γ/φ3 measurements at LHCb
CKM2014, Vienna
Till Moritz Karbach
(on behalf of the LHCb collaboration)
CERN
11.09.2014
Introduction
Introduction
I
LHCb is a forward spectrometer
operated in collider mode.
I
precision measurements of band c-hadron decays
I
rare decays, CP violation, γ
I
very good K ± /π ± separation:
two RICH detectors
I
very good time resolution (Bs0
oscillation): VELO
I
Dataset:
2011: 1 fb−1
2012: 2 fb−1
total: 3 fb−1
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
1 / 21
Introduction
Introduction
0.7
0.6
it can be measured entirely
from tree decays
I
0.5
0.4
excluded area has CL > 0.95
γ is the least well known
angle of the unitarity triangle
I
md
see Brod on Tuesday!
Brod, Zupan 2013 [1]
I
I
K
CKM
fitter
Winter 14
sin 2
0.3
the residual uncertainty is
negligible: δγ/γ ≈ 10−7
I
md & ms
sol. w/ cos 2 < 0
(excl. at CL > 0.95)
K
0.2
Vub
0.1
0.0
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
however: the branching ratios are small, typically at the 10−7 level
measure γ in different “methods”
GLW
ADS
GGSZ
GLS
time-dep.
CP eigenstates, e.g. D → KK
flavored states, e.g. D → Kπ
self-conjugate 3-body decays, e.g. D → KS0 ππ
singly Cabibbo suppressed states, e.g. D → KS0 Kπ
e.g. Bs0 → Ds∓ K ±
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
2 / 21
Introduction
Introduction
Figure: Example interference diagram. Coherence factors appear with multibody
states.
Example observable:
DK,K3π
R+
=
DK,K3π
R+
=
Γ(B + → [πKππ]D K + )
,
Γ(B + → [Kπππ]D K + )
DK 2
K3π 2
K3π DK K3π
DK
K3π
(rB
) + (rD
) + 2κD
rB rD cos(δB
+ δD
+ γ)
DK 2 K3π 2
K3π DK K3π
DK
K3π
1 + (rB ) (rD ) + 2κD rB rD cos(δB − δD
+ γ)
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
3 / 21
Introduction
Introduction
Our new results, LHCb-CONF-2014-004, supersede the previous LHCb
combinations.
Table: Summary of results for γ from the B factories BaBar and Belle, and from
LHCb, and combiners. Errors correspond to 68% confidence or credibility.
experiment
BaBar [2]
Belle [3]
LHCb 3 fb−1 preliminary [4]
LHCb 1 fb−1 [5]
UTfit
CKMfitter
CKMfitter
T.M. Karbach (CERN)
result
◦
(69+17
−16 )
◦
(68+15
−14 )
(67 ± 12)◦
◦
(72.6+9.7
−17.2 )
(68.3 ± 7.5)◦
◦
(70.0+7.7
−9.0 )
+6.3 ◦
(73.2−7.0
)
CKM2014 γ from LHCb
date
Jan 2013
Jan 2013
Apr 2013 (superseded!)
Aug 2013 (superseded!)
post Moriond 2014
Moriond / Jun 2014
CKM2014
11.09.2014
4 / 21
LHCb Inputs
Inputs
new LHCb results and changes
Two combinations:
robust
full
B → DK-like
B → DK-like and B → Dπ
I
updated: Update the auxiliary inputs
I
B + → Dh+ , D → hh, GLW/ADS, 1 fb−1 LHCb [6]
I
I
I
I
I
B + → Dh+ , D → Kπππ, ADS, 1 fb−1 LHCb [7]
updated: B + → DK + , D → KS0 hh, model-ind. GGSZ, 3 fb−1 LHCb [8]
new: B + → DK + , D → KS0 Kπ, GLS, 3 fb−1 LHCb [9]
new: B 0 → D0 K ∗0 , D → hh, GLW/ADS, 3 fb−1 LHCb [10]
new: Bs0 → Ds∓ K ± , 1 fb−1 LHCb [11]
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
5 / 21
new: B + → DK + , D → KS0 Kπ, GLS, 3 fb−1m([K K π ]
0
5200
5400
first GLS measurement! LHCb [9]
I
no significant CP violation was
observed
1
LHCb
1
1.5
2
2.5
K ) [MeV/c2]
3
m2 (K0K) [GeV2/ c4]
S
es selected in (a) the B ± ! [KS0 K⇡]D K ± and (b)
he data in the SS and OS modes, and the two KS0
T.M.
