This document discusses the measurement of the top quark pair production cross section in the muon+jets channel at the LHC using machine learning techniques. It details the theoretical background, experimental setup, data analysis methods, and challenges in simulating particle interactions. The findings aim to provide a precise estimate of the top quark production cross section under specified conditions, emphasizing the importance of various systematic uncertainties.

1. USING MACHINE LEARNING TO
MEASURE THE CROSS SECTION
OF TOP QUARK PAIRS IN THE
MUON+JETS CHANNEL AT THE
COMPACT MUON SOLENOID
Malina KirnSep 6 2011

2. Piled Higher and Deeper
www.phdcomics.com
Sep 6 2011
2

3. 3
A picture is worth 29,658 words…
My slide!

4. High energy physics4
Why measure the rate at which top quarks are produced?

5. The Standard Model
Sep 6 2011
5
 Describes the interactions of
matter via 3 of the 4
fundamental forces.
 Matter (and anti-matter):
 Three generations
 Leptons
 Quarks (observed as jets)
 Forces:
 Electromagnetic (𝛾)
 Weak nuclear (𝑊, 𝑍)
 Strong nuclear (𝑔)
 Does not include gravity Image source: LiveScience

6. Muon+jets top quark event
Sep 6 2011
6
proton proton
𝒕
𝒕
𝒃
𝑾+𝝁+
jet
jet
𝝊 𝝁
jet
𝒃
𝑾−
jet

7. Jets
Sep 6 2011
7
 The strong force regulates particles with „color‟ charge.
 The strong force carrier, the gluon, possesses color charge.
 Therefore, the strong force does not decrease with distance.
 As quarks and gluons propagate further apart, it becomes energetically
favorable to create color neutral hadrons by pulling quark-antiquark pairs
from the vacuum.
 Upshot: Quarks and gluons are never observed directly in particle
detectors. They shower into a „jet‟ of hadrons. This is difficult to simulate.
Jet of color
neutral hadronsImage source:
Homer Wolfe dissertation
Quark
or gluon

8. Units & energy
Sep 6 2011
8
 The electron-volt (eV) is our unit of energy. 1 eV is the energy
required to move a single electron „up‟ a one volt potential „hill.‟
 Einstein‟s 𝐸 = 𝛾𝑚𝑐2
can be written as 𝐸2
= 𝑚2
𝑐2
+ 𝑝2
𝑐4
, where
𝐸=energy, 𝑚=rest mass, and 𝑝=momentum.
 We use 𝑐 = 1, so 𝑬 𝟐
= 𝒎 𝟐
+ 𝒑 𝟐
.
 Energy, mass, and momentum are therefore all in units of eV.
 Protons at the LHC are collided with a total energy (center of mass
energy) of 7 TeV, or 7x1012 eV.
 Most particles have mass much less than 7 TeV.
 The top quark has a mass of 172 GeV, or 1.72x1011 eV, around the
mass of a tungsten atom.

9. Top quark production & decay
Sep 6 2011
9
𝒈
𝒈
𝒈
𝒈
𝒒
𝒒
𝒕
𝒕
𝒕
𝒕
𝒕 𝒕
Top pair production:
70% gluon induced in
7 TeV pp collisions
Top quark decay lifetime:
∝
𝟏
𝒎 𝒕
𝟑
, 𝓞 𝟏𝟎−𝟐𝟓
𝐬𝐞𝐜
Tops decay before they hadronize:
𝒕 → 𝑾𝒃, 𝑾 → 𝒋𝒋 𝒐𝒓 𝒍𝝊
hadronic
44%
di-
lepton
(not τ)
5%
µ+jets
15%
τ+x
21%
e+jets
15%
all jets
44%

10. Production cross section
Sep 6 2011
10
 Related to the probability that an event will occur.
 Units of area, barn: 1b=10-24 cm2
 Hydrogen atom has cross section of 𝒪(10-20) cm2
 Hydrogen nucleus has cross section of 𝒪(10-26) cm2
 𝑡𝑡 production cross section in 7 TeV pp collisions should be 157 pb
according to a Standard Model calculation.
 Luminosity is related to the “brightness” of the particle source (the
LHC), measured in units of inverse area per second: cm-2s-1.
 This analysis uses 36 pb-1 integrated luminosity, ℒ𝑑𝑡.
 𝑁 = 𝐴𝜖𝜎 ℒ𝑑𝑡
 𝐴𝜖=acceptance*efficiency
 𝜎=cross section
 ℒ=luminosity, or instantaneous luminosity

