1
Observation of Time Reversal Violation in the
B
0
Meson System
The
B
A
B
AR
Collaboration
The following includes supplementary material for the Electronic Phy
sics Auxiliary Publication Service.
TABLE I: Breakdown of main systematic uncertainties on the
T
-,
CP
-, and
CPT
-asymmetry parameters and the
(
S
±
ℓ
+
,K
0
S
,C
±
ℓ
+
,K
0
S
) coefficients for
B
0
→
B
−
and
B
+
→
B
0
transitions. The indices
ℓ
+
and
K
0
S
stand for reconstructed fi-
nal states that identify the
B
meson as
B
0
and
B
−
, respectively. The first nine rows in each panel are evaluate
d using similar
procedures as in Ref. [1]. The tenth and eleventh rows (∆Γ
d
/
Γ
d
and PDF normalization) are estimated by varying ∆Γ
d
/
Γ
d
by
±
2%, while the sinh(∆Γ∆
τ
) and cosh(∆Γ∆
τ
) coefficients of the most general time-dependent decay rate
g
±
α,β
(∆
τ
) [2] are
changed around their reference model values, 0 and 1, respec
tively. The PDF normalization also accounts for systematic
effects
related to the ∆
t
range used to normalize the PDF. The total systematic uncert
ainty (last row in each panel) is calculated
adding the individual systematic uncertainties in quadrat
ure.
Systematic source
∆
S
+
T
∆
S
−
T
∆
C
+
T
∆
C
−
T
∆
S
+
CP
∆
S
−
CP
∆
C
+
CP
∆
C
−
CP
Interaction region
0.011
0.035
0.02
0.029
0.012
0.024
0.015
0.026
Flavor misID probabilities
0.022
0.042
0.022
0.022
0.016
0.
040
0.020
0.020
∆
t
resolution
0.030
0.050
0.048
0.062
0.057
0.033
0.012
0.011
J/ψK
0
L
background
0.033
0.038
0.052
0.010
0.002
0.001
0.001
0.002
Background fractions and
CP
content
0.029
0.021
0.020
0.026
0.013
0.012
0.008
0.009
m
ES
parameterization
0.011
0.002
0.005
0.002
0.016
0.008
0.005
0.004
Γ
d
and ∆
m
d
0.001
0.005
0.011
0.008
0.003
0.007
0.011
0.012
CP
violation for flavor ID categories
0.018
0.019
0.001
0.001
0.
009
0.008
0.006
0.006
Fit bias
0.010
0.072
0.013
0.010
0.010
0.007
0.007
0.014
∆Γ
d
/
Γ
d
0.004
0.003
0.002
0.002
0.004
0.003
0.001
0.001
PDF normalization
0.013
0.019
0.005
0.004
0.017
0.012
0.006
0.007
Total
0.064
0.112
0.08
0.077
0.068
0.061
0.033
0.041
Systematic source
∆
S
+
CP T
∆
S
−
CP T
∆
C
+
CP T
∆
C
−
CP T
S
+
ℓ
+
,K
0
S
S
−
ℓ
+
,K
0
S
C
+
ℓ
+
,K
0
S
C
−
ℓ
+
,K
0
S
Interaction region
0.015
0.024
0.023
0.026
0.014
0.009
0.01
5
0.008
Flavor misID probabilities
0.018
0.008
0.009
0.009
0.013
0.
020
0.012
0.010
∆
t
resolution
0.062
0.033
0.051
0.072
0.051
0.030
0.045
0.012
J/ψK
0
L
background
0.046
0.021
0.029
0.015
0.002
0.001
0.001
0.001
Background fractions and
CP
content
0.024
0.020
0.024
0.016
0.012
0.004
0.007
0.007
m
ES
parameterization
0.011
0.002
0.005
0.002
0.011
0.002
0.005
0.002
Γ
d
and ∆
m
d
0.004
0.001
0.002
0.003
0.003
0.003
0.009
0.008
CP
violation for flavor ID categories
0.026
0.010
0.007
0.005
0.
014
0.005
0.003
0.002
Fit bias
0.018
0.026
0.007
0.021
0.005
0.017
0.006
0.015
∆Γ
d
/
Γ
d
0.003
0.002
0.002
0.001
0.002
0.001
0.001
0.001
PDF normalization
0.019
0.015
0.007
0.004
0.008
0.002
0.003
0.003
Total
0.092
0.058
0.067
0.083
0.059
0.041
0.051
0.026
[1] B. Aubert
et al.
