b-tagging at LHC
ATLAS
花垣和則 / 大阪大学

Overviewb-quark起源のジェット(b-jet)を同定すること
ジェットの起源となるパートンの識別b-jet, c-jet, tau-jet, light-jet (u,d,s,gluon)

このトークの流れ
b-taggingがなぜ必要か
Overview -- b-taggingのためのアイデア -アルゴリズムの説明とMCでのperformance
データ取得に向けて（注）このトークは私の偏見で構成されています2

Motivation
終状態にb-quarkを含む物理
Higgsが軽いとき H→bb
ttH, bbH/A, qqH etc.
もしHiggsが発見されたら湯川結合の測定

Figure 2.25: The SM Higgs boson decay branching ratios as a function of MH

Some SUSY signature
top : Br(t→bW)~100%
例として質量測定

b-tagging

Figure 2.26: The SM Higgs boson total decay width as a function of MH .

112

3

b-taggingの概略
bジェット
b-hadronからのトラック
Lxy/σxy
Lxy

Secondary Vertex

Primary Vertex

signed d0 d0signed d0/σd0

b-hadronは崩壊するまでに数ミリ飛べる(cτ~400-500μm)
大きなインパクトパラメータdを持つトラック
secondary vertex の存在 (大きな Lxy )⇐ si-pixel, si-strip で荷電粒子の飛跡を精度よく測定
Br(b→lX)~11% + Br(b→c→lX)~11% (l=e or μ)⇐ ジェット近傍のミューオン（あるいは電子）を見つける4b-taggingの概略
bジェット
b-hadronからのトラック
Lxy/σxy
Lxy

Secondary Vertex

Primary Vertex

signed d0 d0signed d0/σd0

b-hadronは崩壊するまでに数ミリ飛べる(cτ~400-500μm)
大きなインパクトパラメータdを持つトラック
secondary vertex の存在 (大きな Lxy )今日の話
5

ATLAS 内部飛跡検出器群

Pixel
Silicon Strip (SCT)
Transition Radiation Tube (TRT)6

アルゴリズムの説明とMCでのperformance

10

Arbitrary units

Arbitrary units

Arbitrary units

b-jets-11b-jetsLight jets
インパクトパラメータによるtagging
10-2

10-2

Light jets

10-1

Signed Impact Parameter signiﬁcance ( SIP)を使うCounting method
simpleb-jetsある閾値を設けて大きなSLight
IPを持つ
jets
robustトラックの数を数える
Secondary vertex charged energy fraction
Secondary vertex mass (GeV)
Number of two-track vertices
Jet Probability
Tevatron
Figure 12: SecondaryR(s)vertexをresolution
variables: invariantfunction
mass of all tracks
in vertex (left), energy fraction ver
として
でも使用
10-2

-3

10

-3

10

-3

10

10-4

10-4

-5

10

0

1

2

3

4

5

6

7

8

9

10

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

0

5

10

15

20

25

30

|SIP |
tex/jet (center) and number of!two-track
vertices (right) for b-jets and light jets.
R(s)ds← light jet から来る
Ptrk = −a!0R(s)ds
トラックらしさ−a6.1.4 Formalism of likelihood ratio

For both the impact parameter tagging and the secondary vertex tagging, a likelihood ratio method isused: the discriminating variables are compared to pre-defined smoothed and normalized distributions
ratio
for both the b- andLikelihood
light jet hypotheses.
Two-dimensional probability density functions are used as welfor some taggers. Theb-,
ratioc-,of theprobabilitiesb(Si )/u(Si ) defines the track
light-jet
それぞれについてS
IPのor vertex weight, which canbe combined in a jet weight WJet as the sum of the logarithms of the individual weights Wi :likelihoodを用意する
NT

NTb(Si )
WJet = ∑ lnWi = ∑ lnu(Si )i=1
i=1
8

sophisticated
not robust(1)Jet Probability
例としてDØでの分布

Ptrk =! |SIP |positive SIP
R(s)ds−a!0R(s)ds−anegative SIP を使うので(=light jetだけでよい）
calibration sampleに困らない→実験初期でもreliable

negative SIP

positive SIP

negative SIP
9the tracks in the jet is the basis of the first method to tag b-jets. Three taggers are defined in this way:
Likelihood Ratio
alism of likelihood ratioall
IP1D relies on the longitudinal impact parameter, IP2D on the transverse impact parameter and finally
IP3D which uses two-dimensional histograms of the longitudinal versus transverse impact parameters.

Tracks in b-jets-1

Tracks in c-jets

Tracks in light jets

Arbitrary units

Arbitrary units

impact parameter tagging and the secondary vertex tagging, a likelihood ratio method is
criminating variables are compared to pre-defined smoothed and normalized distributions
10
10b-, c-, light-jet
IPの確率分布をb- and light jetShypotheses.
Two-dimensional
probability density
functions are used as well
10 or vertex weight, which cangers. The ratioそれぞれに対して準備of the probabilities b(Si )/u(Si ) defines the track10
in a jet weight WJet as the sumof the logarithms of the individual
weights Wi :10
-1

Tracks in b-jets
Tracks in c-jets-2

Tracks in light jets

-2(reference histogram)
NT

-3

NT

b(Si )
WJet = ∑ lnWi = ∑ lnu(Si )
i=1
i=1
-3

10

10-4

(1)

-5

10

10-4

likelihood
ratio
ion of such a weightis shown on
figureなので別の
13 for b-, c- and light10 jets for two different taggers:-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
-20
-10
0
10
20
30
40
IP2D, combinesdiscriminant
only the transverse
impact parameter significanceof tracks,
while
the
を簡単に足せる
Signedtransverse impact parameter (mm)Signed transverse impact parameter significance
IP3D+SV1, combines in two dimensions the transverse and longitudinal impact parameter
Jet Probability
methodではd0 distribution (left) and signed transverse impact paramFigure 11: Signed transverse
impact parameterof tracks as well as the threevariables
the secondary vertex search.
eter significanced0 /σfromd distribution (right) for b-jets, c-jets and light jets.
-6light-jet の SIP だけを使っている
6.1.3 Secondary vertex taggers
naivëに Wjetのほうがdiscriminant powerが大き
ihood ratio and track
categories
To further increase the discrimination between b-jets and light jets, the inclusive vertex formed by the
decay products of the bottom hadron, including the products of the eventual subsequent charm hadron
いと予想できる
n already that tracks maydecay,
exhibitbehavior
thetrack
selection,
likea goodfor
can bedifferent
sought for [5].
The search evenstarts byafter
building
all thetwo-track
pairs that form
with toa V takeare rejected.
All tracks fromthe remaining
two-trackvertices areth shared hits (Fig. b(c)-jetに対するreferenceの作成が問題
7 on vertex.
page Vertices10). compatible
One ideaadvantageof thedifferent
properties
combined in a single vertex, and three of its properties are exploited: the invariant mass of all the tracks
00

o arrange all tracks into various
categories
andhistograms
forin the vertex,
the ratio of thesumuseof thededicatedenergies of the reference
tracks participating
to the vertex tothe eachsum ofthe energies of all tracks in the jet, the number of two-track vertices. These properties are illustrated
e likelihood ratio formalism
allows then to incorporate
suchmakecategories
in a straightforward
10 The SV taggers
on figure 12 for b-jets and light jets.
use of these properties: SV1 relies on a 2D-

where distance in transverse plane between reconstructed inclusive vertex
vertex is shown. A tail in this figure originates from a presence in the s
the tracks Vertex
from D-mesons
decays. The inclusive secondary vertex reconst
Secondaryreconstruction
gives some mean position between a B-meson decay point and a D-mesonsec. vtx rec. eﬃciency

