1
Evidence for direct
CP
violation in the measurement of the CKM angle
γ
with
B
∓
→
D
(
∗
)
K
(
∗
)
∓
decays
The
B
A
B
AR
Collaboration
The following includes supplementary material for the Elec
tronic Physics Auxiliary Publication Service.
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
100
200
300
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
100
200
300
a)
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
50
100
150
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
50
100
150
b)
Fisher
-1
0
1
Events/0.007
0
50
100
150
200
Fisher
-1
0
1
Events/0.007
0
50
100
150
200
c)
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
20
40
60
80
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
20
40
60
80
d)
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
10
20
30
40
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
10
20
30
40
e)
Fisher
-1
0
1
Events/0.007
0
10
20
30
Fisher
-1
0
1
Events/0.007
0
10
20
30
f)
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
20
40
60
80
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
20
40
60
80
g)
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
10
20
30
40
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
10
20
30
40
h)
Fisher
-1
0
1
Events/0.007
0
20
40
Fisher
-1
0
1
Events/0.007
0
20
40
i)
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
20
40
60
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
20
40
60
j)
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
10
20
30
40
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
10
20
30
40
k)
Fisher
-1
0
1
Events/0.007
0
20
40
Fisher
-1
0
1
Events/0.007
0
20
40
l)
FIG. 1: (color online). The
m
ES
(first column), ∆
E
(second column), and
F
(third column) distributions for (a)-(c)
B
∓
→
DK
∓
, (d)-(f)
B
∓
→
D
∗
[
Dπ
0
]
K
∓
, (g)-(i)
B
∓
→
D
∗
[
Dγ
]
K
∓
, and (j)-(l)
B
∓
→
DK
∗∓
decays, with
D
→
K
0
S
π
+
π
−
. The
distributions are for events in the signal region defined thr
ough the requirements
m
ES
>
5
.
272 GeV
/c
2
,
|
∆
E
|
<
30 MeV, and
F
>
−
0
.
1, except the one on the plotted variable, after all the selec
tion criteria are applied. The curves superimposed represe
nt
the projections of the
CP
fit: signal plus background (solid black lines), the continu
um plus
B
B
background contributions
(dotted red lines), and the sum of the continuum,
B
B
, and
K/π
misidentification background components (dashed blue line
s).
The reconstruction efficiencies (purities) in the signal reg
ion, based on simulation studies, are 22% (68%), 10% (81%), 1
2%
(55%), and 12% (58%), respectively.
2
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
20
40
60
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
20
40
60
a)
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
10
20
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
10
20
b)
Fisher
-1
0
1
Events/0.007
0
10
20
30
Fisher
-1
0
1
Events/0.007
0
10
20
30
c)
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
5
10
15
20
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
5
10
15
20
d)
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
5
10
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
5
10
e)
Fisher
-1
0
1
Events/0.007
0
5
10
Fisher
-1
0
1
Events/0.007
0
5
10
f)
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
5
10
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
5
10
g)
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
5
10
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
5
10
h)
Fisher
-1
0
1
Events/0.007
0
5
10
Fisher
-1
0
1
Events/0.007
0
5
10
i)
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
5
10
15
)
2
(GeV/c
ES
m
5.2
5.25
2
Events/2.25 MeV/c
0
5
10
15
j)
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
2
4
6
8
E (GeV)
∆
-0.05
0
0.05
0.1
Events/5 MeV
0
2
4
6
8
k)
Fisher
-1
0
1
Events/0.007
0
5
10
Fisher
-1
0
1
Events/0.007
0
5
10
l)
FIG. 2: (color online). Same as in Fig. 1 but for (a)-(c)
B
∓
→
DK
∓
, (d)-(f)
B
∓
→
D
∗
[
Dπ
0
]
K
∓
, (g)-(i)
B
∓
→
D
∗
[
Dγ
]
K
∓
,
and (j)-(l)
B
∓
→
DK
∗∓
decays, with
D
→
K
0
S
K
+
K
−
. The reconstruction efficiencies (purities) in the signal re
gion, based on
simulation studies, are in this case 20% (82%), 9% (87%), 12%
(78%), and 11% (81%), respectively.
[1] B. Aubert
et al.
(
B
A
B
AR
Collaboration), Phys. Rev. D
78
, 034023 (2008); Phys. Rev. Lett.
95
, 121802 (2005).
[2] P. del Amo Sanchez
et al.
(
B
A
B
AR
Collaboration), arXiv:1004.5053, accepted by Phys. Rev. L
ett. (2010).