Karbach
(CERN)
ed are required
to have
a refitted
B ± mass in a
Entries / (15 MeV/ c2)
LHCb
−
B+ → [K 0SK π +]D K + (e)
Sum, incl. combinatorics
Signal
20
Mis-ID
Partially reconstructed
10
5200
5400
5600
3
2
1
5800
−
m([K 0SK π+]D K +) [MeV/c2]
(b)
1.5
30
0
2
0.5
5800
−
D
we restrict the phase
space to the more
sensitive
D → K ∗+ K − region
30
LHCb
−
B → [K 0SK +π −]D K
−
(g)
Sum, incl. combinatorics
Signal
20
Mis-ID
Partially reconstructed
10
0
5200
5400
5600
−
5800
m([K 0SK +π−]D K ) [MeV/c2]
Phys. Lett. B733 (2014) 36 [9]
Entries / (15 MeV/ c2)
I
S
m2 (K0π) [GeV2/ c4]
use singly Cabibbo suppressed D decays
to non-CP eigenstates
Entries / (15 MeV/ c2)
Grossman, Ligeti, Soffer 2002 [12]
I
1
OS candidat
GLS method
Entries / (15 MeV/ c2)
I
5600
− +
0
S
Entri
0
new: B + → DK10+ , D → KS
Kπ, GLS, 3 fb−1
Entri
LHCb Inputs
3
2
1
FigureFigure:
1: Distributions
of B ± invariant
mass of th
“opposite-sign”
decays
B ± ! DK ± and (b, d, f, h) B ± ! D⇡ ± candidates i
for (a, b, e, f) B + and (c, d, g, h) B candidates. Fi
CKM2014 γ from LHCb
11.09.2014
66
/ 21
LHCb Inputs
new: B 0 → D 0 K ∗0 , D → hh, GLW/ADS, 3 fb−1
D ! K0 K and one
⇡ ); the fractions of longitudinal polarisation
new:
B → D0 Kfor∗0D, !D⇡ →
hh, GLW/ADS, 3 fb−1 in the
B ! D K and B ! D K backgrounds and the yields for each fit component within
+
⇤
0
+
⇤0
⇤
0
s
⇤0
LHCb
250
B0®D K *0
Bs0® D K *0
Combinatorial
200
B0®D ρ 0
150
Bs0® D* K *0
B 0® D* K *0
100
50
LHCb
250
B0®D K *0
Bs0® D K *0
Combinatorial
200
B0®D ρ 0
150
Bs0® D* K *0
B 0® D* K *0
100
50
5200
140
T.M. Karbach (CERN)
5400
5600
5800
5000
M(D(p K )K * ) [MeV/c ]
–
+
0
2
LHCb
eV/c2
eV/c2
5000
300
140
CKM2014 γ from LHCb
5200
5400
5600
5800
M(D(p K )K * ) [MeV/c ]
+
–
0
LHCb
2
11.09.2014
Phys. Lett. B712 (2012) 203 [10]
300
Candidates per 10 MeV/c2
Candidates per 10 MeV/c2
in B 0 ! D⇤ K ⇤0 decays is allowed by floating
the yields of
Ieach
thiscategory.
mode CP
hasviolation
great potential
exploiting the full D0 Kπ phase
space
this background in the DK ⇤0 and DK ⇤0 categories separately. The di↵erence between the
Gershon
2009
[13]
central
value
of the
Bs0 and B 0 mass is fixed to its known value from Ref. [10] and the
between
the signal Gaussian resolutions is fixed from the simulation.
Iratio
the
K ∗0 decay
tags the B flavour at decay—no time dependent
The non-parametric functions used to model all the specific backgrounds are smeared
measurement
to take into account the di↵erent mass resolutions observed in data and simulation. The
0 →D
0 K ∗0from
−K
+ : 2.9σ
mass distributions
together with
the B
function
resulting
shown
in
Iinvariant
significance
for suppressed
decay
, D0the→fitπare
Figs. 3 and 4. The numbers of signal events in each category are summarised in Table 1.
7 / 21
0
∓ ±
new: Bs
→ Ds
K , 1 fb−1
LHCb-PAPER-2014-038,
1407.6127, sub. to JHEP
Candidates / ( 0.1 ps)
LHCb
2
10
data
±
B0s → Ds K
B0s → D*s − π+
±
B0d → D K
+ −
0
Λb → Λc K
−
0
Λb → Ds p
±
B0d → Ds K
10
±
This new technique gains sensitivity to
γ through Bs0 mixing.
±
I
±
new: Bs0 → Ds∓ K ± , time-dep., 1 fb−1
total
−
B0s → Ds π+
−
B0s → Ds ρ+
B0d → D π±
+
0
Λb → Λc π−
0
Λb → D*s − p
Combinatorial
±
LHCb Inputs
1
B tagging power of eff = 5.07%
I
Lots of hadronic backgrounds: use
multidemsional fit to identify the signal
I
1770 ± 50 signal events
8
2
4
6
8
10
12
14
τ(Bs→ DsK) (ps)
10
12
14
τ (B0s → Ds K± ) [ps]
+
6
LHCb
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
0
See also talk by Vava Gligorov!
T.M. Karbach (CERN)
4
CKM2014 γ from LHCb
0.1
0.2
0.3
τ modulo (2π/∆ms) [ps]
11.09.2014
LHCb-PAPER-2014-038 [11]
I
−
first measurement! Different set of
systematics, pure “LHCb only”
A(Ds K )
I
2
±
2
0
-2
8 / 21
D 0 –D 0 mixing correction
i
0
γ1
2
3
4
D0 –D0 mixing correction
I
D0 –D0 mixing has an effect on
Meca, Silva, Atwood, Grossman
[14, 15, 16, 12, 17]
ti [ps]
0.05
0.135
0.35
1.2
3.5
I
see also Matteo Rama on Tuesday!
I
O(1◦ ) on γ for B → DK
I
The effect can be larger for B → Dπ
[18, Rama 2013]:
q
2 /r Dπ ≈ O(1)
x2D + yD
B
h_D0_TAU
ai
0.0
0.014
0.018
0.0165
0.002
Acceptance function (binned)
Acceptance function (binned)
h_D0_TAU
Entries
0.07
91279
Mean
0.488
RMS
0.3737
0.018
0.018
0.016
0.016
0.014
0.014
0.012
0.012
0.06
0.05
0.04
0.01
0.01
0.008
0.03
0.008
0.006
0.006
0.02
0.004
I
0.01
0.002
0
0
I
0.004
The topic was revisited following
FPCP2013 Rama; Bondar et al. [19, 18].
