observation of bs-bs oscillationshepweb.ucsd.edu/~vsharma/ppt/ringberg06/talks06/cdf/paus... ·...
TRANSCRIPT
Observation ofBs-Bs Oscillations
Christoph PausMassachusetts Institute of Technology
Wine and Cheese SeminarSeptember 22, 2006
Overview
☞ Theory and some History☞ The Method☞ Equipment Used for the Measurements☞ Our Samples☞ b Flavor Tagging☞ Results per Sample☞ Mixing Result Summary☞ Conclusions
1
Theory and some History
2
Matter in the Standard ModelMatter build of families of fermion doublets
Leptons
�
νe
e−
�
L
�
νµµ−
�
L
�νττ −
�L
Quarks
�
ud 0 �
L
�
cs0 �
L�
tb0 �
L
Weak interaction through W ± bosons
cs
W+c
d
W+
In general: weak eigenstates ≠ strong eigenstates☞ mixing between families possible☞ lower quark doublet components absorb difference☞ neutrinos also mix
3
Cabibbo–Kobayashi–Maskawa MatrixExample: two families of quark pairs → one mixing angle�
d 0
s0 � =
�
cos θ sin θ−sin θ cos θ
��
ds
�
rotation matrix
Matrix has to be unitary: V yV = 1
Describe mixing between three quark-pair families0B� d 0
s0
b01CA = V ×
0B� dsb
1CA with V =
0B� Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
1CA
V is Cabbibo–Kobayashi–Maskawa matrix
Three families → 4 degrees of freedom☞ 3 angles☞ 1 complex phase → CP violation
4
CKM MatrixMatrix structure
☞ mostly diagonal☞ crossing of families suppressed☞ the further the less probable☞ values not predicted
Particles are conserved:V yV = 1
→ unitarity condition
u
d
c
t
s b
Wolfenstein parametrization (λ = 0.2272 ± 0.0010):
V =
0B� 1 − λ 2/2 λ Aλ 3(ρ − iη )−λ 1 − λ 2/2 Aλ 2
Aλ 3(1 − ρ − iη ) −Aλ 2 1
1CA + O (λ 4)
Least known parameters: ρ and η5
Unitarity Triangle
Unitarity condition: V yV = 1 V =
0B� Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
1CA
→ VudV ∗ub + VcdV ∗
cb + VtdV ∗tb = 0
→ 1 + VudV ∗ub/VcdV ∗
cb + VtdV ∗tb/VcdV ∗
cb = 0
1
η
γ
≅*
*
*
* λ *
*
λ = sin θV V
V V
V
V V
V
ud
cd cb
ubcd cb
tbtd
c
ts
tdV
V
α
βρ
6
Neutral B Meson Mixing
t
t
(c, u)
(c
, u
)
W+ W−
s
b
b
s
Bs Bs
Vts
Vts W+
W−
s
b
b
s
(c
, u
)t
(c, u)tBs Bs
V
Vts
ts
Quark mixing → non diagonal Hamiltonian for ⟨B|H|B⟩
H =
�
M M12
M ∗12 M
�− i
2�
Γ Γ12
Γ ∗12 Γ
�
Diagonalizing the Hamiltonian results in☞ two masses: mH and mL and ∆m = mH − mL
☞ two decay widths: ΓH and ΓL and ∆Γ = ΓH − ΓL
☞ remember: Γ = 1/τ
Mass and decay width (lifetime) are measurable!!7
Theoretical Predictions - ∆mTheory prediction for B0/B0
s mix through box diagram
∆mq / mBqBBqf 2Bq
��VtbV ∗tq
��2 q = s,d
Lattice QCD calculations
BBdf 2Bd
= (246 ± 11 ± 25) MeV2
Hadronic uncertainties limit|Vtd | determination to ≈ 11%
t
t
(c, u)
(c
, u
)
W+ W−
s
b
b
s
Bs Bs
Vts
Vts
In ratio theory uncertainties are reduced∆ms∆md
= mBsmBd
ξ 2 |Vts|2
|Vtd |2 with ξ = 1.21 +0.047−0.035
Determine |Vts||Vtd | to ≈ 3.4%
8
Unitarity Triangle - Status EPS 2005Apex (ρ, η )
Squeezing alongside b
☞ sin 2β☞ Vub/Vcb
Squeezing alongside c
☞ ∆md
☞ ∆ms
☞ γ
CKM fit result:∆ms = 18.3 +6.5
−1.5 ps−1 -1.5
-1
-0.5
0
0.5
1
1.5
-1 -0.5 0 0.5 1 1.5 2
sin 2β
sol. w/ cos 2β < 0(excl. at CL > 0.95)
excluded at CL > 0.95
γ
γ
α
α
∆md
∆ms & ∆md
εK
εK
|Vub/Vcb|
sin 2β
sol. w/ cos 2β < 0(excl. at CL > 0.95)
excluded at CL > 0.95
α
βγ
ρ
η
excluded area has CL > 0.95
C K Mf i t t e r
EPS 2005
cb
9
First Measurement of B Mixing from UA1
Signature: like sign high pT leptons PLB 186 (1987) 247
Result☞ time integrated
χ = 0.121 ± 0.047☞ implied heavy top
For Bs
☞ too fast: χs = 0.5
Later Argus/Cleo/LEP/SLD/Tevatron/BaBar/Belle ....10
Historic Review: A 20-Year Effort1987
☞ first evidence of B mixing from UA1 PLB 186 (1987) 247
☞ Argus observes B0 mixing: UA1 implies large Bs mixing, mt > 50 GeV/c2PLB 192 (1987) 245
1989☞ CLEO confirms Argus result PRL 62 (1989) 2233
1990s☞ inclusive measurements of B0 mixing from LEP establish Bs mixing
1993☞ first time dependent measurement of ∆md from Aleph PLB 313 (1993) 498
☞ first lower limit on ∆ms from Aleph: ∆ms > 12 ⋅ 10−4 eV/c2PLB 322 (1994) 441
1999☞ CDF Run I result on ∆ms: ∆ms > 5.8 ps−1
PRL 82 (1999) 3576
2005☞ DØ first result on ∆ms: ∆ms > 5.0 ps−1
☞ CDF Run II first result on ∆ms: ∆ms > 7.9 ps−1
2006☞ D0 reports interval: ∆ms ∈ [ 17, 21] ps−1 at 90% CL PRL 97 (2006) 021802
☞ CDF Run II first measurement ∆ms = 17.31 +0.33−0.18 ± 0.07 ps−1
PRL 97 (2006) 062003
11
The Method
12
A Picture Book Event
L xy
ct = L xymp
B
T
���������������
���������������
opposite side
K
K
π
π
0sB
D s
+
+
K+
same side (vertexing)
opposite
D meson
fragmentationkaon
−l
side lepton
B hadronB jet
Collision Point
Creation of bb
side kaonopposite
K −
typically 1 mm
Ingredients to measure mixing☞ proper decay time ct , B rest frame☞ B flavor at decay, final state☞ B flavor at production, flavor tagging
13
An Event Display
14
B Mixing Phenomenology
Behavior in proper timeP(t)B0→B0 = 1
2τ e−t /τ (1 + cos ∆mt)P(t)
B0→B0 = 12τ e−t /τ (1 − cos ∆mt)
Determine asymmetry
A0(t) = N(t)unmixed−N(t)mixedN(t)unmixed+N(t)mixed
= cos ∆m t
In a perfect world
0
0.2
0.4
0.6
0.8
0 1 2 3proper decay time, t [ps]
prob
abili
ty d
ensi
ty
unmixedmixedtotal
-1
-0.5
0
0.5
1
0 1 2 3 4proper decay time, t [ps]
Mix
ed A
sym
met
ry
Perfect tag D=1
15
What Do We See in the End?