10-1

10-2

Arbitrary units

layers and 3(2) disks of pixel detector,1 1%(2%) of modules(chips) ineffib-jetsb-jets
0.5%(1%) inefficiency. WH events with MHiggs = 100(400)
GeV /c2 areLight jets
Light jets
10
10
into bb̄ or uū pair. Jets are reconstructed around primary quarks directions
Arbitrary units

Arbitrary units

p-p衝突地点から有意にProcessεbεu
WH(100 GeV) 3 layers 57.0% 3.9%
離れた b-hadronの崩壊
WH(100 GeV) 2 layers 52.2% 2.8%地点（secondary vertex）
WH(400 GeV) 3 layers 77.2% 12.5%
WH(400 GeV) 2 layers 70.3% 9.0%
を探す
Table 6: Probability to find the inclusive secondary vertex inside jet for dib-hadronの崩壊地点を測定してるわけだから
jet flavours.
secondary vertex の再構築に使われたトラックを使って不変質量The probabilities to find the secondary vertex inside jet for the descr
他にもdiscriminantとして使える変数あり
are shown in tab.6 for the realistic DC0 setup with low luminosity (L =
-2

-1

10-2

-3

10

-3

10

-3

10

b-jetsLight jets

10-4

10-4

-5

10
0

1

2

3

4

5

6

7

8

9

10

Secondary vertex mass (GeV)0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1Secondary vertex charged energy fraction

11

0

5

10

15

20

25

30

Number of two-track vertices

V0 粒子のカット
IP based, secondary vertex based どちらも lightquark 起源の長寿命粒子（Ks, Λ, photon
conversion）は、２トラックの不変質量（とvertexの位置）で除くMarch 10, 2008 – 10 : 22
DRAFT
13

Figure 5: Some distributions for good reconstructed two track vertices.
a) - π + π − invariant mass spectrum with a peak of K 0 decay;12b) - pπ invariant mass spectrum with a peak of Λ decay;Comparison of PV resolution
Vertexingについて
Comparisonof vertex reconstruction resolution of different
algorithms using WHbb/uu with and without pileup:

Deterministic
Annealing
KalmanKalman
MVF and
VKal
with
best
resolution in x and z
Billoir
Influence of pileup
on resolution is small, but problem in pileup is to
直線で近似

find the(signal) vertex
fullcorrect
track parameter
Kai Grybel, University of Siegen, Marseille b-tagging workshop, 11.05.07

ごちゃごちゃありますが、基本的には全部 Kalman Filter
Billoir method も formalism が違うだけ
Deterministic Annealing (adaptive ﬁtter) だけはやっておいたほうがよい
13-7-Adaptive Vertex Fitter

ve Vertex Fitting

ほとんど全てのトラックをエラーにweightをかけること
ove the recognition
で使う of outliers and allow a better separationand secondary
vertices, different robust fitting techniques
今までの方法ではエラー（など）に閾値を設けてveloped [4]クリーンなトラックだけ使っていた[5]. The main idea of robust fitting methods isntribution of distant tracks to the vertex fit.
Fermi Weight Function,according! = 10ve fitting algorithm, track errors are re-weighted
bution to the vertex by a sigmoidal function:
2

1

T=0
T = 0.5

wi =

0.8

1

T=1

(1)

0.6

(χ2i −χ2cutof f )/2T

1+e

0.4

2

contribution of track i to the vertex, χ2cutof f is the distancefunction drops to 0.5, and T is a parameter that controls
the function. Given the analogy with the Fermi function in
Figure 5: Weight of a track with respect to a vertex as a function of the χ
distance
to the vertex for different temperature parameters. In the Adaptive
odynamics, the parameter T is called
temperature.
fitting, all tracks contribute to the fit when T > 0.
0.2

00

5

10

15
20
25
track !2 contribution to the vertex

2

14

2

実際に使われてるアルゴリズム

Arbitrary units

Arbitrary units

ATLASのデフォルトはlikelihood ratio
2D SIP + 1D SIP + 10ページの変数３つ
他にstudyされてるのは
2D SIP 単体、2D+1D SIP, JetProb., charm decayまで考慮してのvertexing + default
b-jetsc-jetsLight jets

10-1

10-2

10-1

10-2

-3

-3

10

10

10-4

10-4
-5

-5

10

-6

10

10

-6

10

-20

b-jetsc-jetsLight jets

-10

0

10

20

30

40

-20

2D impact parameter weight

-10
0
10
20
30
40
3D impact parameter + secondary-vertex weight

Figure 13: Jet b-tagging weight distribution for b-jets, c-jets and purified light jets. The left plot is fora tagger based on the transverse impact parameter significance of tracks. The right plot corresponds toa tagger using the transverse and longitudinal impact parameter significances of tracks as well as theproperties of the secondary vertex found in the jet.

CMSは JetProb. をデフォルトとして薦めてるらしい
他は counting SIP, secondary vtx. reconstruction
6.2 Other spatial algorithms

15

The spatial algorithms based on likelihood ratios require an a-priori knowledge of the properties of boththis note. More detailed information about ATLAS track reconstruction and b-tagging algorithms can befound in [2].
Eﬃciency and Fake Rejection Factor in MC
The efficiency to tag a jet of flavour q as b-jet, εq , is defined as:
Number of jets of real flavour q tagged as bεq =.
Number of jets of real flavour q(1)