3
)
4
/c
2
(GeV
-
s
1
2
3
)
4
/c
2
(GeV
+
s
1
2
3
a)
)
4
/c
2
(GeV
+
s
1
2
3
)
4
/c
2
(GeV
-
s
1
2
3
b)
)
4
/c
2
(GeV
+
s
1
1.2
1.4
1.6
1.8
)
4
/c
2
(GeV
0
s
1
1.2
1.4
1.6
1.8
a)
)
4
/c
2
(GeV
-
s
1
1.2
1.4
1.6
1.8
)
4
/c
2
(GeV
0
s
1
1.2
1.4
1.6
1.8
b)
)
4
/c
2
(GeV
-
s
1
2
3
)
4
/c
2
(GeV
+
s
1
2
3
c)
)
4
/c
2
(GeV
+
s
1
2
3
)
4
/c
2
(GeV
-
s
1
2
3
d)
)
4
/c
2
(GeV
+
s
1
1.2
1.4
1.6
1.8
)
4
/c
2
(GeV
0
s
1
1.2
1.4
1.6
1.8
c)
)
4
/c
2
(GeV
-
s
1
1.2
1.4
1.6
1.8
)
4
/c
2
(GeV
0
s
1
1.2
1.4
1.6
1.8
d)
)
4
/c
2
(GeV
-
s
1
2
3
)
4
/c
2
(GeV
+
s
1
2
3
e)
)
4
/c
2
(GeV
+
s
1
2
3
)
4
/c
2
(GeV
-
s
1
2
3
f)
)
4
/c
2
(GeV
+
s
1
1.2
1.4
1.6
1.8
)
4
/c
2
(GeV
0
s
1
1.2
1.4
1.6
1.8
e)
)
4
/c
2
(GeV
-
s
1
1.2
1.4
1.6
1.8
)
4
/c
2
(GeV
0
s
1
1.2
1.4
1.6
1.8
f)
)
4
/c
2
(GeV
-
s
1
2
3
)
4
/c
2
(GeV
+
s
1
2
3
g)
)
4
/c
2
(GeV
+
s
1
2
3
)
4
/c
2
(GeV
-
s
1
2
3
h)
)
4
/c
2
(GeV
+
s
1
1.2
1.4
1.6
1.8
)
4
/c
2
(GeV
0
s
1
1.2
1.4
1.6
1.8
g)
)
4
/c
2
(GeV
-
s
1
1.2
1.4
1.6
1.8
)
4
/c
2
(GeV
0
s
1
1.2
1.4
1.6
1.8
h)
FIG. 3: (color online). The DP distributions for (a)(b)
B
∓
→
DK
∓
, (c)(d)
B
∓
→
D
∗
[
Dπ
0
]
K
∓
, (e)(f)
B
∓
→
D
∗
[
Dγ
]
K
∓
,
and (g)(h)
B
∓
→
DK
∗∓
decays, with
D
→
K
0
S
π
+
π
−
(left panel) and
D
→
K
0
S
K
+
K
−
(right panel). The distributions are
for events in the signal region defined through the requireme
nts
m
ES
>
5
.
272 GeV
/c
2
,
|
∆
E
|
<
30 MeV, and
F
>
−
0
.
1, after
all the selection criteria are applied, and are shown separa
tely for
B
−
(first and third columns) and
B
+
(second and last
column) decays. For
B
−
and
B
+
decays the variables
s
−
and
s
+
are interchanged. The contours (solid red lines) represent
the
kinematical limits of the
D
decay.
4
TABLE I: Summary of the main contributions to the experiment
al systematic error on the
CP
parameters. All contributions
have been evaluated using the same procedure as in our previo
us analysis [1]. The statistical contribution to the total e
rror
has been decreased, as consequence of the use of larger data a
nd Monte Carlo (with full detector simulation) samples. For
example, larger simulated continuum samples help to signifi
cantly reduce the uncertainty arising from the modeling of t
he DP
distributions for background events containing misrecons
tructed
D
mesons.
Source
x
−
y
−
x
+
y
+
x
∗
−
y
∗
−
x
∗
+
y
∗
+
x
s
−
y
s
−
x
s
+
y
s
+
m
ES
, ∆
E
,
F
shapes
0.001 0.001 0.001 0.001 0.004 0.006 0.008 0.004 0.006
0.003 0.004 0.002
Real
D
0
fractions
0.002 0.001 0.001 0.001 0.003 0.003 0.002 0.002 0.