0.002
0
0.5
1
1.5
2
2.5
3
3.5
4
0
0
0.5
1
1.5
2
2.5
0
3
3.5
4
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
We correct
for the effect of D –D mixing Figure: LHCb D decay time
Figure 34: Left: D decay time distribution of the two-body GLW/ADS analysis, taken
+
0
± ⌥
acceptance
B +decaying
→ DKexpo,
from
the B ± order
! D⇡ ±
in redfor
is the
I in
leading
in, DxD!
, yKD ⇡ 2011 data. Overlayed
nential with PDG lifetime, ⌧ = 410 fs, convolved
with
a single
Gaussian of 60 fs width.
D
→
hh.
0
I taking into account individual D
Middle: Resulting binned acceptance, and a stepwise approximation using straight lines.
decay
acceptances
The red time
lines illustrate
the nominal acceptance, blue corresponds to systematic variation
(see text). Right: Zoom in of the middle plot.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
9 / 21
Auxiliary input
Auxiliary input for D0 → K ± π ∓ π + π −
300charm system.
1σ
I amplitude
250
200
I eff.
ratio:
2 σ
K3π
rD
strong phase diff.:
3 σ
150
I coherence factor:
250
150
κK3π
D
100
50
D
0CLEO legacy.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
RKππ0
I
We use a CLEO [20] and a Belle
measurement [21] on
0
− + − +
→ Konline]
π π Scans
π ) and
ure 5: Γ(D
[Colour
of the
0
− + − +
K3⇡
Γ(D
→
π
K
π
π
)
to
,
)
parameter
space.
K3⇡ D
K3π
constrain rD
.
T.M. Karbach (CERN)
300
200
K3π
δD
100
fit
I We useBest
the histogrammed
50likelihood for δ K3π , κK3π from
D
350
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
RK3π
2
Phys. Lett. B731 (2014) 197 [22]
I The D 0 → K ± π ∓ π + π − ADS
350measurement needs input on the
π
δK3
(deg.)
D
δD
K ππ0
(deg.)
updated:
K3π
Figure: CLEO legacy likelihood
for δD
K⇡⇡ 0
in
the
)
and
(righ
K3π(left) (RK⇡⇡ 0 , D
and κD (labeled “RK3π ”) D → K3π.
Histogram is used in the combination.
CKM2014 γ from LHCb
11.09.2014
10 / 21
Auxiliary input
Other auxiliary input
updated: The GLW/ADS measurements need inputs on the charm
system:
I
Kπ
Kπ
for the D0 → K − π + and D0 → π − K + decays: rD
, δD
I
for charm mixing: xD , yD
I
dir
for direct CP violation in D0 → h+ h− decays: Adir
CP (KK), ACP (ππ)
I
We use the recent HFAG charm fit (FPCP 2014).
new: Input for D → KS0 Kπ GLS
I
KS Kπ
KS Kπ
S Kπ
We use a CLEO measurement for rD
, δD
, κK
CLEO [23].
D
new: Input for B 0 → D 0 K ∗0 GLW/ADS
I
We use a MC-based estimate for κDK
B
∗0
= 0.95 ± 0.03 LHCb [10].
new: Input for Bs0 → Ds∓ K ± time-dep. to interpret γ − 2βs
I
We use the LHCb measurement of −2βs ≈ φs = 0.01 ± 0.07 ± 0.01 rad
LHCb [24].
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
11 / 21
Evolution
Evolution from the previous preliminary result
LHCb preliminary [4]
2. Update the auxiliary inputs
3. Add new B + → DK + ,
D → KS0 hh GGSZ measurement
4. Add new B + → DK + ,
D → KS0 Kπ GLS measurement
5. Add new B 0 → D0 K ∗0 ,
D → hh GLW/ADS
measurement
1-CL
1. previous result
1.2
old preliminary
1
LHCb
0.8
Preliminary
67+12
−12
0.6
0.4
68.3%
0.2
95.5%
0
6. Add new Bs0 → Ds∓ K ±
time-dependent measurement
50
60
70
80
90
100
110
γ [°]
Figure: Making one change at a time.
Robust combination.
7. robust nominal
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
12 / 21
Evolution
Evolution from the previous preliminary result
LHCb preliminary [4]
2. Update the auxiliary inputs
3. Add new B + → DK + ,
D → KS0 hh GGSZ measurement
4. Add new B + → DK + ,
D → KS0 Kπ GLS measurement
5. Add new B 0 → D0 K ∗0 ,
D → hh GLW/ADS
measurement
1-CL
1. previous result
1.2
old preliminary
...new auxiliariy input
1
LHCb
0.8
Preliminary
0.6
0.4
68.3%
67+12
−12
64+14
−15
0.2
95.5%
0
6. Add new Bs0 → Ds∓ K ±
time-dependent measurement
50
60
70
80
90
100
110
γ [°]
Figure: Making one change at a time.
Robust combination.