11. Experimental apparatus11
Where do we make top quarks and how do we observe them?

12. Sep 6 201112
The LHC

13. The CMS detector
13
Solenoid
Trackers
Calorimeters

14. Sep 6 201114

15. Sep 6 201115

16. 𝜂 = −ln(tan 𝜃/2 )
Δ𝑅 = Δ𝜂 2 + Δ𝜙 2
𝜃
𝑧
𝑥
𝑦
𝜙
Coordinates
16

17. Grid computing17
What computing facilities are required?

18. Services
18
 Computing sites provide a Compute Element (CE), Storage Element
(SE), or both. OSG CEs provide Globus services and SEs provide SRM.
Users authenticate via certificate/proxy private key infrastructure.
 Sites publish availability and specs to grid database, BDII.
 CMS tracks dataset metadata and location in DBS/DLS.
CMS

19. Software
19
 User data analysis jobs are sent to the site hosting the dataset via CRAB.
CRAB supports several schedulers, including gLite-UI and Condor-glideIn.
 Physics requests for simulations are regularly compiled and selected for
production. Several ProdAgent instances manage all production at a group of
sites.
 Datasets are transferred between sites with PhEDEx. PhEDEx is based on an
agent-blackboard architecture - independent software agents schedule and
perform transfers that are tracked in the PhEDEx database.

20. Tiers
Sep 6 2011
20
Tier-0
Tier-1 Tier-1
Tier-2 Tier-2 Tier-2 Tier-2
Tier-3 Tier-3 Tier-3 Tier-3
Tier-1
Unpredictable communication Predictable communication
Load balancing
User requests for data & simulations
Data distribution
Official simulations
Event reconstruction
Stores complete dataset
Reprocessing
Stores complete dataset
Official simulation
User analysis & simulation
User driven storage,
analysis & simulation

21. Event reconstruction and selection21
How do we recognize different types of particles?

22. Particle identification
Sep 6 2011
22

23. Top quark pair candidate event
23

24. Muon reconstruction
 Particle track reconstruction:
 hypothesis = helix
 radius, 𝑓(𝑝 𝑇)
 displacement from the origin, 𝑑0
 „coil separation‟, 𝑓(𝑝 𝑧)
 data = tracking „hits‟
 location of particle in layers of tracker
 uncertainty is partially a function of sensor
size
 seed (first hypothesis)
 inner tracker: three hits or two
hits+beamspot
 muon chambers: hits that form track
segments in a large chamber
 Muon:
 global
 start with track in muon chambers
 search for matching inner track
 efficient at high 𝑝 𝑇
 tracker
 start with inner track
 search for matching hits in muon
chambers
 efficient at low 𝑝 𝑇
24
Kalman filter: iteratively update a hypothesis
using data with measured uncertainties
𝒛𝒙
𝒚

25. Jet reconstruction
 Particle flow:
 Creates the partons to be used in
the jet cone algorithm
 inner tracks:
 repeatedly reconstruct inner tracks
 remove associated hits each time
 progressively loosen quality criteria
 calorimeter clusters:
 seed = calorimeter cells with
energy above some threshold
 add cells with energy above
another threshold to cluster if cell is
geometrically adjacent to cluster
 adjust cluster energy and position
by fractionally sharing cell energy
across clusters
 Jet from Anti-𝑘 𝑇 algorithm:
 distance metric:
𝑑𝑖𝑗
2
= 𝑚𝑖𝑛 𝑝 𝑇,𝑖
−2
, 𝑝 𝑇,𝑗
−2
∆𝑅𝑖𝑗
2
/𝑅2
 We use 𝑅 = 0.5
 Make a jet when its 𝑝 𝑇
−2
is smaller
than any 𝑑𝑖𝑗.
 infrared and collinear safe
25
Jet cone: iteratively add partons to jets with smallest distance metric,
create jet when distance too large
𝒛𝒙
𝒚

26. 𝑏 tags
Sep 6 2011
26
 The 𝑏 quark hadronizes into a 𝐵
meson, which has a lifetime of
𝒪(10−12
) seconds.
 The decay of the 𝐵 meson occurs within
the beampipe, but a resolvable
distance from the interaction point.
 Jets from 𝑏 quarks can be „tagged‟ by
the presence of displaced tracks.
 We require the impact parameter
significance of the 2nd track be larger
than 3.3.
 Efficiency of 55% to 74% and light
fake rate of 1% to 6% (varies with jet
𝑝 𝑇 and 𝜂).