Light jet rejection

Light-jet rejection

Usually εb islikelihood
called taggingを作るための
efficiency and εudsc reference- mistagging ratehistogram
The inverse of は
the mistagging rate
rudsc = 1/εudsc is called b-tagging rejection power or simply rejection. The assignment of a certain
ttjj sample
flavour to a large
jet is nottt,
unambigously
defined. For reconstruction and analysis purposes the following
definition has been
introduced:pthe
jet flavour is the flavour of the heaviest quark after gluon radiation
注意：jetT, ηなどでbin切りされていないのでand splitting within a cone of some size around jet direction. The default cone size used in ATLAS andperformancesampledependence
in the current noteis ∆R < 0.3. To testには
the purealgorithmic
performance of the あり
algorithms, a procedure
called “purification” may be applied. Here,a light quark
jet is only considered if there is no heavy parton
10
ip2d
10
(b- or c-quark) or τ lepton within a coneip3dof 0.8 around the jet direction.
sv1
デフォルト
jetprob
Several jet reconstruction algorithms
are available in ATLAS [3]. The b-tagging performance may
jetfitter1010depend on the jet algorithm,
but the studies of this dependence
is outside the scope of this note. For thestudies in this note, an iterative cone algorithm with a cone size of ∆R = 0.4 using combined calorimeter
towers as input, has beenused. Charged particle tracks
have been reconstructed with a Kalman filter
10
10
based algorithm [12].
Offline ATLAS jet reconstruction and track reconstruction are completely independent. An assign1
1
ment of tracks to jets isnecessaryfor0.9secondary
b-jet1 tagging. The current
0.3 thus
0.4
0.5
0.6
0.7
0.8
1
0.3vertices
0.4
0.5 search
0.6
0.7 and0.8
0.9
b-jet efficiency
b-jet efficiency
ATLAS method used also in(a)thisnote is again based on a geometricalcone around the jet direction. All
WH events (m =120 GeV)(b) WH events (m =400 GeV)
charged tracks withina certain cone (default value is ∆R < 0.4) around the jet axis are assigned to a jet.
Figure 16: Rejection of light jets with purification versus b-jet efficiency for WH (mH =120 GeV) events
ハードなprocessplot) andand WH(mH =400 GeV)itself
events (rightplot)beandchanged
for the following
JetProb,
IP2D, IP3D,
The assignment比較的ソフトなprocesscone(leftsize
proceduremay
intaggers:
future(kt jetsare evident candidate) if
IP3D+SV1, JetFitterCOMB.
better tagging efficiency is achievable with them. 16
3

2

H

3

IP2D
IP3D

IP3D+SV1
JetProb

IP3D+JetFitter2

Hinteractions. This also holds for the high |η| region, where the amount of material in the tracking region
increases very significantly. In addition, there is currently no rejection of secondary interactions foundto be produced in the pixel disks, unlike what is done in the barrel (cf. Section 6.1.3).

300

Light jet rejection

Light jet rejection

Jet pT and η dependence
IP3D+SV1
IP2D

250

200

400

IP3D+SV1
IP2D

350
300
250
200

150

150

100

100
50

50

0
0

50

100

150

200

250

0
0

300

p (GeV/c)

0.5

1

1.5

2

2.5

|!|

T

(a) Rejection versus jet pT(b) Rejection versus jet |η|

pTとη分布自体に相関があることに注意
Figure 18: Rejection of light jets with purification obtained with two b-tagging algorithms (IP2D and
IP3D+SV1) operating at a fixed b-tagging efficiency of 60% in each bin, for t t¯ events.
本当はηpT 平面上で見るべき
effects conspire to reduce the b-tagging performance as the jet p increases. First of all, theLownumber
pSeveral, fragmentationhighηでのdegradation
Tof
tracks increases with the parton transverse momentum, as shown on Fig. 19,
while the jet is collimated into a narrower cone: since a fixed-size cone is currently used to associate
粒子の多重散乱←of物質量が多い（後述）tracks to the jet this leads to a dilution
the discriminating power in b-jets. The density of tracks in thecore of energetic jets challenges the pattern-recognition ability of the software and of the inner detector
High
T での
itself,pleading
to either degradation
a reduced tracking efficiency or a high level of fakes as shown on Figure 6 inpage 9 for jets with E > 100 GeV. Finally, for very energetic B-hadrons the Lorentz boost leads to
粒子がよりcollimateされて粒子密度が上がる
a much enhanced decay length. The typical cτ (∼ 450µm) of B-hadrons is thus scaled by a factorγ ∼ |p |/m which begins to be significant. For high p jets, the B-hadron can decay at a rather large
そもそもfragmentationからの粒子が増える
radius R , as illustrated in Table 7: close to the inner radius of the pixel detector, leading to more tracking
24
ビームパイプの外まで粒子が飛んでしまう
T

T

B

B

T

B

17

(mH =120 GeV) events and several taggers.
IP3D+SV1, JetFitterCOMB.
JetProb
Purified light jet rejection, 50% 83±1
Purified light jet rejection, 60% 30±0

IP2D
116±2
42±0

IP3D
190±3
59±1

IP3D+SV1
457±13
117±2

JetFitterCOMB
554±17133±2

Summary of Performance at ATLAS

Table 2: Integrated rejection of purified light jets for two fixed b-tagging efficiencies and for WH
WHphysics(MHprocesses=120GeV)(mH =120
GeV)
eventsand several
taggers.
To study
moreenergetic
jets, similar
have been studied for a different Higgs boson
JetProb
IP2D butIP3D
IP3D+SV1
JetFitterCOMB
mass, mH =400 GeV (again such a choice
is unphysicaluseful forthese studies).
The results are
Purified
light 16(b)jet rejection,50%
83±1 116±2 190±3457±13554±17shown
on Figureand Table
3.
Purified light jet rejection, 60% 30±0
42±0
59±1
117±2
133±2
Table
Integrated
rejectionof purified
light jetsTheandbenchmark
c-jets for two
fixed
b-taggingand foreven 3:more
ambiguous
as discussed
previously.
curvesof jetrejectionefficiencies
versus b-tagging
WH(M=400GeV)To study
moreenergeticjets,
physics
processes
studieda different
boson
WH(mH =400
GeV)
eventsandsimilar
severaltaggers.
efficiency
are shownon Figure
17,
for
light
jetsH
(purifiedorhavenot),beenc− andτ-jetsforandfor severalHiggs
taggers.
mass,
GeV (againsucha choice
is unphysicalbutIP3D
usefulstudies).
The results
JetProb
IP2D
JetFitterCOMB
H =400
ThemTable
4 shows
the light
jet rejection
achieved
in t t¯ eventsand infor
tIP3D+SV1
t¯ jthese
j events,
both
samplesbeing arePurified
light16(b)jet rejection,50%
71±1
163±3are t t¯ 179±3
shown
on Figureand Table
3. Thegenerated
with
MC@NLO+Herwig.
latter events
events which297±7
were filtered in395±11order to have
27±0 Since
56±1
58±1 in those
95±1
at Purified
least sixlight
jets, jetof rejection,
which four60%
are taggable.
the performancetwo samples 123±2
were similar,
Purifiedc-jet merged.
rejection, 50%
7.9±0.1 9.7±0.1 10.7±0.2 12.5±0.2
12.7±0.2
they
been
Table
3:haveIntegrated
rejection of purified light jets and c-jets for two fixed b-tagging efficiencies and for
Purified c-jet rejection, 60%
4.7±0.0 5.7±0.1 6.1±0.1
6.8±0.1
7.3±0.1