7. robust nominal
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
12 / 21
Evolution
Evolution from the previous preliminary result
LHCb preliminary [4]
2. Update the auxiliary inputs
3. Add new B + → DK + ,
D → KS0 hh GGSZ measurement
4. Add new B + → DK + ,
D → KS0 Kπ GLS measurement
5. Add new B 0 → D0 K ∗0 ,
D → hh GLW/ADS
measurement
1-CL
1. previous result
1.2
...new GGSZ
...new auxiliariy input
1
LHCb
0.8
Preliminary
0.6
0.4
68.3%
69+11
−11
64+14
−15
0.2
95.5%
0
6. Add new Bs0 → Ds∓ K ±
time-dependent measurement
50
60
70
80
90
100
110
γ [°]
Figure: Making one change at a time.
Robust combination.
7. robust nominal
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
12 / 21
Evolution
Evolution from the previous preliminary result
LHCb preliminary [4]
2. Update the auxiliary inputs
3. Add new B + → DK + ,
D → KS0 hh GGSZ measurement
4. Add new B + → DK + ,
D → KS0 Kπ GLS measurement
5. Add new B 0 → D0 K ∗0 ,
D → hh GLW/ADS
measurement
1-CL
1. previous result
1.2
...new GGSZ
...adding D→KSKπ GLS
1
LHCb
0.8
Preliminary
0.6
0.4
68.3%
69+11
−11
67+11
−11
0.2
95.5%
0
6. Add new Bs0 → Ds∓ K ±
time-dependent measurement
50
60
70
80
90
100
110
γ [°]
Figure: Making one change at a time.
Robust combination.
7. robust nominal
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
12 / 21
Evolution
Evolution from the previous preliminary result
LHCb preliminary [4]
2. Update the auxiliary inputs
3. Add new B + → DK + ,
D → KS0 hh GGSZ measurement
4. Add new B + → DK + ,
D → KS0 Kπ GLS measurement
5. Add new B 0 → D0 K ∗0 ,
D → hh GLW/ADS
measurement
1-CL
1. previous result
1.2
...adding DK*0 GLWADS
...adding D→KSKπ GLS
1
LHCb
0.8
Preliminary
0.6
0.4
68.3%
71.0+9.4
−10.1
67+11
−11
0.2
95.5%
0
6. Add new Bs0 → Ds∓ K ±
time-dependent measurement
50
60
70
80
90
100
110
γ [°]
Figure: Making one change at a time.
Robust combination.
7. robust nominal
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
12 / 21
Evolution
Evolution from the previous preliminary result
LHCb preliminary [4]
2. Update the auxiliary inputs
3. Add new B + → DK + ,
D → KS0 hh GGSZ measurement
4. Add new B + → DK + ,
D → KS0 Kπ GLS measurement
5. Add new B 0 → D0 K ∗0 ,
D → hh GLW/ADS
measurement
1-CL
1. previous result
1.2
...adding DsK time-dependent
...adding DK*0 GLWADS
1
LHCb
0.8
Preliminary
71.0+9.4
−10.1
72.9+9.2
−9.9
0.6
0.4
68.3%
0.2
95.5%
0
6. Add new Bs0 → Ds∓ K ±
time-dependent measurement
50
60
70
80
90
100
110
γ [°]
Figure: Making one change at a time.
Robust combination.
7. robust nominal
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
12 / 21
Evolution
Evolution from the previous preliminary result
LHCb preliminary [4]
2. Update the auxiliary inputs
3. Add new B + → DK + ,
D → KS0 hh GGSZ measurement
4. Add new B + → DK + ,
D → KS0 Kπ GLS measurement
5. Add new B 0 → D0 K ∗0 ,
D → hh GLW/ADS
measurement
1-CL
1. previous result
1.2
...adding DsK time-dependent
1
LHCb
0.8
Preliminary
72.9+9.2
−9.9
0.6
0.4
68.3%
0.2
95.5%
0
6. Add new Bs0 → Ds∓ K ±
time-dependent measurement
50
60
70
80
90
100
110
γ [°]
Figure: Making one change at a time.
Robust combination.
7. robust nominal
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
12 / 21
Statistical procedure
Statistical procedure
The method is unchanged from previous combinations.
I
We assume (almost) all observables to be Gaussian distributed.
I
We assume Gaussian systematic fluctuations.
I
We don’t allow non-physical parameter values.
I
Use the plugin method for nominal results (Feldman-Cousins based
frequentist method nuisances at their best-fit values).
I
Use the profile likelihood method for 2D illustration.
I
Estimate the frequentist coverage.
I
Additional Bayesian interpretation with uniform priors.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
13 / 21
Results
robust combination
Result of the robust combination
LHCb-CONF-2014-004
Table: Credibility regions and most probable values for the hadronic parameters
extracted from the robust combination. The second part of the table repeats the
frequentist results for comparison.
Observable
Frequentist
γ[◦ ]
DK ◦
δB
[ ]
DK
rB
Bayesian
γ[◦ ]
DK ◦
δB
[ ]
DK
rB
Central value
72.9
126.8
0.0914
71.9
127.4
0.091
Intervals
68%
95%
[63.0, 82.1]
[52.0, 90.5]
[115.3, 136.7]
[101.6, 145.2]
[0.0826, 0.0997] [0.0728, 0.1078]
68%
95%
[61.9, 81.8]
[50.9, 91]
[115.6, 137.3]
[100.3, 147.1]
[0.0826, 0.0984] [0.0740, 0.106]
The agreement of frequentist and Bayesian results is quite good.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
14 / 21
Results
robust combination
1-CL
Result of the robust combination
LHCb-CONF-2014-004
1
LHCb
Preliminary
0.8
72.9+9.2
−9.9
0.6
0.4
68.3%
0.2
95.5%
0
50
60
70
80
90
100
110
γ [°]
Figure: Graphs for the robust combination (left: frequentist 1 − CL curves, right:
Bayesian posterior).