Flavor tagging Vertex Vertex and Momentum
-1
-0.5
0
0.5
1
0 1 2 3proper decay time, t [ps]
asym
met
ry
Realistic tag D=0.2
-1
-0.5
0
0.5
1
0 1 2 3proper decay time, t [ps]
asym
met
ry
Realistic resolution: vtx: 50 µm
-1
-0.5
0
0.5
1
0 1 2 3proper decay time, t [ps]
asym
met
ry
Realistic resolutions: vtx: 50 µm pt: σ(p)/p = 5%
1/σA =
qnSεD2
2q
nSnS+nB
exp(−(∆msσct)22 )
σct =r
(σ0ct)2 +
�
ct σpp
�2
16
Perfect to Realistic
-1
-0.5
0
0.5
1
0 1 2 3proper decay time, t [ps]
asym
met
ry
Perfect tag and resolutions
-1
-0.5
0
0.5
1
0 1 2 3proper decay time, t [ps]
asym
met
ry
Realistic tag D=0.2Realistic resolutions: vtx: 50 µm pt: σ(p)/p = 5%
Unbinned likelihood fit: p ∼ exp(−t /τ )(1 ± AD cos ∆mt)☞ scan ∆m for signal: determine amplitude, A☞ measure ∆ms with A = 1
17
Status: Scanning for Bs Oscillation SignalBefore this analysis
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25
∆ms (ps-1)
Am
plitu
de
data ± 1 σ 95% CL limit 14.4 ps-1
1.645 σ sensitivity 18.2 ps-1
data ± 1.645 σdata ± 1.645 σ (stat only)
Average for PDG 2006
before Spring 2005
]-1 [pssm∆0 5 10 15 20 25
Am
pli
tud
e
-4
-2
0
2
4 (stat.)σ 1.645 ±data
syst.)⊕ (stat. σ 1.645 ±data
σ 1 ±data
-195% CL limit: 14.8ps -1Expected limit: 14.1ps
DØ Run II
-11 fb
recent DØ resultPRL 97 (2006) 21802
17 ps−1 < ∆ms < 21 ps−1 at 90% CL
p-value about 5.0%
18
Last CDF Result PRL 97 (2006) 062003
]-1 [pssm∆0 10 20 30
Am
plitu
de
-2
0
2
σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-116.7 ps-125.8 ps
-π +π +π _ s D→ 0
s, B+π _ s D→ 0
s X, B_ s D+ l→ 0
sB
CDF Run II -1L = 1.0 fb
A = 1.03 ± 0.28(stat) compatible with 1 for ∆ms ∼ 17.3 ps−1
19
Last CDF Result PRL 97 (2006) 062003
Signature: minimum of log(L (A = 1)) − log(L (A = 0))
)-1
(pssm∆15 16 17 18 19 20
log(
L)∆-
-5
0
5
10
15
20hadronicsemileptoniccombined
CDF Run II Preliminary -11 fb
Minimum: -6.75
p-value: 0.2%
Analysis was blinded
∆ms = 17.31 +0.33−0.18(stat) ± 0.07(syst) ps−1
20
Plan After April
Close box again
Refine analysis methods
Go for 5σ
21
What We Improved
Unchanged☞ same data: 1 fb−1
Improvements☞ flavor tagging
☞ added opposite side kaon tagger☞ applied NN to combine all opposite side taggers☞ applied NN to same side tagger
☞ signal yields☞ added partially reconstructed decays☞ used particle identification in selection☞ used NN for hadronic selection☞ added trigger path in `D−
s
Added effective statistics of factor of 2.522
Equipment Used for theMeasurements
23
CDF II Detector
24
CDF II Detector - Key Features
’Deadtimeless’ trigger system☞ 3 level, pipelined, flexible system☞ Silicon Vertex Trigger (SVT) at 2nd level (≈25 kHz)
Charged particle reconstruction☞ redundancy for pattern reco in busy environment☞ excellent momentum resolution: R = 1.4m,B = 1.4T☞ excellent vertex resolution: L00 at 1.5cm
Particle identification☞ energy loss in drift chamber (dE /dx)☞ Time-of-Flight system at 1.4 m radius☞ electron and muon identification
25
Our Samples
26
Sample Luminosity
Store Number
Tot
al L
umin
osity
(pb
-1)
0
250
500
750
1000
1250
1500
1750
2000
1000 1500 2000 2500 3000 3500 4000 4500
1 4 7 10 1 4 7 101 4 7 1 4 7102002 2003 2004 2005 2006Year
Month
DeliveredTo tape
Bs Mixing Analysis uses: 1 fb−1
now: 1.8 fb−1 delivered, 1.6 fb−1 on tape27
Samples Used in the Analysis
Sample to tune flavor taggers (largest)☞ `+track sample (track is required to be displaced)
Calibration samples (taggers, vertex resolutions)☞ B+ → J/ψK +,D
0π+(π+π−), D0`+X ,
☞ B0 → J/ψK ∗ 0, D−π+(π+π−), D−`+X , D∗− `+X☞ Bs → J/ψφ☞ with D∗− → D0π−, D0 → K −π+(π+π−), D− → K +π−π−
Signal samples☞ hadronic: Bs → D−
sπ+(π+π−)☞ semileptonic: Bs → D−
s`+X☞ with D−
s → φπ−,K ∗ 0K −, π+π−π−
28
Samples - Semileptonic Versus Hadronic
]2
) [GeV/cπ,πφmass(5.2 5.4 5.6 5.8
2ca
ndid
ates
per
10
MeV
/c
0
100
200
300
400
data
fit+/K+π -
s D→ s B
+ρ-s D→ s B
+/K+π*-s D→ s B
X-s D→ b
+π - D→ 0 B-π +
cΛ → bΛ
comb. bkg.