WH (mH =400 GeV) events and several taggers.
Table 4: Integrated rejection of lightJetProb
jets, c-jets andτ-jets, withand without
purification,
for t t¯ and t t¯ j j
IP2D
IP3D
IP3D+SV1
JetFitterCOMB
eventsTopandfor jetseveraltaggers.
7.2
andmulti-jets
channels
Purifiedlight
rejection,
50%
71±1tt and
163±3ttjj 179±3
297±7
395±11
JetProb
IP2D
IP3D
IP3D+SV1
JetFitterCOMB
Purifiedlightjetrejection,
60%
27±0
56±1
58±1
95±1
123±2
TheRawcaselightof pair-produced
top
quarksisnow
examined.
In
this
case,
the
jet
multiplicity
ismuch
higher,jetrejection,
50%
92±0
142±1
219±1
423±4
593±6
Purifiedc-jet
rejection,channel
50% considered
7.9±0.1thereafter,
9.7±0.1since
10.7±0.2
12.5±0.2
12.7±0.2
even
for
the
lepton+jets
thereisusually
at
least
four
jets from the
Purifiedlightjetrejection,
50%
99±0
181±1
293±2
732±10863±12
Purifiedc-jet
rejection,60%
4.7±0.0
5.7±0.1
6.1±0.1
6.8±0.1
7.3±0.1
hardprocess
and
extra
jets
from
radiation.
Severalflavorsofjets
arepresent
at
the
same
time
in the event:
Raw light jet rejection, 60%
31±0
49±0
67±0
144±1
180±1
twoPurifiedb-jets fromtops, light60%
jet(s) andoften a c-jet
from the76±0
W decaying194±1
hadronically. This
increases
light thejet rejection,
33±0
56±0
213±2
likelihoodof havinglightjets contaminatedwith heavy10.6±0.0
flavor and also
makes the labeling
c-jet
50%
8.4±0.0
9.4±0.0
12.4±0.1
12.3±0.1of jets
7.2theRaw
Top
andrejection,
multi-jets
channels

Purifiedc-jet rejection, 50%
8.4±0.0
9.5±0.0 10.6±0.0 12.5±0.1
12.3±0.1
数字を現段階で真剣に受け取らないで下さい
21
The casepair-produced
top quarks 5.1±0.0
is now examined.
case, the 7.4±0.0
jet multiplicity7.4±0.0
is much higher,
Rawof
c-jet
rejection, 60%
5.8±0.0In this
6.4±0.0
even Purified
for the lepton+jets
channelthere is usuallyat least four
jets from thec-jet rejection,
60% considered
5.1±0.0thereafter,
5.8±0.0since6.5±0.0
7.4±0.0
7.4±0.0
performanceを落とす様々な効果は次頁以降
hard processandextra jetsfrom radiation.
Several13.2±0.1
flavors of 19.0±0.2
jets are present
at the same timein the event:Raw τ-jetrejection,50%10.2±0.1
39.4±0.7
32.9±0.5
18
two b-jetsfromtherejection,
tops, lightoften a c-jet
from theW decaying
hadronically.
This increases
Purifiedτ-jet
50%jet(s) and10.2±0.1
13.4±0.1
19.3±0.2
40.7±0.733.3±0.5

実験家が気になること

8.3.1 Fraction of dead and special pixel channels

検出器のPerformance
The impact of varying the fractionof random deadpixels as discussed in section 4.1.3 was studied forthree taggers and the results are shown on Table 10. When decreasing from 5% to the more realistic 1%
the fraction of dead pixels, the tracking efficiency for tracks fulfilling the b-tagging quality cuts improves
by up to 2.5% (around η ∼ 0) leading to a gain in rejection of at most 20%. As expected, the tagger
using secondary vertex is the most sensitive to such changes.

Baselineの解析ではPixelの５％が死んでると仮定
１％、あるいは３％のdeadだと…
Table 10: Baseline
light jet rejection for several taggers and the relative change with various configurations of the pixel system (see text) for a 60% b-tagging efficiencies in t t¯ events. The used reference
tracking eﬃciency は最大2.5%程度向上
histograms were produced with the respective samples.
IP2D

IP3D

IP3D+SV1εb = 60%
Baseline rejection (5% of dead pixels)
48 ± 1 90 ± 2
201 ± 8Relative change with 1% of dead pixels
1.08
1.09
1.20
Relative change with 3% of dead pixels
1.00
1.00
1.09
Relative change with a dead half-stave on b-layerのほうがRelative Secondarychange with a deadvertex
bi-stave onreconstruction
b-layer
Relative change with a dead half-stave on L3
sensitive
Relative change with a dead bi-stave on L3
もっと死んでるときのRelativechange with digital clustering study はされていない（？）
0.65
0.64
0.81
8.3.2 Dead modules
During the pixel operation, it is thought that the two most likely sources of potential failures could be an
20

TRT
SCT
PixelsBeam Pipe

180!(d ) (µm)

180

Thickness in radiation length (%)

Thickness in radiation length (%)

Baseline rejection (CSC-01-02-00)
53±1
72±2
219±10ID Material DC3-02 layout
ID Material CSC-01-02-00 layout
200
200
Relativechangewith
DC3-02+55% 250 +42%
+56% two studies
To confirm this andestimate the relative importanceand secondaries,
Services
Services of resolution effects
TRT
SCT
PixelsBeam Pipe|"| < 0.5!(z ) (µm)εb = Baseline
60% rejection (CSC-01-02-00)
181±7 The297±15833±71first noticeable
effect is the degradation of the im
for two bins 219±10
in +71%
track pseudo-rapidity are compa
Baseline
rejection
53±1
Relativechange(CSC-01-02-00)
with DC3-02+61%results72±2+70%pT ∼ 1 GeV, the transverse impact parameter resolution w
Relativechangewith
DC3-02
+55%
+42%
+56%
物質量
εb = 60%in the forward region.