004 0.001 0.001 0.001
Charge-flavor correlation
0.003 0.003 0.002 0.001 0.005 0.0
05 0.008 0.002 0.001 0.001 0.003 0.001
Efficiency in the DP
0.003 0.001 0.003 0.001 0.001 0.001 0.001 0
.001 0.003 0.001 0.002 0.001
Background DP distributions 0.005 0.002 0.005 0.003 0.003 0
.002 0.004 0.004 0.010 0.004 0.007 0.002
B
−
→
D
∗
0
K
−
cross-feed
–
–
–
–
0.002 0.003 0.009 0.002
–
–
–
–
CP
violation in
Dπ
and
B
B
0.002 0.001 0.001 0.001 0.017 0.001 0.008 0.004 0.017 0.002 0
.011 0.001
Non-
K
∗
B
−
→
DK
0
S
π
−
decays
–
–
–
–
–
–
–
–
0.020 0.026 0.025 0.036
Total experimental
0.007 0.004 0.006 0.004 0.019 0.009 0.01
7 0.008 0.029 0.027 0.029 0.036
TABLE II: Summary of the main contributions to the
D
0
decay amplitude model systematic uncertainty on the
CP
param-
eters. We evaluate the different contributions using a simil
ar, but not identical, procedure to that adopted in our previ
ous
analysis [1]. The reference
D
0
decay amplitude models and parameters are used to generate 1
0 data-sized signal samples of
pseudo-experiments of
D
∗
+
→
D
0
π
+
and
D
∗−
→
D
0
π
−
events, and 10
B
∓
→
D
(
∗
)
K
∓
and
B
∓
→
D K
∗∓
signal samples 100
times larger than each measured signal yield in data, with
D
0
→
K
0
S
h
+
h
−
. The
CP
parameters are generated with values in the
range found in data. We then compare experiment-by-experim
ent the values of
z
(
∗
)
∓
and
z
s
∓
obtained from the
CP
fits using the
reference amplitude models and a set of alternative models o
btained by repeating the
D
0
→
K
0
S
h
+
h
−
amplitude analyses on
the pseudo-experiments with alternative assumptions [2].
This technique, although it requires large computing resou
rces, helps
to reduce statistical contributions to the amplitude model
uncertainties arising from changes in sensitivity between
alternative
models (e.g. alternative K-matrix solutions and P-vector m
ass dependence in the
ππ
S-wave parameterization). A variety of
studies using data have been performed to test the consisten
cy of the results using this procedure with those obtained in
our
previous analysis, where the alternative models were obtai
ned by repeating the
D
0
→
K
0
S
h
+
h
−
amplitude analyses on data.
Nevertheless, the largest decrease in the amplitude model u
ncertainty compared to our previous result is a consequence
of
the improvements in the experimental analysis of tagged
D
mesons [2], which is reflected in smaller experimental syste
matic
uncertainties on the
D
0
decay amplitudes (variations of the reconstruction efficien
cy across the DP, modeling of the DP distri-
butions for background events containing misreconstructe
d
D
mesons, mistag rates, etc.), and thus smaller amplitude mod
el
uncertainties on the
CP
parameters.
Source
x
−
y
−
x
+
y
+
x
∗
−
y
∗
−
x
∗
+
y
∗
+
x
s
−
y
s
−
x
s
+
y
s
+
Mass and width of Breit-Wigner’s 0.001 0.001 0.001 0.002 0.0
01 0.002 0.001 0.002 0.001 0.002 0.001 0.002
ππ
S-wave parameterization
0.001 0.001 0.001 0.001 0.001 0.00
1 0.001 0.002 0.001 0.001 0.001 0.002
Kπ
S-wave parameterization
0.001 0.004 0.003 0.008 0.001 0.00
6 0.002 0.004 0.003 0.002 0.003 0.007
Angular dependence
0.001 0.001 0.002 0.001 0.001 0.001 0.00
1 0.002 0.002 0.001 0.002 0.001
Blatt-Weisskopf radius
0.001 0.001 0.001 0.001 0.001 0.001
0.001 0.001 0.001 0.001 0.002 0.001
Add/remove resonances
0.001 0.001 0.001 0.001 0.001 0.002 0
.001 0.001 0.001 0.001 0.001 0.002
DP efficiency
0.003 0.002 0.003 0.001 0.001 0.001 0.001 0.001 0
.004 0.002 0.003 0.001
Background DP shape
0.001 0.001 0.001 0.001 0.001 0.001 0.00
1 0.001 0.001 0.001 0.001 0.001
Mistag rate
0.003 0.003 0.002 0.001 0.001 0.001 0.001 0.001 0
.003 0.003 0.001 0.001
Effect of mixing
0.003 0.001 0.003 0.001 0.001 0.001 0.001 0.0
01 0.003 0.001 0.003 0.001
DP complex amplitudes
0.001 0.001 0.001 0.002 0.001 0.001 0.
001 0.002 0.002 0.001 0.001 0.002
Total
D
0
decay amplitude model 0.006 0.006 0.007 0.009 0.002 0.007 0.