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
15 / 21
Results
robust combination
1-CL
Result of the robust combination
LHCb-CONF-2014-004
1
LHCb
Preliminary
0.8
126.8+9.9
−11.5
0.6
0.4
68.3%
0.2
95.5%
1-CL
0
80
100
120
140
160
δDK
B [°]
1
LHCb
Preliminary
0.8
0.0914+0.0083
−0.0088
0.6
0.4
68.3%
0.2
95.5%
0
0.06
0.08
0.1
0.12
rDK
B
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
16 / 21
Results
full combination
Lets add B + → Dπ + information
LHCb-CONF-2014-004
Table: Confidence intervals and central values for the full combination.
quantity
γ (◦ )
68% CL (◦ )
95% CL (◦ )
DK
rB
68% CL
95% CL
DK ◦
δB
( )
68% CL (◦ )
95% CL (◦ )
Dπ
rB
68% CL
95% CL
Dπ ◦
δB
( )
68% CL (◦ )
95% CL (◦ )
T.M. Karbach (CERN)
full
78.9
72.8
[71.5, 84.7]
[54.6, 91.4]
0.0928
[0.0845, 0.1008]
[0.0732, 0.1085]
128.9
[118.9, 137.9]
[102.0, 145.9]
0.027
0.006
[0.016, 0.034] [0.005, 0.007]
[0.001, 0.040]
341.8
215.6
[328.7, 351.4] [210.2, 231.5]
no constraint
CKM2014 γ from LHCb
11.09.2014
17 / 21
Results
full combination
LHCb-CONF-2014-004
1-CL
Lets add B + → Dπ + information
1.2
robust
full
1
LHCb
0.8
Preliminary
0.6
0.4
68.3%
0.2
95.5%
0
50
60
70
80
90
100
110
γ [°]
Figure: 1 − CL curve for the robust and full combinations.
I
I
I
A second minimum appears.
The 1σ errors are misleadingly small: highly non-Gaussian!
At 2σ, the agreement with the robust combination is very good.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
18 / 21
Results
full combination
LHCb-CONF-2014-004
1
1-CL
1-CL
Result of the full combination
LHCb
Preliminary
0.8
0.0928+0.0080
−0.0083
0.6
0.4
1
LHCb
Preliminary
0.8
128.9+9.0
−10.0
0.6
0.4
68.3%
0.2
68.3%
0.2
95.5%
0
0.06
95.5%
0.08
0.1
0
0.12
80
100
1
1-CL
1-CL
rDK
B
LHCb
Preliminary
0.8
0.6
0.4
140
160
δDK
B [°]
1
LHCb
Preliminary
0.8
0.6
0.4
68.3%
0.2
68.3%
0.2
95.5%
0
0
120
0.01
0.02
0.03
0.04
0.05
0.06
rDBπ
95.5%
0
180 200 220 240 260 280 300 320 340 360
δDBπ [°]
Dπ is compatible with 0.
At 2σ, rB
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
19 / 21
Results
full combination
LHCb-CONF-2014-004
0.05
LHCb
Preliminary
0.04
rDBπ
rDBπ
Result of the full combination
0.05
LHCb
0.03
0.03
0.02
0.02
0.01
0.01
contours hold 68%, 95% CL
0
Preliminary
0.04
50
60
contours hold 68%, 95% CL
70
80
90
100
0
γ [°]
200
250
300
350
Dπ
δB [°]
Figure: Profile likelihood contours, full combination. The contours are the
two-dimensional 1σ and 2σ contours.
Dπ also pulls up γ.
The high observed value of rB
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
20 / 21
Coverage test
LHCb-CONF-2014-004
toys
Coverage test
We test the frequentist coverage at the
minima of the combinations.
I
We find that the profile likelihood
construction undercovers quite a bit.
I
α (prof. LH.)
0.6158
0.5593
0.5454
α (plugin)
0.6494
0.6154
0.6120
120
full (1)
Prob
Plugin
80
60
The coverage of the full combination is
worse than of the robust. Expected due to
Dπ .
the low value of rB
η = 0.683
robust
Dπ
full (1), rB
= 0.027
Dπ
full (2), rB
= 0.006
140
100
40
20
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
p-value
toys
I
The robust plugin method has good
coverage.
robust
p-value
toys
I
140
Prob
120
Plugin
100
80
60
40
20
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
180
Prob
160
Plugin
140
120
100
80
60
40
20
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
full (2)
p-value
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
21 / 21
Conclusion
Conclusion
I
We updated the LHCb γ combination of tree-level measurements.
I
The effect of D0 –D0 mixing is taken into account, the frequentist
coverage was tested.
I
robust Bayesian results are available and agree.
I
We explore B + → Dπ + channels: they show up early all obstacles on
the way to high precision.
I
The robust coverage is good.
I
Robust frequentist combination:
◦
γ = (72.9+9.2
−9.9 )
@ 68% CL ,
◦
@ 68% CL ,
◦
@ 95% CL .