]2
) [GeV/cπ,πφmass(5.2 5.4 5.6 5.8
-1CDF Run II L = 1 fb
Hadronic Dsπ(ππ)☞ reconstruct: ct = Lxy
mB
pBT
☞ great ct , mass resolution☞ sample is clean☞ small branching ratio
]2
mass [GeV/c--l+π φ
3 4 5
2ca
ndid
ates
per
35
MeV
/c
0
500
1000
1500
2000 data
fit
signal0sB
false lepton & physics
comb. bkg.
]2
mass [GeV/c--l+π φ
3 4 5
]2
mass [GeV/c+π φ1.94 1.96 1.98 2.00
2ca
nd. p
er 1
MeV
/c
0
1000
2000
3000
4000
]2
mass [GeV/c+π φ1.94 1.96 1.98 2.00
Semileptonic `DsX☞ reconstruct: ct ∗ = Lxy
mB
p`DT
☞ large branching ratio☞ inferior ct , mass resolution☞ sample composition issue
29
b Flavor Tagging
30
Flavor Tagging Introduction
L xy
ct = L xymp
B
T
���������������
���������������
opposite side
K
K
π
π
0sB
D s
+
+
K+
same side (vertexing)
opposite
D meson
fragmentationkaon
−l
side lepton
B hadronB jet
Collision Point
Creation of bb
side kaonopposite
K −
typically 1 mm
Crucial parameters☞ efficiency: ε, dilution: D = 1−2pw (pw prob. for wrong decision)☞ εD2 expresses statistical power
31
Flavor Tagging IntroductionTagging algorithms used
☞ opposite side: electron, muon, jet charge, kaon☞ same side: pion (B+, B0), kaon (Bs)
Tuning the algorithm☞ based on huge heavy flavour rich `+track sample☞ find dependencies and determine parametrizations☞ find optimal point for the algorithm
Calibration of the tagger☞ verify algorithms on B0 and B+ semileptonic/hadronic samples☞ determine scale factor S in
B+ : p ∼ exp(−t /τ )(1 ± SD)B0 : p ∼ exp(−t /τ )(1 ± SD cos ∆md t)
☞ use single scale factor: should be consistent with 1
Scheme for combination of taggers32
OST Flavor TaggersIndividual performance and combination (`+track sample)
tagger [%] efficiency dilution εD2
Muon 4.6 ± 0.0 34.7 ± 0.5 0.58 ± 0.02Electron 3.2 ± 0.0 30.3 ± 0.7 0.29 ± 0.01JQT 95.5 ± 0.1 9.7 ± 0.2 0.90 ± 0.03Kaon 18.1 ± 0.1 11.1 ± 0.9 0.23 ± 0.02OST old 95.6 ± 0.1 11.9 ± 0.1 1.34 ± 0.03OST NN 95.8 ± 0.1 12.7 ± 0.2 1.54 ± 0.04
Opposite Side Taggers☞ new kaon tagger☞ not mutually exclusive → hierarchical scheme☞ new NN combination: tag decisions as input
33
OST Flavor Taggers - Neural Network
predicted dilution0 0.05 0.1 0.15 0.2 0.25 0.3
mea
sure
d di
lutio
n
0
0.05
0.1
0.15
0.2
0.25
0.3
/ ndf 2χ 45.06 / 9S 0.008463± 0.9917
/ ndf 2χ 45.06 / 9S 0.008463± 0.9917 CDF Run II Preliminary
combined OS tagger
0.01±S = 0.99
= 96 %∈
Linear parametrization works wellImprovement of εD2
☞ hadronic 1.81 ± 0.10% from 1.51%☞ semileptonic 1.82 ± 0.04% from 1.54%
34
Same Side Kaon TaggingFragmentation
☞ Bd /u likely accompanied by π+/π−
☞ Bs likely accompanied by a K +
☞ processes differ☞ no direct transfer B+,B0 → Bs
☞ need MC to measure tagger dilution
Strategy☞ tune MC with B+ and B0
☞ apply PID to de-weight pions☞ use MC to parametrize dilution
ParticleID very important☞ significantly improves εD2
☞ reduces systematic uncertainty
→TOF (dE /dx) very important!
+
b b
b b
b b
d
u s
u
s
d s
u d
B0
B0
B
K+
0∗K
K0∗
K
d
u s
d s
u
s
u d
}
}
}
}
}
}
s
π
π
35
Flavor Tagging - SSKT Calibration: B+, B0
max PID dilution D [%]
5 10 15 20 25 30
max PID dilution D [%]
5 10 15 20 25 30
CDF Run II Preliminary -1 355 pb≈L
+ Kψ J/→ +B
+π 0
D → +B
π 30
D → +B
*0 Kψ J/→ 0B
+π - D→ 0B
π 3- D→ 0B
data
MC
syst.