were performed.
The light jet rejection160for DC3 and CSC geometries versus b-tagging efficiency is shown160
To25(a)confirm
estimatethe140relative
importanceeffects and resolution
secondaries,fortwothestudies140
on FigureforthistheandIP2Dtagger.
On Figure25(b), oftheresolution
impact parameter
DC3
120 performed. The light jet rejection
120
were
for
DC3
and CSC geometries
versusb-taggingefficiency
is shown
geometrywasrescaled
to
mimic
the
one
of
the
CSC-01-02-00
geometry.
Thisrescalingwasobtainedby100
100
ona Figure25(a)forwhichthe IP2D
tagger.
On Figure 25(b),the impact
parameter
for pthe andDC3η
addinggaussianterm
sigma
is 80pT -dependent(∼ 15µm
at 5 GeV).
Belowresolution
5 GeV, both
80
Tgeometry
was rescaled
to mimic
the60This
one ofthe CSC-01-02-00
geometry.
This rescaling
obtainedby60
dependencies
weretaken into
account.
correction
reduces thediscrepancy
between was
the twosamples40
addinga gaussian term which sigma40 is pT -dependent (∼ 15µm at 5 GeV). Below 5 GeV, both pT and ηfrom 60%20 to 17%. Finally, 8% of the tracks
coming from secondaries were randomly removed from the20
dependencies were taken into account. This correction reduces the discrepancy between the two samples
CSC sample
in ordertogetonaveragethesame
numberof2 secondaries
in both samples. The results
after
0
0
p (GeV)
-4
-3
-2
-1
0
1
2
3
4
-4
-3
-2
-1
0
1
3
4
from 60% to 17%. Finally, 8%
were randomly removed from the! of the tracks coming from secondaries!
(a) Transverse
impact70%
parameter
the two corrections
can11be seen on Figure 25(c),(b) andagree within 10%. Therefore,
aboutof the loss(a)
Release
Release12
CSC sample in order to get on average the same number of secondaries in both samples. The results afterof rejection
comingfromthebeofextra
materialin25(c),theCSC
geometry
with
the
DC3
geometrycanDegradation
comes
from
Figurerespect
24:
Trackto
impactparameter
resolutions
versus trac
thetwocorrections
canseenFigureagree
10%.
Therefore,
about
70%
of
the
loss
Figure1: Distributionof the thickness
the Inneron
Detectorin percentage
ofandradiation
lengthwithinversusPerformanceはこの
the current
geometry(CSC-01-02-00,
in black). Both th
the pseudo-rapidity.
Theworsening
contributions from of
the various
systems andparametercomponents are shownin different andbe explainedby thethe impact
resolution,
atrespect
most
20%
byDC3
extrageometry
secondaries.
ofrejection
comingfrom theextra
materialin the CSC
geometrywithto the
can
200

10

0

0

2.0 < |"| < 2.5

8

150

6

100

4

50

0

2

1

102

10

T

worse resolution
thegeometryを使って評価
forward region 2 < |η| < 2.5 (open symbols) with mo
be explained by the worsening of the impact parameter resolution, and at most 20% by extra secondaries.
In addition to the known increase in the material budget, Monte Carlo events for the CSC exercise
secondary
The other effect is an increased fraction of particle
have been generatedmore
with distorted material,
to account for potentialparticles
approximations in the detector
600

700
600

CSC-01-02-00
CSC-01-02-00
700
description.
In the inner detector,
this additional material has700
been placed at φ > 0 and is notCSC-01-02-00
symmetric
detector700
and producing secondary particles
which can, di
500 length amounts to about 8% (15%) at η ∼ 0
500
in z.
The corresponding increase of the thickness in radiation
600
600
600
tracks. The average
number of tracks p
CSC-01-02-00
CSC-01-02-00fake non-prompt
CSC-01-02-00
DC3-02
DC3-02
DC3-02(∼ 1). Unless otherwise specified, all the Monte Carlo events used in this note have been generated with400
which 400are
500release 12.0.31.
500 matched to a secondary particle is XX in thethis500
distorted geometry ATLAS-CSC-01-02-00, within Athena

IP2D

DC3-02

IP2D

DC3-02

Light jet rejection

400

Light jet rejection

500

700

Light jet rejection

600

Light jet rejection

700

Light jet rejection

Light jet rejection

colors. The geometry used in release 11 (DC3-02) and in release 12 (CSC-01-02-00) are compared.

IP2D

DC3-02300
After theidentification of two-track vertices and rejection
400
2.3300 Treatment of inefficiencies and dead channels
YY2 respectively.
200
200 300
200
300
The
net impact on the b-tagging performance is sum
To200
achieve the best b-tagging performance, reconstructed
100
100 tracks
100
200 have to fulfill tight requirements. In
200
particular, two hits are required in the pixel detector. An accurate description of the pixel inefficiencies
likelihood were re-calibrated on the corresponding samp
100
100
100
0
0
0
mandatory.
A
pixel inefficiencyof 5%
has been0.5used to0.55
simulate 0.6
the events.
0.45 is therefore
0.5
0.55
0.6single 0.65
0.7
0.45
0.65This 0.7also rebuilt
0.45 in situ
0.5 with0.55
0.6 in each
0.65 sample.
0.7
the tracks
With
b-jet
efficiency
b-jet
efficiency
b-jet
efficiency
number0 is very conservative. Measurements on the pixel staves
0 before the installation in the pit give a
0
0.45
0.5
0.55
0.6
0.65
0.7
0.45
0.5
0.55
0.6
0.65
0.7
0.45
0.5 50%,0.55all other
0.6
0.65 being
0.7 equal.
decreasedby about
thingssingle pixel inefficiency below ∼ 0.3% (and∼ 0.1% for the b-layer for which the best components
b-jetbelow
efficiency
b-jet efficiency
b-jet efficiency
were used). The effect of this inefficiency is especially relevant at low |η| where half of the pixel clusters(a) Baseline(b) DC3 impact parameter rescaled sophisticated(c) DC3ones.
impact parameter rescaled and
300

400

300

400

contain only one pixel. Some events with a single pixel inefficiency of 3% (the canonical number used(a) Baseline(b) DC3 impact parameter rescaled
in previous studies [2]) and 1% have also been generated to estimate the improvement of performancein less conservative and more realistic scenarios. Their impact on tracking and b-tagging
21 performance is(c) DC3
parameter
rescaled andCSC
extra impact
secondaries
removed
CSC extra secondaries removed