γ ∈ [63.0, 82.1]
γ ∈ [52.0, 90.5]
I
More precise than the B factory legacy.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
22 / 21
Backup
L
0
Backup
Auxiliary
input
for D → KS
Kπ
0
Tag
KK
ππ
KS0 π 0 π 0
KS0 π 0
KS0 ω
KS0 η(γγ) KS0 η(πππ
)
KS0 η ′
Kπ SS
0
S(KS Kπ|G) 6.0±14.2 2.0±11.1 43.7±37.8 233.1±57.9 199.9±68.7 47.8±28.2 10.1±18.1 83.0±87.5 288.9±48.7
Auxiliary input for D → KS0 Kπ
TABLE XXIII. Efficiency–corrected signal yields in the re0
L.
stricted region for the CP tags with a K
new:
Tag
KL0 π 0
KL0 ω
KL0 η
KL0 π 0 π 0
0
IS(KSimilar
input 25.9±38.9
is needed
as186.4±194.0
in the
−4.7±8.5
S Kπ|G) 116.2±37.1
case of D → Kπππ.
KS Kπ
I
rate
RinD
tainty
if theratio:
migration
both directions is equal, but
the presence of the resonance means that a larger fracS Kπ
tion
of
events
will
migrate
out diff.:
of the restricted
region
I eff. strong phase
δ isKdetermined
than migrate in. The net migration factor D
from the simulated data. It is different
different types
Kπ
Sfor
I
coherence
factor:
κK
of tags
due to the quantum
correlations
D which alter the
0
distribution of the KS Kπ decay on the Dalitz plot. The
I
usefactor
a single
net We
migration
is treatedCLEO
in the same way as a systematic uncertainty on the efficiency in the analysis. The
net migration factor, that is the net loss of events inside
the region, varies between tag categories and is of order
1% of the yield within the region.
K
S Kπ
Tables
XXVI–XXIX give the results for the observable
D its uncertainties for the K ∗ (892)± bin. The average FIG. 10. The best–fit point for R ∗ and δK∗ K which are
κ and
K K
D S Kπ
K
values
are κ+ = 0.44 ± 0.30 and κ− = 3.18 ± 1.08 with a Figure:
KS Kπ
and
CLEO
likelihood
fortheδregions
measured over
the restricted
region, and
enclosing
D
χ2D
/dof of 6.5/10. The uncertainties due to non–uniform
1,
2,
and
3
standard
deviations
from
that
point.
KS Kπ
(labeled “RK ∗ K ”) [23].
efficiency are 0.002 and 0.001 for p and q, respectively. κD
KS are
Kπreduced in comparison to the full Dalitz plot
They
Histogram
is not used in the
D
measurement as the efficiency is more uniform over the
restricted region.
combination.
ues for γ, δB , and rB are consistent with current knowlThe fitted values of p and q are p = 0.893 ± 0.089 and
edge [4]. The data samples are fit with only the parameq = 0.446 ± 0.304, with χ2 /dof given by 48.7/40. ∗This
ter γ free. The width of the best–fit γ distribution is 10◦ .
K K γ from LHCb
T.M.
(CERN)
CKM2014
11.09.201460% of24the
/ 21
leads
to aKarbach
measurement
of RK ∗ K = 1.00±0.16 and
δD
=
The restricted region will have approximately
measurement [23].
R
δ
κ
= 0.356 ± 0.034 ± 0.007 ,
= 0.46 ± 0.28 ,
= 1.00 ± 0.16 .
Backup
Auxiliary input from HFAG
Auxiliary input from HFAG
taking a step back
Comparing the old auxiliary inputs to the new ones:
old:
I
I
we needed input on the D → Kπππ system from CLEO
that measurement had some influence on the charm mixing
parameters xD , yD
I
it was obtained using the HFAG status as of 2009 as input
I
. . . so we took the 2009 CLEO input and added the new LHCb D0
wrong sign mixing measurement
I
we also added “∆ACP ”
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
25 / 21
Backup
Auxiliary input from HFAG
Auxiliary input from HFAG
taking a step back
Comparing the old auxiliary inputs to the new ones:
new:
I
the input for D → Kπππ was updated using more CLEO-c data
I
the new measurement no longer impacts xD , yD , as the world
average is much stronger now
I
it was obtained using the HFAG status as of 2014 as input
I
. . . so now we can use HFAG directly, including up-to-date charm
mixing, and “∆ACP ”
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
25 / 21
Backup
Auxiliary input from HFAG
Auxiliary input from HFAG
comparing old and new
yD
rKπ
0.015
0.064
old
old
new
0.062
new
0.01
0.06
0.058
0.005
0.056
0.054
contours hold 68%, 95% CL (etc.)
160
180
200
contours hold 68%, 95% CL (etc.)