☞ find good agreement: particle Id and kinematic variables☞ use kinematic variables to improve tagger
36
SSKT Particle Id Algorithm
log(LH(PID))
-20 -10 0 10 20
entr
ies
per
bin
0
200
400
Pythia Data MC pions MC kaons MC protons
log(LH(PID))
-20 -10 0 10 20
entr
ies
per
bin
0
200
400
+π -s D→ sB
CDF Run II Preliminary -1 1 fb≈L
[GeV/c]Tp0 1 2 3
entr
ies
per
bin
0
100
200
Pythia Data MC pions MC kaons MC protons
[GeV/c]Tp0 1 2 3
entr
ies
per
bin
0
100
200
+π -s D→ sB
CDF Run II Preliminary -1 1 fb≈L
[GeV/c]Tp0 1 2 3
entr
ies
per
bin
0
10
20
Pythia Data MC pions MC kaons MC protons
PID > 1 [GeV/c]Tp
0 1 2 3
entr
ies
per
bin
0
10
20
+π -s D→ sB
CDF Run II Preliminary -1 1 fb≈L
+πs- -> DsB
log(LH(PID)) of tagging track-20 -10 0 10
dilu
tion
[%] (
agre
emen
t)
-10
0
10
20
30
40
50
60
70
CDF Run II Monte Carlo
Pid algorithm works well
Kinematic of tag track not
used
algorithm)relL [GeV/c] (max pTtagging track p
1 2 3 4 5 6
dilu
tion
(agr
eem
ent)
0.1
0.2
0.3
0.4
0.5
algorithm)relL [GeV/c] (max pTtagging track p
1 2 3 4 5 6
dilu
tion
(agr
eem
ent)
0.1
0.2
0.3
0.4
0.5
(MC)+π -s D→ s B
CDF Run II Monte Carlo
ex.: max. prelL algorithm shows dependencies → use it
37
Neural Network SSKTAlgorithm
☞ variables: pid, ∆R, pT , prelL , prel
T , b (bool tags have same charge)☞ train: signal - RS kaons, bg - WS kaons, pions and protons☞ decision: track charge of highest NN tag candidate
Expected improvement☞ MC ≈ 6% relative
Measured improvement☞ 0% relative hadronic
→ εD2 = 3.5%☞ 8% relative semileptonic
→ now εD2 = 4.8%
Neural Network output0 0.2 0.4 0.6 0.8 1
Dilu
tion
[%] (
agre
emen
t)
0
0.2
0.4
0.6
0.8
1CDF Run II Monte Carlo
)πφ(s D→ sB
38
Results per Sample
39
Samples - Semileptonic SelectionUse of particle identification in selection
☞ standard practice at B factories☞ applied in hadronic and semileptonic analyses☞ using combined Time-of-Flight and dE/dx (see SSKT)
Effects☞ strongest in Ds → K ∗ 0K☞ no explicit D+ → K −π+π+
rejection (+35%)☞ combinatorial background
dominated by π
Yields: 62k (was 37k)☞ S/Bx2 for D−
s → K ∗ 0K −,φπ−
☞ added trigger paths]
2 mass [GeV/c--l+ K*0K
3 4 5
2ca
ndid
ates
per
35
MeV
/c
0
2000
4000
data
fit
signal0sB
false lepton & physics reflection+ D
comb. bkg.
]2
mass [GeV/c--l+ K*0K3 4 5
]2
mass [GeV/c+ K*0K1.95 2.00
2ca
nd. p
er 2
MeV
/c
0
2000
4000
6000
]2
mass [GeV/c+ K*0K1.95 2.00
40
Semileptonic Amplitude Scan
]-1 [pssm∆
0 5 10 15 20 25 30 35
Am
plitu
de
-4
-3
-2
-1
0
1
2
3
4σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-116.5 ps-119.3 ps
X_ s D+ l→ 0
sB
A compatible with 1 for ∆ms ∼ 17.75 ps−1
A/σA(∆ms = 17.75 ps−1) ≈ 2, can set two sided 95% CL limit
41
Semileptonic Likelihood Profile
Minimum17.89 ps−1
Depth☞ sets 95% CL interval☞ 1σ equiv. to ± 0.3 ps−1
]-1 [pssm∆15 16 17 18 19 20
-log(
L)
-2
-1
0
1
2
3
4
42
Samples - Hadronic: Bs → D−sπ+(π+π−)
Bs Modes Signal S/B(φπ)π 2000(1600) +13%partial 3100(–) –(K ∗ 0K )π 1400(800) +35%(3π)π 700(600) +22%(φπ)3π 700(500) +92%(K ∗ 0K )3π 600(200) +110%(3π)3π 200(–) –total 8700(3700) –
Golden signature☞ Bs → D−
s(φπ−)π+
]2
) [GeV/cπ,πφmass(5.2 5.4 5.6 5.8
2ca
ndid
ates
per
10
MeV
/c
0
100
200
300
400
data
fit+/K+π -
s D→ s B
+ρ-s D→ s B
+/K+π*-s D→ s B
X-s D→ b
+π - D→ 0 B-π +
cΛ → bΛ
comb. bkg.
]2
) [GeV/cπ,πφmass(5.2 5.4 5.6 5.8
-1CDF Run II L = 1 fb
Improvements:☞ partial reconstruction, particle Id, NN in selection
43
How Good are Partially Reconstructed Decays?