003 0.006 0.007 0.006 0.006 0.008
5
TABLE III:
CP
-violating complex parameters
z
(
∗
)
∓
=
x
(
∗
)
∓
+
iy
(
∗
)
∓
and
z
s
∓
=
x
s
∓
+
iy
s
∓
as obtained from the
CP
fit to
K
0
S
π
+
π
−
and
K
0
S
K
+
K
−
final states separately. The first error is statistical, the s
econd is the experimental systematic uncertainty and
the third is the systematic uncertainty associated with the
D
0
decay amplitude models. These results yield for the weak pha
se
γ
=
`
61
+19
−
17
́
◦
{
3
,
3
}
◦
and
γ
=
`
87
+43
−
37
́
◦
{
8
,
3
}
◦
, respectively.
K
0
S
π
+
π
−
K
0
S
K
+
K
−
Real part (%)
Imaginary part (%)
Real part (%)
Imaginary part
(%)
z
−
3
.
6
±
4
.
6
±
0
.
9
±
0
.
6
6
.
7
±
4
.
9
±
0
.
4
±
0
.
6
12
.
6
±
7
.
6
±
1
.
5
±
0
.
5
4
.
4
±
11
.
7
±
2
.
3
±
1
.
2
z
+
−
8
.
3
±
4
.
1
±
0
.
7
±
0
.
8
−
0
.
8
±
4
.
9
±
0
.
4
±
1
.
0
−
19
.
0
±
8
.
7
±
2
.
2
±
0
.
5
−
2
.
0
±
18
.
8
±
6
.
0
±
1
.
5
z
∗
−
−
8
.
9
±
5
.
8
±
1
.
7
±
0
.
2
−
7
.
1
±
6
.
8
±
0
.
9
±
0
.
7
−
17
.
0
±
11
.
0
±
2
.
0
±
0
.
4
8
.
8
±
17
.
1
±
3
.
6
±
1
.
2
z
∗
+
15
.
4
±
5
.
9
±
1
.
4
±
0
.
4
−
3
.
6
±
8
.
7
±
0
.
9
±
0
.
7
11
.
7
±
11
.
7
±
4
.
2
±
0
.
4
−
2
.
5
±
16
.
4
±
1
.
9
±
0
.
5
z
s
−
12
.
8
±
10
.
5
±
3
.
4
±
0
.
8
12
.
0
±
10
.
5
±
2
.
5
±
0
.
6
−
11
.
7
±
20
.
8
±
8
.
2
±
0
.
8
14
.
3
±
22
.
4
±
9
.
5
±
1
.
4
z
s
+
−
9
.
6
±
9
.
2
±
3
.
2
±
0
.
8
3
.
8
±
10
.
9
±
3
.
7
±
0
.
9
−
36
.
6
±
20
.
1
±
5
.
8
±
0
.
6
−
17
.
1
±
39
.
9
±
13
.
5
±
1
.
7
TABLE IV: Statistical correlation coefficients for the vecto
r
z
of measurements, (in order)
x
−
,
y
−
,
x
+
,
y
+
,
x
∗
−
,
y
∗
−
,
x
∗
+
,
y
∗
+
,
x
s
−
,
y
s
−
,
x
s
+
,
y
s
+
, as obtained from the
CP
fit to
K
0
S
π
+
π
−
and
K
0
S
K
+
K
−
final states (upper panel), and to
K
0
S
π
+
π
−
(bottom
left panel) and
K
0
S
K
+
K
−
(bottom right panel) separately. Only lower off-diagonal te
rms are written, in %.
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
100
-2 100
0 0 100
0 0 6 100
0 0 0 0 100
0 0 0 0 -1 100
0 0 0 0 0 0 100
0 0 0 0 0 0 -3 100
0 0 0 0 0 0 0 0 100
0 0 0 0 0 0 0 0 -20 100
0 0 0 0 0 0 0 0 0 0 100
0 0 0 0 0 0 0 0 0 0 10 100
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
100
-4 100
0 0 100
0 0 4 100
0 0 0 0 100
0 0 0 0 4 100
0 0 0 0 0 0 100
0 0 0 0 0 0 -7 100
0 0 0 0 0 0 0 0 100
0 0 0 0 0 0 0 0 -18 100
0 0 0 0 0 0 0 0 0 0 100
0 0 0 0 0 0 0 0 0 0 10 100
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
100
5 100
0 0 100
0 0 13 100
0 0 0 0 100
0 0 0 0 -10 100
0 0 0 0 2 0 100
0 0 0 0 0 0 15 100
0 0 0 0 0 0 0 0 100
0 0 0 0 0 0 0 0 -19 100
0 0 0 0 0 0 0 0 0 0 100
0 0 0 0 0 0 0 0 0 0 -7 100
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A