220
240
δKπ [°]
0
0
0.005
0.01
0.015
xD
Figure: Profile likelihood contours: The “old” contour corresponds to what was
used in the previous (2013) combination (the 2009 CLEO input [25] together with
the 2013 LHCb charm mixing measurement [26]). The “new” contour is what is
used in this combination (HFAG 2014). The contours are two-dimensional 1–4σ
contours.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
26 / 21
Backup
Auxiliary input from HFAG
Auxiliary input from HFAG
RD
Kπ
The parameter RD
is the squared ratio of the doubly-Cabibbo-suppressed
0
amplitude D → π − K + to the favored one D0 → K − π + . It is not the ratio of
branching ratios. It gets often measured in time-dependent wrong-sign D0 mixing
measurements:
2
q
2
t
x2D + yD
t
Kπ
Kπ
Kπ
Kπ
RW S = RD + RD x cos(δD ) ± y sin(δD )
+
τ
4
τ
0.0037
0.00365
nominal errors
0.0036
diff.-in-squares to previous
0.00355
0.0035
0.00345
0.0034
0.00335
0.0033
0.00325
0.0032
EPS 09
FPCP 10
CHARM 10
LP 11
Mar 12
Apr 13
CHARM 13
FPCP 14
Kπ
Figure: Evolution of HFAG results on RD
.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
27 / 21
Backup
Auxiliary input for D 0 → K ± π ∓ π + π −
Auxiliary input for D0 → K ± π ∓ π + π −
K3π
updated: We use an updated CLEO-c measurement of κK3π
and δD
D
(histogrammed likelihood). For the amplitude ratio
K3π
rD
= A(D0 → π − K + π − π + )/A(D0 → K − π + π − π + )
(1)
we use
I
a CLEO measurement [20] of Γ(D0 → K − π + π − π + ),
Γ(D0 → K − π + π − π + ) = 0.08290 ± 0.00043 ± 0.00200 ,
I
a Belle measurement [21] of Γ(D0 → π − K + π − π + ),
Γ(D0 → π − K + π − π + ) = 0.00026 ± 0.00001 ± 0.00001 .
I
(2)
(3)
K3π
These are related to rD
through the equation
RW S (D → Kπππ) =
(4)
1
2
K3π 2
K3π
K3π
K3π
(rD
) − κK3π
− xD sin δD
) + (x2D + yD
).
D rD (yD cos δD
2
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
(5)
28 / 21
Backup
Goodness of fit
Goodness of fit
Table: Fit probabilities of the best fit values of the two combinations.
Combination
robust
full
T.M. Karbach (CERN)
P (Prob)
89.7%
97.2%
CKM2014 γ from LHCb
P (toy-based)
(89.4 ± 0.5)%
(96.8 ± 0.3)%
11.09.2014
29 / 21
Backup
robust combination: Frequentist 2D
0.14
LHCb
Preliminary
0.12
0.1
δDK
B [°]
rDK
B
Result of the robust combination
180
LHCb
Preliminary
160
140
0.08
120
0.06
100
contours hold 68%, 95% CL
50
60
70
80
90
100
γ [°]
rDK
B
0.04
40
40
contours hold 68%, 95% CL
50
60
70
80
90
100
γ [°]
LHCb
Preliminary
0.1
0.05
contours hold 68%, 95% CL
90 100 110 120 130 140 150 160 170 180
δDK
B [°]
Figure: Profile likelihood contours, robust combination. The contours are the
two-dimensional 1σ and 2σ contours.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
30 / 21
Backup
full combination: Frequentist 2D
0.14
LHCb
Preliminary
0.12
rDBπ
rDK
B
Result of the full combination
0.05
LHCb
0.1
0.03
0.08
0.02
0.06
0.01
contours hold 68%, 95% CL
0.04
Preliminary
0.04
50
60
contours hold 68%, 95% CL
70
80
90
100
γ [°]
0
50
60
70
80
90
100
γ [°]
Figure: Profile likelihood contours, full combination. The contours are the
two-dimensional 1σ and 2σ contours.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
31 / 21
Backup
full combination: Frequentist 2D
δB [°]
LHCb
Dπ
δDK
B [°]
Result of the full combination
Preliminary
160
140
LHCb
300
Preliminary
200
120
100
100
contours hold 68%, 95% CL
60
0
70
80
90
100
γ [°]
0.14
LHCb
Preliminary
0.12
100
200
300
LHCb
Preliminary
0.04
0.03
0.08
0.02
0.06
γ [°]
0.05
0.1
0.01
contours hold 68%, 95% CL
0.04
contours hold 68%, 95% CL
0
rDBπ
rDK
B
50
100
T.M. Karbach (CERN)
120
contours hold 68%, 95% CL
140
160
δDK
B
0
[°]
CKM2014 γ from LHCb
200
250
300
350
Dπ
δB [°]
11.09.2014
32 / 21
Backup
Coverage test
Coverage test
Table: Measured coverage α of the confidence intervals for γ. The expected
coverage is denoted as η.
robust
η = 0.6827
η = 0.9545
η = 0.9973
Dπ
full, rB
= 0.027
η = 0.6827
η = 0.9545
η = 0.9973
Dπ
full, rB
= 0.006
η = 0.6827
η = 0.9545
η = 0.9973
T.M. Karbach (CERN)
α (profile likelihood)
0.6158 ± 0.0089
0.9200 ± 0.0050
0.9923 ± 0.0016
α (profile likelihood)
0.5593 ± 0.0091
0.9160 ± 0.0051
0.9929 ± 0.0015
α (profile likelihood)
0.5454 ± 0.0091
0.9026 ± 0.0054
0.9906 ± 0.0018
(α − η)
−0.0669
−0.0345
−0.0050
(α − η)
−0.1234
−0.0385
−0.0044
(α − η)
−0.1373
−0.0519
−0.0067
CKM2014 γ from LHCb
α (Plugin)
0.6494 ± 0.0087
0.9358 ± 0.0045
0.9919 ± 0.0016
α (Plugin)
0.6154 ± 0.0089
0.9402 ± 0.0043
0.9929 ± 0.0015
α (Plugin)
0.6120 ± 0.0089
0.9314 ± 0.0046
0.9933 ± 0.0015
(α − η)
−0.0333
−0.0187
−0.0054
(α − η)
−0.0673
−0.0143
−0.0044
(α − η)
−0.0707
−0.0231
−0.0040
11.09.2014
33 / 21
References
[1]
J. Brod and J. Zupan, The ultimate theoretical error on γ from
B → DK decays, JHEP 1401 (2014) 051, arXiv:1308.5663.