sB
T/pReconstructedT = pκ
0.4 0.6 0.8 1.0
prob
abili
ty d
ensi
ty
5
10
ν l (*)s D→ 0
sBall 2 3.1 GeV/c≤ lsD 2.0 < m2 4.5 GeV/c≤ lsD 4.3 < m2 5.1 GeV/c≤ lsD 4.9 < m
π *s D→ 0
sB
ρ s D→ 0sB
CDF Run II
sB
T/pReconstructedT = pκ
0.4 0.6 0.8 1.0
Proper decay time [ps]0 1 2 3
Pro
per
deca
y tim
e re
solu
tion
[fs]
0
200
400
600
800
-1Osc. / 18 ps
π s D→ 0sB
ρ s / Dπ *s D→ 0
sB
2 5.1 GeV/c≤ lsD, 4.9 < mν l (*)s D→ 0
sB
2 4.5 GeV/c≤ lsD, 4.3 < mν l (*)s D→ 0
sB
2 3.1 GeV/c≤ lsD, 2.0 < mν l (*)s D→ 0
sB
CDF Run II
Decay modes: Bs → D∗−s (Dsγ(π0))π+, Bs → D−
sρ+(π0π−)☞ need to correct for missing momentum, as semileptonic☞ large reconstructed mass → missing momentum small
Partial reco almost as good as full reco44
Amplitude Scan Partial Reconstruction Only
]-1 [pssm∆0 10 20 30
Am
plitu
de
-4
-2
0
2
4 σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-117.0 ps-118.3 ps
+π_*
s,D+ρ_ s D→ 0
sB
CDF Run II Preliminary -1L = fb
A = 1.02 ± 0.57(stat)consistent with 1 for ∆ms ∼ 17.75 ps−1
45
Amplitude Scan Golden Mode Only
]-1 [pssm∆0 10 20 30
Am
plitu
de
-4
-2
0
2
4 σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-117.0 ps-122.7 ps
+π_*
s,D+ρ_ s,D+π
_ s D→ 0
sB
CDF Run II Preliminary -1L = fb
A = 1.27 ± 0.34(stat)consistent with 1 for ∆ms ∼ 17.75 ps−1
46
Likelihood Curves - Golden Channel Only
Golden LikelihoodMinimum: −7.4p-value: 0.15%
→ 3.2σ
Spring analysisMinimum: −6.4p-value: 0.2%
Golden sample
∆ms = 18.01 +0.17−0.18 ps−1
]-1 [pssm∆16 18 20
-ln(L
)
-8
-6
-4
-20
2
4
6
8
10
12
14Total golden
Part.Reco’d
Full.Reco’d
Consistent results: full and partial reconstruction47
Non-Golden Channels, Bs → Dsπ
Particle Id☞ opt. D+ rejection☞ relax kinematic
cuts
Neural Net☞ larger signal at
same bg☞ add new mode
Bs → Ds(3π)3π
]2 mass [GeV/cBπ -) K-π +(K*K
5.4 5.6 5.82
Can
dida
tes
per
5 M
eV/c
0
50
100
150
data
fit+π -
s D→ s B
background
π - D→ 0 B
π cΛ → bΛ
]2 mass [GeV/cBπ -) K-π +(K*K
5.4 5.6 5.8
/ NDF = 83.54 / 60, Prob = 2.40%2χ
]2 mass [GeV/cBπ -π -π +π5.4 5.6 5.8
2C
andi
date
s pe
r 5
MeV
/c
0
50
100 data
fit
+π -s D→ s B
background
π cΛ → bΛ
]2 mass [GeV/cBπ -π -π +π5.4 5.6 5.8
/ NDF = 71.40 / 64, Prob = 24.55%2χ
proper time [cm]0 0.2 0.4
mµC
andi
date
s pe
r 50
1
10
210
data
fit+π -
s D→ s B
background
π - D→ 0 Bπ cΛ → bΛ
proper time [cm]0 0.2 0.4
/ NDF = 46.61 / 29, Prob = 2.04%2χ
proper time [cm]0 0.2 0.4
mµC
andi
date
s pe
r 50
1
10
210
data
fit+π -
s D→ s B
backgroundπ cΛ → bΛ
proper time [cm]0 0.2 0.4
/ NDF = 35.48 / 25, Prob = 7.99%2χ
48
Non-Golden Channels, Bs → Ds3π
]2 mass [GeV/cBπ 3-π) - K+
(Kφ5.4 5.6 5.8
2C
andi
date
s pe
r 5
MeV
/c
0
50
100
data
fitπ 3s D→ s B
background
π 3- D→ 0 Bπ 3cΛ → bΛ
satellites
]2 mass [GeV/cBπ 3-π) - K+
(Kφ5.4 5.6 5.8
/ NDF = 41.73 / 45, Prob = 61.14%2χ
]2 mass [GeV/cBπ 3-
) K-π +(K*K
5.4 5.6 5.82
Can
dida
tes
per
5 M
eV/c
0
50
100 data
fitπ 3s D→ s B
background
π 3- D→ 0 Bπ 3cΛ → bΛ
satellites
]2 mass [GeV/cBπ 3-
) K-π +(K*K
5.4 5.6 5.8
/ NDF = 41.67 / 39, Prob = 35.54%2χ
]2
mass [GeV/c-π +π + π) π (3sD5.4 5.6 5.8
2C
andi
date
s pe
r 5
MeV
/c
0
10
20
30
data
fitπ 3s D→ s B
backgroundπ 3cΛ → bΛ
satellites
]2
mass [GeV/c-π +π + π) π (3sD5.4 5.6 5.8
/ NDF = 24.54 / 24, Prob = 43.13%2χ
proper time [cm]0 0.2 0.4
mµC
andi
date
s pe
r 50
1
10
210 data
fitπ 3s D→ s B
background
π 3- D→ 0 Bπ 3cΛ → bΛ
proper time [cm]0 0.2 0.4
/ NDF = 28.01 / 26, Prob = 35.82%2χ
proper time [cm]0 0.2 0.4
mµC
andi
date
s pe
r 50
1
10
210 data
fitπ 3s D→ s B
background
π 3- D→ 0 Bπ 3cΛ → bΛ
proper time [cm]0 0.2 0.4
/ NDF = 40.82 / 24, Prob = 1.74%2χ
proper time [cm]0 0.2 0.4
mµC
andi
date
s pe
r 50
1
10
data
fitπ 3s D→ s B
backgroundπ 3cΛ → bΛ
proper time [cm]0 0.2 0.4
/ NDF = 19.38 / 18, Prob = 36.86%2χ
49
Performance of Neural Network Selection
2ca
ndid
ates
per
20.
0 M
eV/c
500
1000
1500
2000
2500
3000
CDF Run II Preliminary
Neural Network
-1L = 1.0 fb
Cut Based
]2candidate mass [GeV/c4.8 5 5.2 5.4 5.6 5.8 6
2ca
ndid
ates
per
20.
0 M
eV/c
0
500
1000
1500
2000
2500
3000
]2candidate mass [GeV/c4.8 5 5.2 5.4 5.6 5.8 6
2ca
ndid
ates
per
20.