(
B
A
B
AR
Collaboration), Phys. Rev. D
79
, 072009 (2009).
[2] J. Bernabeu, F. Martinez-Vidal, P. Villanueva-Perez, J
HEP
1208
, 064 (2012).
2
t (ps)
∆
0
2
4
6
8
CP
A
-0.5
0
0.5
a)
t (ps)
∆
0
2
4
6
8
CP
A
-0.5
0
0.5
b)
t (ps)
∆
0
2
4
6
8
CP
A
-0.5
0
0.5
c)
t (ps)
∆
0
2
4
6
8
CP
A
-0.5
0
0.5
d)
FIG. 1: (color online). The four independent
CP
-violating asymmetries for transition a)
B
0
→
B
−
(
ℓ
+
X,c
cK
0
S
), b)
B
+
→
B
0
(
c
cK
0
S
,ℓ
+
X
), c)
B
0
→
B
+
(
ℓ
+
X,J/ψK
0
L
), d)
B
−
→
B
0
(
J/ψK
0
L
,ℓ
+
X
), for combined flavor categories with low misID (leptons
and kaons), in the signal region (5
.
27
< m
ES
<
5
.
29 GeV
/c
2
for
c
cK
0
S
modes and
|
∆
E
|
<
10 MeV for
J/ψK
0
L
). The points
with error bars represent the data, the red solid and dashed b
lue curves represent the projections of the best fit results w
ith
and without
CP
violation, respectively.
t (ps)
∆
0
2
4
6
8
CPT
A
-0.5
0
0.5
a)
t (ps)
∆
0
2
4
6
8
CPT
A
-0.5
0
0.5
b)
t (ps)
∆
0
2
4
6
8
CPT
A
-0.5
0
0.5
c)
t (ps)
∆
0
2
4
6
8
CPT
A
-0.5
0
0.5
d)
FIG. 2: (color online). The four independent
CPT
-violating asymmetries for transition a)
B
+
→
B
0
(
c
cK
0
S
,ℓ
+
X
), b)
B
+
→
B
0
(
c
cK
0
S
,ℓ
−
X
), c)
B
−
→
B
0
(
J/ψK
0
L
,ℓ
+
X
), d)
B
−
→
B
0
(
J/ψK
0
L
,ℓ
−
X
), for combined flavor categories with low misID (leptons
and kaons), in the signal region (5
.
27
< m
ES
<
5
.
29 GeV
/c
2
for
c
cK
0
S
modes and
|
∆
E
|
<
10 MeV for
J/ψK
0
L
). The points
with error bars represent the data, the red solid and dashed b
lue curves represent the projections of the best fit results w
ith
and without
CPT
violation, respectively.
3
±
CP
S
∆
-1
0
1
±
CP
C
∆
-1
-0.5
0
0.5
1
±
CPT
S
∆
-1
0
1
±
CPT
C
∆
-1
-0.5
0
0.5
1
FIG. 3: (color online). The central values (blue point and re
d square) and two-dimensional CL contours for 1
−
CL = 0
.
317,
4
.
55
×
10
−
2
, 2
.
70
×
10
−
3
, 6
.
33
×
10
−
5
, 5
.
73
×
10
−
7
, and 1
.
97
×
10
−
9
, calculated from the change in the value of
−
2∆ ln
L
compared with its value at maximum, for the pairs of
CP
- (left) and
CPT
- (right) asymmetry parameters (∆
S
+
CP
,
∆
C
+
CP
) and
(∆
S
+
CP T
,
∆
C
+
CP T
) (blue dashed curves) and (∆
S
−
CP
,
∆
C
−
CP
), (∆
S
−
CP T
,
∆
C
−
CP T
) (red solid curves). Systematic uncertainties are
included. The
CP
- and
CPT
-invariance points are shown as a plus sign (+).
TABLE II: Measured values of the (
S
±
α,β
,C
±
α,β
) coefficients. The first uncertainty is statistical and the se
cond systematic. The
indices
α
=
ℓ
−
,ℓ
+
and
β
=
K
0
S
,K
0
L
stand for reconstructed final states that identify the
B
meson as
B
0
,
B
0
and
B
−
,
B
+
,
respectively.
Transition
Parameter
Result
B
−
→
B
0
(
J/ψK
0
L
,ℓ
−
X
)
S
−
ℓ
−
,K
0
L
−
0
.
83
±
0
.
11
±
0
.
06
B
0
→
B
−
(
ℓ
−
X,c
cK
0
S
)
S
+
ℓ
−
,K
0
S
−
0
.