[2]
Babar collaboration, J. P. Lees et al., Observation of direct CP
violation in the measurement of the Cabibbo-Kobayashi-Maskawa
angle γ with B ± → D(∗) K (∗)± decays, Phys. Rev. D87 (2013)
052015, arXiv:1301.1029.
[3]
K. Trabelsi, Study of direct CP in charmed B decays and
measurement of the CKM angle γ at Belle, arXiv:1301.2033.
[4]
LHCb collaboration, A measurement of γ from a combination of
B ± → DK ± analyses including first results using 2 fb−1 of 2012
data, LHCb-CONF-2013-006.
[5]
LHCb collaboration, R. Aaij et al., Measurement of the CKM angle γ
from a combination of B ± → Dh± analyses, Phys. Lett. B726
(2013) 151, arXiv:1305.2050.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
21 / 21
References
[6]
LHCb collaboration, R. Aaij et al., Observation of CP violation in
B + → DK + decays, Phys. Lett. B712 (2012) 203,
arXiv:1203.3662.
[7]
LHCb collaboration, R. Aaij et al., Observation of the suppressed ADS
modes B ± → [π ± K ∓ π + π − ]D K ± and B ± → [π ± K ∓ π + π − ]D π ± ,
Physics Letters B723 (2013) 44, arXiv:1303.4646.
[8]
LHCb collaboration, Measurement of the CKM angle γ with a
model-independent Dalitz plot analysis of B ± → DK ± ,
D → KS0 π + π − and D → KS0 K + K − decays,
LHCb-PAPER-2014-041.
[9]
LHCb collaboration, R. Aaij et al., A study of CP violation in
B ± → DK ± and B ± → Dπ ± decays with D → KS0 K ± π ∓ final
states, Phys. Lett. B733 (2014) 36, arXiv:1402.2982.
[10] LHCb collaboration, Measurement of CP violation parameters in
B 0 → DK ∗0 decays, LHCb-PAPER-2014-028.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
21 / 21
References
[11] LHCb collaboration, Measurement of CP asymmetry in
Bs0 → Ds∓ K ± decays, LHCb-PAPER-2014-038.
[12] Y. Grossman, Z. Ligeti, and A. Soffer, Measuring gamma in
B ± → K ± (KK∗)(D) decays, Phys. Rev. D67 (2003) 071301,
arXiv:hep-ph/0210433.
[13] T. Gershon and A. Poluektov, Double Dalitz Plot Analysis of the
Decay B 0 → DK + π − , D → KS0 π + π − , Phys. Rev. D81 (2010)
014025, arXiv:0910.5437.
[14] C. C. Meca and J. P. Silva, Detecting new physics contributions to
the D0 - anti-D0 mixing through their effects on B decays, Phys. Rev.
Lett. 81 (1998) 1377, arXiv:hep-ph/9807320.
0
[15] J. P. Silva and A. Soffer, Impact of D0 –D mixing on the
experimental determination of γ, Phys. Rev. D61 (2000) 112001,
arXiv:hep-ph/9912242.
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
21 / 21
References
[16] D. Atwood, I. Dunietz, and A. Soni, Improved methods for observing
CP violation in B ± → KD and measuring the CKM phase γ, Phys.
Rev. D63 (2001) 036005, arXiv:hep-ph/0008090.
[17] Y. Grossman, A. Soffer, and J. Zupan, The Effect of D–D mixing on
the measurement of γ in B → DK decays, Phys. Rev. D72 (2005)
031501, arXiv:hep-ph/0505270.
[18] M. Rama, Effect of D–D mixing in the extraction of γ with
B − → D0 K − and B − → D0 π − decays, Phys. Rev. D89 (2014)
014021, arXiv:1307.4384.
[19] A. Bondar, A. Dolgov, A. Poluektov, and V. Vorobiev, Effect of direct
CP violation in charm on γ extraction from
B → DK ± , D → KS0 π + π − Dalitz plot analysis, Eur. Phys. J. C73
(2013) 2476, arXiv:1303.6305.
[20] CLEO Collaboration, G. Bonvicini et al., Updated measurements of
absolute D+ and D0 hadronic branching fractions and
T.M. Karbach (CERN)
CKM2014 γ from LHCb
11.09.2014
21 / 21
References
σ(e+ e− → DD) at Ecm = 3774 MeV, Phys. Rev. D89 (2014)
072002, arXiv:1312.6775.
[21] Belle Collaboration, E. White et al., Measurement of the wrong-sign
decay D0 → K + π − π + π − , Phys. Rev. D88 (2013), no. 5 051101,
arXiv:1307.5935.
[22] J. Libby et al., New determination of the D0 → K − π + π 0 and
D0 → K − π + π + π − coherence factors and average strong-phase
differences, Phys. Lett. B731 (2014) 197, arXiv:1401.1904.
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