oducesmisalignments
the threehierarchy
withlevelsof misalignment
in
Inlevels
thisof section
hits
will
refer
togivenclustersin the silicon detectors (pixel andual
misalignment
for atRandom10.
Gaussiandistribution
withsigmasas
Shifts60tabulated.
2.rotations are in mrad.
the TRT. In order to correct the
40 hit errors, The diagonal elements of the erro
100
Level
x
y
z RotX RotY RotZ
twoparametersandc:Module10 30
30
0.3 a0.5
0.2
idual misalignment for Random10. Gaussian distribution with sigmas as20
tabulated. Shifts
layer
10
10
15
0.05
0.05
0.1
10
Random10
Random5
Perfect
AlignedRandom10
Random5
Perfect
Alignedd rotations arerandom
in mrad.
disk
10 10 30
0.2 Alignment
0.2
0.1
!2
set
Alignment
set 2
Level
x
y
z RotX RotY RotZ
2
2 scenarios.
Table
3:
Error
scaling
parametersforthedifferentalignment
The parameter a was tun
σ
=
a
·
σ
+
c
Whole Pixel 10 10 15
0.1
0.1
0.1
Module10 30 30
0.3
0.5
0.2
the Perfect case and used for all alignment scenarios.
layer
10 10 15 0.05
0.05
0.1
All Perfect Random10 Random5 Aligned
disk
10 10 30
0.2
0.2
0.1
a
c(µm)
c(µm)
c(µm)
c(µm)
FigureComparison
the light
rejections
taggers,
SV131and the 13
Pixel Barrel
Phi IP2D,
1.03 IPD3D,
0
3Whole5:Pixel
10 10 of15
0.1 jet 0.1
0.1 for the different
where:
dual misalignment
fortagger
Random5.
Gaussian Left
distribution
withb-tagsigmasas tabulated.
Shiftsare60%
Pixel
BarrelEta
0.97
071Results 34
13
combined
IP3D+SV1.
plot: 50%
efficiency.
Right
plot:
b-tag efficiency.
random
5 using t t¯ events.
Pixel Endcap Phi 1.05
0
30
14
3
ations are are
in mrad.
witherror scaling
Pixel Endcap Eta 1.08
0
43
11
15
Level
x •y σz is RotX
RotY RotZ
the originalerror assigned
to
the
hit
which
shouldnormally
be cloSCT
Barrel0.78
0027Module
5 15Gaussian
15 distribution
0.15
0.3with sigmas
0.1
dual misalignmentfor Random5.
as tabulated.
Shiftsare
SCT
Endcap
0.86
0
6
5
8
if
properly
determined.
layer
7
7
10
0.02
0.02
0.05
tations are in mrad.
TRT Barrel
0.82
0
11
3
37
March
27,
2008
–
18
:
45
DRAFT
disk
7
7
20
0.1
0.1
0.05
Level
x y
z RotX RotY RotZ
TRT Endcap
0.77
0
11
10
19
Whole
7 15
0.05
0.05
0.05
ModulePixel 75 •15
0.3to the0.1 error, which is meant to correct for inaccuracies in th
a10is a0.15
factorlayer
7 7 10 0.02
0.02 0.05
disk
7 7 200.1
0.1
0.05 The values of a are seen to be well below 1 for the SCT and TRT. This is due to an over est
ATLAS7 •7 c10
ATLAS
500 Pixel
ATLAS
is a0.05
constant
in160
quadraturetothe error.
This
is meant to correcA
Whole
0.05 added
0.05
the intrinsic
errors.
In later500
softwarereleases
this has been
improved.
IP3D+SV1
IP3D+SV1160
IP2D

Light jet rejection

400

Light jet rejection

IP3D

Light jet rejection

Light jet rejection

Scaling

Misalignment of Pixel detector

The value for c gives some indicationof the level of residual misalignment. For the Rand
IP3D+SV1
IP3D
residual misalignments.
Random10140
sets, the values of c are higher than what was input for the module shifts. This is
IP2D

140

400 to compensate for the effects of the layer and disc movemen
due to a larger error being needed
SV1
SV1
Scaling Procedure120
be seen thatthe real alignment results in small values of c compared to the hand made120
sets. I
Scaling 300depend on a number of factors such as the
direction
gets 3andµmtrack
and indithe η measurement direction one gets around 15 µm.
error of a hit willclusterone
width

Since each detector component can have significantly different behavi
100
300
100 o
detector
component
has
to
be
taken
into
account, and therefore different setse factors are taken into account when calculating the intrinsic error of the hit. In the case
Scaling Procedure
80expects
3
Effectsof Misalignmenton
Tracking
and Vertexingaligned detector, if theseseparately
intrinsic errorsfor
are properly
determined
one
the
pull
80 as
the
barrelandendcapregionsfor
eachdetector
technology,
200
error
a hit willtodepend
ontoa one.
number of factors such as the cluster width
and track200
dithe hitofresiduals
be close60
ttbarreconstruction,
With ESFor the of
study
thetheimpactof residual
misalignments
ondetector.
track
a sample of60
abou
and when
φ ofmeasurement
directions
in
of
the
pixel
e factors
are taken
calculatinghits
the andintrinsic
theofbyhit.
thecasecase
ences
betweenthe into
realaccountpositionsindividual
thoseerror
recordedaInmisaligned
ES
W H(120) → bb events is used, no pile-up being included. ttbar
ThisNosample
has been reconstruct
40expects the pull
yo aligned
detector,
thesethat
intrinsic
errorsaretoproperlyone
100
an additional
errorif term
must beadded
intrinsicdetermined
error
of
the
hits.
40
WH(120)With
different
scenarios
forpairs,
the 100
detectorlayoutand for error scaling,
with
allES
other settings beingForthederivation
of
the
(a,
c)
the
distributionsofhitresiduals
andf the hit residuals to be close to one.
WH(120)
No
ES
same:
20
20va
3
rences between the real positionsofindividual
hits
and
those
recordedbya misaligned of the pull widths from the ideal
analyzed,andinparticularthedeviations
Random10
Aligned • ”nominal”,
Random5
Perfect
AlignedRandom10
Perfect
Rando
where the reconstruction
isRandom5
performed using
the nominal Aligned
detector geometry,reto an additional error
term that Random5
must be addedPerfectto intrinsic errorof the hits.Random10
set
Alignment
set ing
Alignment
setAlignment
case when theis perfectly
Since the scale
factora theisideal
intended
todetector
correct
thealigned,
intrinsic
resolutions,t
3

22• ”misaligned”, where residual misalignment is added using the Random10 set as describedCalibration
Light jet rejection

Jet Probability
A
A
B
B
A: ジェットに含まれる全てのC
C
トラックを使ってcalibration
B: 真にIPから来てるトラック
のみを使った場合トラックのcategory分けがされていない
Figure 32: Symmetrized and normalized resoluFigure 33: Purified light jet rejection versus b2/3 , pixel(SCT)の数、などで分けるべき
function (transverse
impact parameter sigtagging efficiency for the JetProb tagger runningp tion(sinθ)
nificance) for the JetProb tagger, as extracted folon the same t t¯ events but using different resoluvarious scenarios (cf. text).← d0の分布自体でやれる
tion functions.
σd0 lowingのチューニング
The Bratio
scenario indicates the best performance that could ideally be achieved if all spurious sources
Likelihoodof lifetime contamination could be eliminated. The ratio of the rejection levels for scenario B versus
A is about
1.15 at a 50% tagging efficiency. Therefore just using the b-tagging quality cuts seems tot-tbarを使う（？）
give already very reasonable performance, which do not seem depend much on the calibration of theresolution function, even though many more hypotheses should be checked.
eﬃciencyの測定は出来るかもしれないが、multi8.5.2 Likelihood-basedtaggers
dimensional
likelihoodに耐え得る統計を集める
For the likelihood-based taggers, the p.d.f’s for all the variables (cf. Section 6.1) are built for the b-jetのは難しい
and light jet hypotheses using Monte Carlo. The t t¯ channel can be used in data to isolate a sample of
-1

10

-2

10

200
180
160
140
120
100

-3

10

80
60

-4

10

40
20

-5

10 -20

-15

-10

-5

0

5

10

15

20
a0/!

