 ? 0.023 ? 0.007 aDp -0.040 ?
0.023 ? 0.010 aDr -0.024 ? 0.031 ? 0.009
Frequentist confidence level
cDp -0.033 ? 0.042 ? 0.012 cDp 0.049 ?
0.042 ? 0.015 cDr -0.098 ? 0.055 ? 0.018
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sin(2f1f3) (Belle)
New! Preliminary!
New! hep-ex/0604013
357 fb-1 392 ? 106 B Bbar
Dp partial rec (only lepton tags)
Dp full rec
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sin(2f1f3)
New! hep-ex/0604013 submitted to PRD
S-
S-
S (Dp)0.0490.0200.011 S (Dp)0.0310.0190.
011 S (Dp)0.0310.0300.012 S
(Dp)0.0680.0290.012
Full-rec partial-rec
Full-rec
CPV significance (SS-) 2.5s Dp, 2.2s Dp
S
S
sin(2f1f3)gt0.46 (0.13)
Using RDp 0.021?0.007 ? 0.006
sin(2f1f3)gt0.48 (0.07) at 68 (95) CL
Using RDp 0.021?0.004 ? 0.006
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HFAG averages a and c parameters
a 2r sin(2bg) cos (d) clept 2 r
cos(2bg) sin(d)
a (-1)l(SS-)/2 belle
More statistics will help! Individual
measurements of a close to the 3s statistical
significance!
c small ? dDp and dDp small?
30
Bf(B0 ? Ds() p)
New!
hep-ex/0604012, submitted to PRL
230 ? 106 B Bbar
Ds? fp, K0SK, K0K
Measure also
W-exchange diagrams are small
SU(3)
r(Dp) (1.3 ? 0.2 ? 0.1 ) ?10-2 r(Dp) (1.9 ?
0.2 ? 0.2 ) ?10-2
31
B0?D(s)()a-0(2)
Theory papers Phys.Lett.B 517,125 (2001) JHEP
0106067 (2001 PRD 67, 014011 (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)ltltfp
a0(2)

• Test B of the suppressed decay using the SU(3)
  related mode

Ds()
B0?Ds()a-0(2)
a0(2)
32
B0-gtDs()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.

Mode not usable to measure sin (2ß?)
33
sin(2bg) with B0 /?B0 ? D()0K()0
?3 ?(?2?2) e-ig

• Vub and Vcb mediated amplitudes both color
  suppressed
• Expect large asymmetries
• But smaller branching fractions than for Dp

l2
l
1
A1?VcbVus
A2 rB A1e-igeid

• Critical parameter

?

• Measure the different D()0K()0 Bf
• Measure rB in self-tagging final state D0K0
  (assuming that rB for DK ? same as rB for DK0)

34
D()0K()0

• 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)
35
Summary

• Many new or final results since last summer
• GLW BaBar (Belle) with 232 (275) million Bs
• Clean but statistically limited. Best precision
  is in the D0K channel
• ADS 232 (386) million Bs
• rB is small rB(D0K)lt0.18, rB2(D0K)lt0.162 _at_ 90
  CL
• Hints of larger rB in the DK channel need
  confirmation
• Dalitz 232 (386) million Bs
• 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 _at_3s is within reach.
• 2bg with D()p/r 232 (386) million Bs
• Difficult and challenging analysis
• Observation of CPV _at_ 3s is within reach.

Good perspectives with higher statistics since
the theoretical uncertainties are very low stay
tuned
36

• Backup Slides

37
Numeric results of the daliz (x,y) fit
babar
belle
PRL 95 (2005) 121802
38
Time dependent distribution for B0 ?D?
oscillation frequency
Warning definition of C and S slightly different
between Belle BaBar
D-p unmixed
D-p mixed
D-p- mixed
Ideal case
CP violation
Only cosine r 0
r 0.02 ? 0 sin(2??) 1 w0
Dt (ps)
39
B0? D()p, Dr full reco (BaBar)
Babar full reco hep-ex/0602049
232 ? 106 B Bbar
Dp- 15038 evts purity 87
Dp 14002 evts purity 87
Dp 8736 evt purity 82
40
HFAG averages D p-
More statistics will help! Individual
measurements of a close to the 3s statistical
significance!
41
Determination of rf
f Dp, Dp, Dr
2 observables for 3 unknowns ? need to know r
to determine 2??
We currently use SU(3) to estimate rf
Note New Babar measurement of Bf(B?Ds()p) see
next
We add theoretical uncertainty on rf ? 30-100
(under discussion among theorists)

• SU(3) may not hold
• Exchange diagrams neglected