0 M
eV/c
0
500
1000
1500
2000
2500
3000 Neural Network, butnot Cut Based
]2candidate mass [GeV/c4.8 5 5.2 5.4 5.6 5.8 6
Cut Based, butnot Neural Network
50
Amplitude Scan Non-Golden Modes
]-1 [pssm∆
0 5 10 15 20 25 30 35
Am
plitu
de
-3
-2
-1
0
1
2
3σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-117.1 ps-128.3 ps
A = 1.29 ± 0.29(stat)consistent with 1 for ∆ms ∼ 17.75 ps−1
51
Likelihood Curves - Non-Golden Channels
Non-Golden LikelihoodMinimum: −9.6
Spring analysisMinimum: −6.4p-value: 0.2%
Non-Golden sample
∆ms = 17.66 ± 0.11 ps−1
]-1 [pssm∆15 16 17 18 19 20
log(
L)∆
-10
-5
0
5
10
15
CDF Run II Preliminary -1L = 1.0 fb
Consistent result with Golden Only
52
Combined Amplitude ScansSemileptonic Hadronic
]-1 [pssm∆
0 5 10 15 20 25 30 35
Am
plitu
de
-4
-3
-2
-1
0
1
2
3
4σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-116.5 ps-119.3 ps
X_ s D+ l→ 0
sB
]-1 [pssm∆
0 5 10 15 20 25 30 35
Am
plitu
de
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-117.1 ps-130.7 ps
Signal at ≈ 17.75 in hadronic analysis
Note☞ world best semileptonic analysis: 19.3 ps−1
☞ hadronic analysis in different league: 30.7 ps−1
53
Combined Amplitude Scan
]-1 [pssm∆
0 5 10 15 20 25 30 35
Am
plitu
de
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-117.2 ps-131.3 ps
A = 1.21 ± 0.20(stat) compatible with 1 for ∆ms ∼ 17.75 ps−1
A/σA(∆ms = 17.75 ps−1) = 6.05, but what is the p-value?
54
Likelihood Profile
Difference, −∆ log(L)
log(L (A = 1)) − log(L (A = 0))
Minimum: −17.26
]-1 [pssm∆0 5 10 15 20 25 30 35
log(
L)∆
-30
-20
-10
0
10
20
30 data
expected no signal
expected signal
Key question:How often can random tags produce a minimum at least as deep?
55
Likelihood Significance
min log(L)∆
-30 -25 -20 -15 -10 -5 00
2
4
6
8
10
12
14
610×
observed
randomly tagged
=17.77sm∆signal
min log(L)∆-20 -15 -10 -5 0p-
valu
e
-910
-810
-710
-610
-510
-410
-310
-210
-110
1
σ5
28 trials out of 350 millionp-value ≈ 8 × 10−8 corresponding to 5.4σ
(5 standard deviations is = 5.7 × 10−7)→ passed observation criterion
56
∆ms Measurement∆ms = 17.77 ± 0.10(stat) ± 0.07(syst) ps−1
was submitted to PRL on Monday
]-1 [pssm∆15 16 17 18 19 20
log(
L)∆
-10
0
10
20
30combinedhadronic
semileptonic
Systematic☞ well behaved☞ ct scale uncertainty☞ rest: small
Agrees with SM18.3 +6.5
−1.5 ps−1EPS 2005
Agrees with 1st result17.31 +0.33
−0.18(stat) ± 0.07(syst) ps−1
PRL 97 (2006) 62003
57
Visualizing the Result
∆ms = 17.77 ± 0.10(stat) ± 0.07(syst) ps−1
[ps]sm∆/πDecay Time Modulo 20 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Fitt
ed A
mpl
itude
-2
-1
0
1
2
data
cosine with A=1.28
CDF Run II Preliminary -1L = 1.0 fb
Proper decay time folded onto a 2π interval
58
Direct Measure of |Vtd /Vts|Relation between ∆mq and Vtq
∆ms∆md
= mBsmBd
ξ 2|VtsVtd
|2
Inputs☞
mBdmBs
= 0.98390 PRL 96 (2006) 202001
☞ ξ = 1.21 +0.047−0.035 M.Okamoto hep-lat/0510113
☞ ∆md = 0.507 ± 0.005 PDG 2006
|Vtd ||Vts| = 0.2060 ± 0.0007(exp) +0.0081
−0.0060(theo)
Best so far Belle: PRL 96 221601 (2006)
|Vtd ||Vts| = 0.199 +0.026
−0.025(exp) +0.018−0.016(theo)
59
ConclusionsLong journey ended☞ 19 years of search to see Bs-Bs oscillations☞ found signal consistent with Bs-Bs oscillations☞ significance: 5.4σ corresponding to p = 8 × 10−8
]-1 [pssm∆
0 5 10 15 20 25 30 35
Am
plitu
de
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2σ 1 ± data
σ 1.645
σ 1.645 ± data
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-117.2 ps-131.3 ps
∆ms = 17.77 ± 0.10(stat) ± 0.07(syst)60
Accomplishments in the Course of the AnalysisPhD Theses
C.Chen UPenn Charm Cross Section MeasurementI.Furic MIT Reconstruction of Bs → D−
sπ+
A.Bolshov MIT Reconstruction of Bs → D−s3π
S.DaRonco Padova Lifetimes from Exclusive ReconstructionJ.Piedra Cantabria B0 Mixing and Tagger CalibrationG.Giurgu CMU Muon TaggingV.Tiwari CMU Electron TaggingD.Usynin UPenn Charged Particle Composition Around B MesonsG.Salamanna Rome I Opposite Side Kaon TaggingA.Belloni MIT SSKT and Neural Network for Hadronic DecaysN.Leonardo MIT Likelihood FrameworkJ.Miles MIT Proper Time Resolution and Partial DecaysG.Di Giovanni Paris Same Side Kaon Tagging (next gen. analysis)B.Casal Cantabria Neural Network (next gen. analysis)
2006 Tollestrup AwardG.Ceballos (Cantabria), I.Furic (Chicago), S.Menzemer (MIT/Cantabria)
61
The End
62
New Physics in Loops?from Murayama et al. hep-ph/0212180
bR
g~g~
bR
sR
sR
bR~
bR~
sR~
sR~
(δ23)RRd
(δ23)RRd
b
b
L
L
g~g~
sR
sR
b
b
R
R
~
~
b
b
L
L
~
~
s
s
R
R
~
~
δd23( )
RRtanβµmb
tanβµmb δd23( )
RR
Supersymmetry model☞ gluino in loop☞ squarks in loop☞ describes all data☞ allows very high ∆ms
☞ ∆ms excludes models→ ∆ms sensitive to
New Physics0
50
100
150
200
250
300
350
400
450
500
−1 −0.5 0 0.5 1
κ= −1.1
0
50
100
150
200
250
300
350
400
450
500
−1 −0.5 0 0.5 1
κ= −1.5
0
50
100
150
200
250
300
350
400
450
500
−1 −0.5 0 0.5 1
κ= −2.0
0
50
100
150
200
250
300
350
400
450
500
−1 −0.5 0 0.5 10
50
100
150
200
250
300
350
400
450
500
−1 −0.5 0 0.5 1
κ= −0.7
∆ Βs
∆ Βs
M vs. SφΚ
M
−1(ps )
SφΚ
m
[1/p
s]∆
s400
500
300
200
100
0SM Expectation
63
Observables: Neutral B Meson Mixing
For Bs no imaginary matrix element involved|Bs,H ⟩ = 1p
2(|Bs⟩ + |Bs⟩) CP odd |Bs,L⟩ = 1p
2(|Bs⟩ − |Bs⟩) CP even
Initial particles and anti-particles|Bs⟩ = 1p
2(|Bs,H⟩ + |Bs,L⟩) |Bs⟩ = 1p
2(|Bs,H ⟩ − |Bs,L⟩)
Behavior in proper timeP(t)B0→B0 = 1
2τ e−t /τ (1 + cos ∆mt)P(t)
B0→B0 = 12τ e−t /τ (1 − cos ∆mt)
Determine asymmetry
A0(t) = N(t)unmixed−N(t)mixedN(t)unmixed+N(t)mixed
= cos(∆m t)0
0.2
0.4
0.6
0.8
0 1 2 3proper decay time, t [ps]
prob
abili
ty d
ensi
ty
unmixedmixedtotal
64
Accelerator Setup at FermilabComplex accelerator system
C D F D0
Tevatron Collider☞ Tevatron 1 km ring radius, CM energy
p
s = 1.96 TeV☞ 36x36 colliding p, p bunches, 1011(1010) p(p) per bunch
65
CDF Detector – Opened Up
66
b Production: Tevatron versus B FactoriesDisadvantages
☞ nqq = 1000 x nbb
☞ hostile environment☞ second b often outside fiducial
Advantages☞ larger cross section x105
☞ larger boost x10☞ b hadrons: B+, B0, Bs, Bc, Λb, ..