0
0.45

0.5

0.55

0.6

0.65
0.7
b-jet efficiency

pure b-jets from which the various distributions can be derived: preliminary studies [13] indicate thanmore than 100 pb−1 of data are needed however. For the light jets, it seems very difficult to isolate a pure23
enough sample in data.

Eﬃciency と Fake Rejection の 測定
from t-tbar events

b-tagging efficiency

Eﬃciencyt-tbar で b-tag を使わずに
b-jetサンプル
dijet事象を用いて Sytem 8
100 pb "data"と呼ばれる方法
MC truth
Fake Rejection Factor
SIP のマイナスの分布（=検出器のresolutionによって生じる）を使って評価
Sample dependence をなくすためには、上記２つを以下のn次元空間で測定する必要がある
7 Calibration of b-tagging likelihoods in data
jet pT, η ← 最低この２つ
jet multiplicity, luminosity
などなど
1

0.9
0.8
0.7

0.6
0.5
0.4

-1

0.3
0.2

0.1

0
20

40

60

80

100

120

140

160

180
200
ET [GeV]Figure 28: Likelihood method: simulation of b-tagging efficiencies vs. pT for a 100 pb−1 sample
using the best permutation for events selected with a discriminant cut. The solid line shows thetrue b-tagging efficiencies from the full MC sample using truth information. (b-tag weight=6.0,
discriminant cut 0.985)

topological selection method, leading to a 20 % larger uncertainty.

More work is required to resolve these points and perform a fully consistent comparison. However, it isalready clear that with 100 pb−1 of data, the counting method can measure the overall b-tagging efficiency
to a precision of better than 5 %, and, particularly as the luminosity increases through 200 pb−1 several
alternative approaches are possible that also enable the efficiency dependence on other variables (jet ETand η) to be studied.

The ATLAS multivariate b-tagging algorithms rely heavily on likelihood reference distributions for lightand b-quark jets derived from Monte Carlo simulation. Section 4 has already discussed the advantages tobe obtained in using a sample of t t¯ Monte Carlo events rather than the generic mixture used in the defaultb-tagging algorithm configuration. A further step, which would also remove the reliance on Monte Carlosimulatons, is to derive the reference distributions for b-jets directly from b-jets selected in real data.
In principle, the b-jet selection methods discussed in Section 5 would allow this to be done. However, none the methods produce a pure b-jet sample without the need for background subtraction, andhence do not identify a pure sample of b-jets from which multiple variables can be extracted simultaneously on a jet-by-jet basis. Instead, background-subtracted distributions are produced. These can be2440Conclusions
ATLAS (LHC) で使われる b-jet tagging の方法について紹介したシミュレーションから期待されるPerformanceは様々な効果によってdegradeする可能性
Calibrationするのが難しい場合は n次元空間で
eﬃciency と Fake Rejection を測定すべし
実験初期にreliableなのは Jet Probability
豊富な calibration sample
もっときめ細かなcalibrationが不可欠
Sample dependence
少なくともトラックのqualityに応じたcalibration←劇的な改善が期待できる（現在進行中）
25

Backup

CMS

27

-3
-3
efficiency
in the coreof thesein z at this pseudo-rapidity, and therefore explains 66%of the gainin efficiency
observed
onhigh-p
the T has decreased substa
10long10tracking

absolute
efficiency)
bottom plot. The gain decreases steadily with |η| as the clusters
becomelonger.with
Thereleaseamount13,ofwhile
dead the level of fakes has im
Thepixelsplays an important role for b-tagging, as discussed in Section
8.3.1.of such changes on b-tagging are discussed in Section 7.
-4-4 impact

10
Tracking Performance

10

-20
0.8
0.75

-10

0

10

20

30

Efficiency: reconstruction

40

Efficiency: standard quality(a)Transverse
impact quality
parameter significance d0.014
Efficiency: b-tagging
0 /σd0
0.7

0.012
0.01
0.008
0.006
0.004
0.002

Efficiency

Fake rate: standard quality
Fake rate: b-tagging quality

0

0.04
0.03

-10

0

10

20

Fake rate

Fake rate

0.85

30

40

0.007
1.5Efficiency:
2 Ejet < 502.5
GeV
T
jet
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Efficiency: E > 100 GeVTjet(b) Longitudinal impact
parameterz0 /σz00.005
Fake
rate: ET <significance50 GeVjet
Fake rate: ET > 100 GeV
0.004
0.5

1

0.02
0.01
0
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-0.04
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-0.2
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0.95

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0.02
Figure 8: Impact parameter significances for tracks
in light jets. Two categories of tracks 0.003
are used:
0.01
0.002
regular ones (red plain curves) and tracks with shared hits (blue dashed curves). Both distributions
are
0
0.001
normalized to unity.
-0.01

0.5

1

1.5

2

2.5
|!|

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0.5
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2
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Figure 1000
3: Differencein tracking
efficiency
Figure4: Tracking
efficiency(left Y veraxis, solid
Figure 5: Dif
900 pseudo-rapidity
sus track
for two
scenarios:
re- symsymbols)
and fake rate(rightY axis, openplot) and relat
800
lease 13bols)
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releasedistance
12 (top)toandjetrelease
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forwithb-taggingplot) between
700
1% deadpixelscuts,minus
12 (bottom),thehigh-pT
quality
forreleaselow (black
triangles)forand
sus distance t
three levels
track selection
indicated
600 ofcircles)(greenjets. Release
13. in the capgles) and hightion of Figure
2.
500
400 Finally, on Figure 6 the tracking efficiency and fake rates obta
100
Figure 4 shows the tracking efficiency and fake rate foralgorithm
tracks inandt t¯ events
as a functionof theirin release 13. The first plo
with iPatRec
are compared
300
bins
200 in the track pT , while the second plot is as a function of the dista
50
7
note
100 that the two algorithms have a different working point: NewTraat 0the price of loosing in efficiency, while the alternate choice was
0
2
10
102
1
10
1
10
in
treatment
will
lead
to
differentb-taggingperformancefor jets wip (GeV)p (GeV)T
T
particular in Section 8.1. The features seen on these plots are speci(a) Transverse impact parameter(b) Longitudinal impact parameter
jets: for instance the decrease of the NewTracking efficiency at hig
tracks, this is here correlated with the local track density since high-p
28|"| < 0.5
0.5 < |"| < 1.0
1.0 < |"| < 1.5
1.5 < |"| < 2.0
2.0 < |"| < 2.5

0250
Figure2: Tracking efficiency (left Y axis, solid
symbols) and fake rate (right Y axis, open sym200
bols)
versus track pseudo-rapidity, for three levels of track selection: matching (blue triangles),standard
quality cuts (red squares) and b-tagging
150
quality cuts (black circles). Release 13.