76
±
0
.
06
±
0
.
04
B
−
→
B
0
(
J/ψK
0
L
,ℓ
+
X
)
S
−
ℓ
+
,K
0
L
0
.
70
±
0
.
19
±
0
.
12
B
0
→
B
−
(
ℓ
+
X,c
cK
0
S
)
S
+
ℓ
+
,K
0
S
0
.
55
±
0
.
09
±
0
.
06
B
0
→
B
+
(
ℓ
−
X,J/ψK
0
L
)
S
+
ℓ
−
,K
0
L
0
.
51
±
0
.
17
±
0
.
11
B
+
→
B
0
(
c
cK
0
S
,ℓ
−
X
)
S
−
ℓ
−
,K
0
S
0
.
67
±
0
.
10
±
0
.
08
B
0
→
B
+
(
ℓ
+
X,J/ψK
0
L
)
S
+
ℓ
+
,K
0
L
−
0
.
69
±
0
.
11
±
0
.
04
B
+
→
B
0
(
c
cK
0
S
,ℓ
+
X
)
S
−
ℓ
+
,K
0
S
−
0
.
66
±
0
.
06
±
0
.
04
B
−
→
B
0
(
J/ψK
0
L
,ℓ
−
X
)
C
−
ℓ
−
,K
0
L
0
.
11
±
0
.
12
±
0
.
08
B
0
→
B
−
(
ℓ
−
X,c
cK
0
S
)
C
+
ℓ
−
,K
0
S
0
.
08
±
0
.
06
±
0
.
06
B
−
→
B
0
(
J/ψK
0
L
,ℓ
+
X
)
C
−
ℓ
+
,K
0
L
0
.
16
±
0
.
13
±
0
.
06
B
0
→
B
−
(
ℓ
+
X,c
cK
0
S
)
C
+
ℓ
+
,K
0
S
0
.
01
±
0
.
07
±
0
.
05
B
0
→
B
+
(
ℓ
−
X,J/ψK
0
L
)
C
+
ℓ
−
,K
0
L
−
0
.
01
±
0
.
13
±
0
.
08
B
+
→
B
0
(
c
cK
0
S
,ℓ
−
X
)
C
−
ℓ
−
,K
0
S
0
.
03
±
0
.
07
±
0
.
04
B
0
→
B
+
(
ℓ
+
X,J/ψK
0
L
)
C
+
ℓ
+
,K
0
L
−
0
.
02
±
0
.
11
±
0
.
08
B
+
→
B
0
(
c
cK
0
S
,ℓ
+
X
)
C
−
ℓ
+
,K
0
S
−
0
.
05
±
0
.
06
±
0
.
03
4
TABLE III: Statistical correlation coefficients for the vect
or of (
S
±
α,β
,C
±
α,β
) measurements given in the same order as in Table II.
Only lower off-diagonal terms are written, in %.
100
0 100
-14 0 100
2 -6 0 100
8 0 41 0 100
0 18 0 38 0 100
6 0 19 0 -7 0 100
0 10 0 16 0 -9 1 100
-45 0 38 -1 31 0 9 0 100
0 -33 0 31 0 28 0 6 0 100
27 0 -9 0 23 0 18 0 -14 0 100
0 28 0 -14 0 23 0 18 1 -15 0 100
15 0 21 0 -21 0 27 0 -16 0 22 0 100
0 18 0 21 0 -18 0 29 0 -16 0 21 0 100
1 0 25 0 31 0 -37 0 22 0 -15 0 -20 0 100
0 7 0 23 0 31 0 -41 0 20 0 -17 0 -20 0 100
TABLE IV: Systematic correlation coefficients for the vector
of (
S
±
α,β
,C
±
α,β
) measurements given in the same order as in Table II.
Only lower off-diagonal terms are written, in %.
100
6 100
18 -14 100
44 3 66 100
16 -4 57 58 100
37 -19 67 66 44 100
-5 -5 10 8 -4 -3 100
30 -19 57 59 10 58 6 100
-28 -10 39 13 43 21 -8 -1 100
42 -20 60 68 57 72 -6 47 30 100
-31 0 23 17 20 8 11 6 58 18 100
41 -27 70 66 46 64 0 71 32 81 20 100
31 -16 63 63 39 67 -23 59 39 63 24 73 100
1 -1 15 7 2 2 -31 5 23 7 5 18 49 100
28 -23 73 72 52 61 -1 64 43 69 28 84 83 39 100
-14 -13 12 -6 -34 11 2 34 23 0 31 17 26 15 15 100