Conclusion☞ fast event selection necessary, we call this trigger☞ typical rejection factors are 1/50,000
67
Upgrades: Displaced Track Trigger
Decay PointB
Sketch of a B Decay
p
B Production Point
d0 − impact parameter
Challenge:☞ fast readout☞ track above 25 kHz
B Signatures☞ electrons, muons☞ high momentum tracks☞ displaced tracks
−600 −400 −200 0 200 400 6000
2000
4000
6000
8000
10000
12000
14000
16000
18000
m)µ (0SVT d
25≤SVT2χ 2 GeV/c; ≥tP
mIncludes
beamspot33 mµ µ = 47 σ
mµtr
acks
per
10
68
Vertexing - Key Detector
Layer 00☞ innermost silicon layer: mounted on beampipe☞ at distance of about 1.5 cm from the beamline☞ significant boost for vertexing resolution
69
Flavor Tagging - Key Detector
Time-of-Flight Detector☞ distinguish pions/kaons to p ≈ 1.5 GeV/c, 100 ps resolution☞ most important information for same side tagger
70
Unbiased Analysis Upgrade
Upgrade power estimated in an unbiased fashion
Signal Improvements☞ fits of mass spectra provide estimate of S/
pS + B
Flavor tagging☞ OST improvement measured in calibration samples:`+track, B0/B+
☞ SSKT improvement obtained from Monte Carlo
71
Proper Time Resolution
72
Proper Time Resolution - Basics
Significance revisited
1/σ =
q
nSεD2
2
q
nSnS+nB
exp(−(∆msσct)22 )
Reconstructed proper decay timect = LB
xymBpB
Thadronic
ct = L`Dxy
mBp`D
T⋅
�
p`DT
pBT
LBxy
L`Dxy
�
MCsemileptonic
Understanding of resolution☞ irrelevant for lifetime measurements☞ critical piece for Bs oscillations☞ the faster the more important☞ calibration on data needed
-1
-0.5
0
0.5
1
0 1 2 3proper decay time, t [ps]
asym
met
ry
Realistic resolution: vtx: 50 µm
-1
-0.5
0
0.5
1
0 1 2 3proper decay time, t [ps]
asym
met
ry
Realistic resolutions: vtx: 50 µm pt: σ(p)/p = 5%
73
Proper Decay Time Resolution- CalibrationUse prompt D+ and track
☞ large sample of prompt D+
☞ most tracks from PV☞ same topology as signal☞ measure of ct resolution
proper time [cm]
-0.2 -0.1 0.0 0.1 0.2
mµca
ndid
ates
/ 20
10
210
310
410
data+π - D
fit
+ f
++ f
prompt
proper time [cm]
-0.2 -0.1 0.0 0.1 0.2
CDF Run II Preliminary
Calibrated on our data
74
Proper Decay Time Resolution - Results
m]µproper time resolution [0 20 40 60 80 100
mµP
roba
bilit
y pe
r 5
0.00
0.05
0.10
0.15
0.20
0.25
m]µproper time resolution [0 20 40 60 80 100
mµP
roba
bilit
y pe
r 5
0.00
0.05
0.10
0.15
0.20
0.25+π (3)-
s D→ sB
mµ> = 26.0 ctσ <
-1 1 fb≈CDF Run II Preliminary L
one oscillation at m = 18/ps∆ s
Optimal use of data☞ PV per candidate☞ resolution per candidate
Superior resolution☞ access to high ∆ms
☞ CDF plays in a newleague
75
Proper Decay Time Resolution - Results
sB
T/pReconstructedT = pκ
0.4 0.6 0.8 1.0
prob
abili
ty d
ensi
ty
5
10
ν l (*)s D→ 0
sBall 2 3.1 GeV/c≤ lsD 2.0 < m2 4.5 GeV/c≤ lsD 4.3 < m2 5.1 GeV/c≤ lsD 4.9 < m
π *s D→ 0
sB
ρ s D→ 0sB
sB
T/pReconstructedT = pκ
0.4 0.6 0.8 1.0
Proper decay time [ps]0 1 2 3
Pro
per
deca
y tim
e re
solu
tion
[fs]
0
200
400
600
800
π s D→ 0sB
ρ s / Dπ *s D→ 0
sB
2 5.1 GeV/c≤ lsD, 4.9 < mν l (*)s D→ 0
sB
2 4.5 GeV/c≤ lsD, 4.3 < mν l (*)s D→ 0
sB
2 3.1 GeV/c≤ lsD, 2.0 < mν l (*)s D→ 0
sB
Hadronic Bs → Ds(3)π☞ σ0
ct ∼ 26 µm, 87 fs; σp/p < 1%Semileptonic Bs → `DsX
☞ σ0ct ∼ 30-70 µm, 100-230 fs; σp/p ∼ 3-20%
76
Flavor Taggers - Overview
L xy
ct = L xymp
B
T
���������������
���������������
opposite side
K
K
π
π
0sB
D s
+
+
K+
same side (vertexing)
opposite
D meson
fragmentationkaon
−l
side lepton
B hadronB jet
Collision Point
Creation of bb
side kaonopposite
K −
typically 1 mm
Production flavor tagging☞ combine same side and opposite side tags☞ opposite side: muon, electron, kaon and jet charge taggers
jet selection algorithms: vertex, jet probability and highest pT