-0.020!(z ) (µm)

0!(d ) (µm)

0|"| < 0.5
0.5 < |"| < 1.0
1.0 < |"| < 1.5
1.5 < |"| < 2.0
2.0 < |"| < 2.5

Figure 9: Track impact parameter resolutions versus track pT , for several bins in the track pseudo-as the ratio between the total number of reconstructed vertices to the total number of truth
4: Efficiencyof track reconstruction (statistical errors only)
has been found that this remains constant, at a value of 99.7 ± 0.6%,Table
irrespectiveof the008 – 18 : 39
DRAFT
6
Setup
efficiency [%]nt scenario considered.
Perfect
97.1 ± 0.2
mber of primary vertex outliers has also been investigated. In the following, a primaryvertex95.3 ± 0.2
s “outlier” if the distance of the reconstructed to the truth position, shifted with theRandom10
mean ofRandom10
97.1 ± 0.2
Table
4: Efficiency
track
reconstruction(statisticalerrors150
only)vertices,is larger
than 30 ofµm
in thex direction andlarger thanµm in the z direction.
The + error scaling
Aligned96.9 ± 0.2
Setup
efficiency[%]misalignment introduces additionalof outliers is shownin Table 6, which shows that
residual
Aligned + error scaling
96.9 ± 0.2
97.1 ± vertex
0.2
d therefore causesPerfecta loss of precision in the primaryfinding. The number of outliers
Random10± 0.2for “Random10”. For the “Aligned”
partially diminishedby the application of error95.3
scaling
Random10+ errorscaling
97.1± 0.2
e corresponding scaling
factors
are muchsmallerthanfor “Random10” and the effect of error
Aligned96.9 ± 0.2
5: Ratio of faketracks from the total accepted tracks (statistical errors only)
he primary vertex performance is negligible. The modification ofTable
the investigatedparameters
Aligned + error scaling
96.9 ± 0.2
Setup
fake tracks [%]ection is similar to that in the x direction.
2.33 ± 0.02
ar behavior is observed for the primary vertex resolution. The difference between Perfect
the reconRandom10
2.46 ± 0.02
d the truth vertex positions, for x and z, is displayed in Figure 1. The introduction ofresidualRandom10 + error scaling
2.29 ± 0.02
Table
5: Ratio
fake tracks fromthe total
accepted(statisticalerrorsnt causes
the ofdistributions
to becomewider
due totracks
the random
shiftsandonly)
rotations introducedEﬀect of misalignment

Aligned2.34 ± 0.02
Setup
fake tracks [%]Aligned + error scaling
2.20 ± 0.02
Perfect
2.33 ± 0.02
2.46(statistical± 0.02 errors only)
Table 6: Random10
Ratio of primary vertex outliers
2.29± 0.02outliers in z [%]Setup Random10 + error scaling
outliers inx [%]Aligned2.34 ± 0.02
4.1 Vertexing
Perfect
1.7 ± 0.1
4.1 ± 0.1 Performance
Aligned + error scaling
2.20 ± 0.02
Random10
5.5 ± 0.2
8.3 ± 0.2 of the primary vertex finding algorithm is also investigated for the five sce
The performance
Random10 + error scaling
2.8 ± 0.1
6.1geometry± 0.2 and error scaling. In a first step, the efficiency for the primary vertex fi
detectorMarch
18 : 45DRAFT
7Aligned
3.2 ±27,0.12008 –computed
8.2 ±as0.2
the ratio between the
total number of reconstructed vertices to the total number
exing Performancevertices.
It 0.2has been found that this remains constant, at a value of 99.7 ± 0.6%, irrespectiv
Aligned + error scaling
3.2 ± 0.1
8.0 ±misalignment
considered.
mance of the primary vertex finding algorithm is also investigatedfor scenario
the five scenariosofThe
numberofprimaryvertexalso beenerrors
investigated.
7: Primaryvertex resolution(statisticalonly) In the following, a prima
ometry and error scaling. In a first step, the efficiency for theTable
primaryvertex finding
isoutliers has
is flagged
as “outlier”
distanceof thetruth position,
Setup vertices
res.ifinthe
xof[µm]
in reconstructed
x [µm] res. tointhez [µm]
shift in zshifted[µm] with thes the ratio between the total number of reconstructedto thetotal number
truth shift
all the truth vertices, is larger than 30 µm in the x direction and larger than 150 µm in the z direc
has been found that this remains constant, atPerfecta value of
99.7 ± 0.6%, irrespectiveof the −0.13 ± 0.07
11.4 ± 0.1
51.1 ± 0.4−8.2 ± 0.3
percentage of outliers is shown in Table ??, which shows that residual misalignment introduces a
nt scenario considered.
Random10outliers, and therefore15.1± 0.1
4.2 ± 0.1
63.0 ± 0.4
1.4 ± 0.4
causes a loss of precision in the primary vertex finding. The number omber of primary vertex outliers has also been investigated.
the following,a primaryvertexRandom10isIn+howevererror
scaling
13.2±
0.1± 0.1 of error
56.6scaling± 0.4 for “Random10”.
2.3 ± 0.4 For the “partially diminished by the 2.6
applications “outlier” if the distance of the reconstructed tothe truth position, shifted with
the±mean
Aligned
13.9
0.1 offactors−0.18are± much0.09 smaller
53.7than± 0.4−91.5 ± 0.4
scenario the corresponding
scaling
for “Random10”
and the effec
vertices, is larger than 30 µm in the x direction andlarger+ than150
µm in the z direction.
The −0.15 ± 0.09
Alignederror
scaling
13.8
±
0.1
55.4
±
0.4
−91.6
±
0.4
scaling on the primary vertex performance is negligible. The modification of the investigated pa
of outliers is shown in Table ??, which shows that residual misalignment introduces additionalin the y direction is similar to that in the x direction.
29
d therefore causes a loss of precision in the primary vertex finding. The numberof outliers
A similar behavior is observed for the primary vertex resolution. The difference between th

ncl are non-b- (c- and light) jets, and the signal sample has p jethen we can write the following
8 equations:
System8n = nb + ncl
p = pb + pcl
n

LT

=

p

LT

=

n

SM T

=

p

SM T

=

n

both

=

p

both

=

LT
LT
nb εb + ncl εclLTLT
pb εb + pcl εcl
SM T
SM T
nb εb
+ ncl εcl
SM T
SM T
pb ε b+ pcl εcl
LT SM T
LT SM Tnb εb εb+ ncl εcl εcl
LT SM T
LT SM Tpb ε b ε b+ pcl εcl εclm of eight equations (hence the name of the method) has eight un
LT , !SM T , !SM T , where !LT is theur tagging efficiencies !LT
,
!
b
cl
b
cl
b
both
30 jets tagged by both tagging a
nd nrefer to the number of