☞ same side: particle ID based Kaon Tagger77
Flavor Taggers - Maximize PerformanceParametrize tagger performance in dependent variables:here muon tagger and prel
T
Tune on large B+, B0 samples: transfers directly to Bs
→ each event has predicted dilution
78
Flavor Taggers - Fit for Tagger Performance
Fit B+ and B0
☞ `D and Dπ(ππ) are fitseparately
☞ parameters: D and ∆md
☞ depicted: combined `Dsamples with combinedlepton tags
proper decay-length [cm]
0.05 0.1 0.15 0.2
asym
met
ry
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
CDF Run II Preliminary
D Xµ e/→B
Soft Lepton Taggers
-1 355 pb≈L
proper decay-length [cm]
0.05 0.1 0.15 0.2
asym
met
ry
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
data
fit projection
contribution0 B contribution+ B
B0 Mixing Result☞ 0.536 ± 0.028(stat) ± 0.006(syst) ps−1 hadronic
☞ 0.509 ± 0.010(stat) ± 0.016(syst) ps−1 semileptonic
☞ 0.507 ± 0.005 ps−1 PDG 2006
79
Flavor Taggers - ResultsUsage of flavor taggers
☞ OST: selection of best available OS tag☞ OST and SST use disjunct input information☞ simple uncorrelated OST/SST combination algorithm
εD2[%] Hadronic SemileptonicMuon 0.48 ± 0.06 0.62 ± 0.03Electron 0.09 ± 0.03 0.09 ± 0.01JQ/Vertex 0.30 ± 0.04 0.28 ± 0.02JQ/JetCharge 0.46 ± 0.05 0.34 ± 0.02JQ/highPt 0.14 ± 0.03 0.11 ± 0.01OST 1.47 ± 0.10 1.44 ± 0.04SSKT 3.42 ± 0.96 4.00 ± 1.12
SSKT improves tagging by factor of 380
Unbinned Likelihood Fit Overview
For each sample component and event
L = Lm ⋅ Lt ⋅ Lσt ⋅ LD
Most complex is proper decay time description
Lt =1N
κe−κ t 0
τ
τ1 ± ASDD cos(∆msκ t 0)
2⊗ R(t − t 0; Sσtσt) ⋅ ε(t)⊗ F (κ )
81
Amplitude Scan Method - Using B0
]-1
[psdm∆0 10 20 30
Am
plitu
de
-1
0
1
2σ 1 ± data
σ 1.645
(stat. only)σ 1.645 ± data
95% CL limit
sensitivity
-10.4 ps-127.5 ps
CDF Run II Preliminary -1 355 pb≈L
]-1
[psdm∆0 0.5 1 1.5 2
Am
plitu
de
-1
0
1
2
σ 1 ± data
σ 1.645
(stat. only)σ 1.645 ± data σ 1 ± dm∆
95% CL limit
sensitivity
-10.3 ps-1> 2.0 ps
CDF Run II Preliminary -1 355 pb≈L
Unbinned likelihood fit☞ p ∼ ( 1 ± AD cos(∆mt))☞ scan fixed values of ∆m☞ record A and σ(A)
Signal ≡ unit amplitude☞ else A consistent with 0☞ exclude ∆m @95%CL for
(1 − A) > 1.645σ(A)
82
Systematic Uncertainties on Amplitude
Hadronic Semileptonic
]-1
[pss m∆
0 5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45Total
ctσNon-Gaus Cabibbo DConSSTOST+SST Corr
ctσSΓ / Γ ∆
]-1 [pssm∆0 10 20 30 40
syst
.Aσ
0.05
0.1
0.15
0.2
physics bkg.
ctS
DS
prompt dil.
promptf tailsctσ
total
Systematic uncertainties ∼ 0.15-0.20 at high ∆ms:→ analysis is statistically limited
83
Probabilities of Uncertainties
]-1 [pssm∆Uncertainty on 0 0.2 0.4
-1E
xper
imen
ts p
er 1
0 fs
1
10
210
Positive Unc. Golden Mode
Prob: 43%
]-1 [pssm∆Uncertainty on 0 0.1 0.2 0.3 0.4 0.5
-1E
xper
imen
ts p
er 1
0 fs
1
10
210
Positive Unc. Other Hadronic
Prob: 38%
]-1 [pssm∆Uncertainty on 0 0.05 0.1 0.15 0.2
-1E
xper
imen
ts p
er 4
fs
1
10
210
Positive Unc. Hadronic + Golden
Prob: 37%
]-1 [pssm∆Uncertainty on 0 0.1 0.2 0.3 0.4 0.5
-1E
xper
imen
ts p
er 1
0 fs
1
10
210
Negative Unc. Golden Mode
Prob: 37%
]-1 [pssm∆Uncertainty on 0 0.1 0.2 0.3 0.4 0.5
-1E
xper
imen
ts p
er 1
0 fs
1
10
210
Negative Unc. Other Hadronic
Prob: 38%
]-1 [pssm∆Uncertainty on 0 0.05 0.1 0.15 0.2
-1E
xper
imen
ts p
er 4
fs
1
10
210
Negative Unc. Hadronic + Golden
Prob: 18%
Uncertainties as expected for this sample84
Systematic on ∆ms
Relevant systematic uncertainties☞ all related to ct scale☞ common for hadronic and semileptonic samples
Source Value [ps−1]SVX alignment 0.04Track fit bias 0.05P.V. bias from tagging 0.02Others < 0.01Total 0.07
85