27. ≥4 jets
𝑽+jets
37%
Single top
2%
QCD
2%
≥3 jets
𝑽+jets
57%
Single top
3%
QCD
4%
Event selection
27
𝒕𝒕
 Can‟t observe 𝑡𝑡 directly.
 We choose to search for 𝑡𝑡 → 𝜇+jets:
𝑡𝑡 → 𝑊+
𝑏 𝑊−
𝑏 → 𝜇𝜈𝜇 𝑗𝑗𝑏𝑏
 Require exactly one isolated 𝜇:
 𝑝 𝑇 > 20 GeV
 |𝜂| < 2.1
 Δ𝑅 𝜇, 𝑗 > 0.3
 𝑅𝑒𝑙𝐼𝑠𝑜 < 0.05
𝑅𝑒𝑙𝐼𝑠𝑜=(𝐸 𝑇 near 𝜇)/(𝜇 𝑝 𝑇)
 Veto on an electron
 Expect ≥4 jets, require ≥3:
 𝑝 𝑇 > 30 GeV
 |𝜂| < 2.4
 We need to discriminate between 𝑡𝑡
and 𝑉+jets (𝑉 = 𝑊/𝑍).

28. Discrimination28
Can we differentiate between top quarks and other particles?

29. Neural network
Sep 6 2011
29
 Given measureables as inputs (e.g., muon 𝜂 or jet 𝑝 𝑇).
 Combines the inputs using nested sums of functions:
𝑦 =
𝑓 𝑎 + 𝑏1 𝑓 𝑐 + 𝑑1 𝑓 … + 𝑑2 𝑓 … + ⋯ + 𝑏2 𝑓 … + ⋯
 Outputs the discriminant, 𝑦, which takes values near 0 for
background and near 1 for signal.
 Learning algorithm finds the parameters that yield the
desired 𝑦 values.
 We use sigmoid function for 𝑓: 𝑓 𝑥 =
1
1+𝑒−𝑥

30. Neuron
Sep 6 2011
30
 Takes as input either the:
 physical measureables
 output from other
neurons
 Calculates 𝑣, a shifted
sum of weighted inputs.
 Outputs 𝑓(𝑣).
𝑤𝑗0
𝑟
∑
f
𝑣𝑗
𝑟
𝑦𝑗
𝑟𝑦 𝑘
𝑟−1 k
𝑤𝑗𝑘
𝑟

31. Multi layer perceptron
Sep 6 2011
31
𝑤10
3
𝑦5
1
𝑖
𝑥1 𝑖
𝑥2 𝑖
𝑥3 𝑖 𝑦4
1
𝑖
𝑦3
1
𝑖
𝑦1
1
𝑖
𝑦2
1
𝑖
𝑦1
3
𝑖
𝑦4
2
𝑖
𝑦3
2
𝑖
𝑦2
2
𝑖
𝑦1
2
𝑖
𝑤40
2
𝑤30
2
𝑤20
2
𝑤10
2
𝑤14
3
𝑤11
3
𝑤11
1
𝑤11
2
𝑤45
2
𝑤53
1
𝑤10
1
𝑤20
1
𝑤30
1
𝑤40
1
𝑤50
1

32. Inputs
Sep 6 2011
32
 Presence of a 𝑏-tagged jet
 Angular separation of two
leading jets, Δ𝑅12
 Position |η| of the muon

33. Neural network outputNeural network output
Neural network output Neural network output
FractionofeventsFractionofevents
FractionofeventsFractionofevents
𝒕𝒕 simulations 𝑽+jets simulations
Single top
simulations
QCD simulations
Output
Sep 6 2011
33
 Two peak structure
due to 𝑏 tag boolean
 We form fit
templates for signal
and background.

34. Correcting or replacing simulations using data34
Some simulations aren‟t as good as others. How do we correct or
replace them using data?

35. 𝑏 tag efficiency
Sep 6 2011
35
 The 𝑏 tag boolean is an important input to the NN.
 The shape is dependent on the efficiency and fake rate of
tagging jets.
 Jets in selected events have 𝑏 tag efficiency of 55% to 74% and
light fake rate of 1% to 6% according to simulations.
 Simulations aren‟t perfect.
 The tag efficiency and fake rate are measured from
(nearly) independent data samples.
 𝑆𝐹 𝑏 =
𝑒 𝑏,𝑑𝑎𝑡𝑎
𝑒 𝑏,𝑀𝐶
= 0.9 and 𝑆𝐹𝑙 =
𝑒 𝑙,𝑑𝑎𝑡𝑎
𝑒 𝑙,𝑀𝐶
= 1.06 − 1.32.

36. 𝑡𝑡 and single top
data corrected templates
Sep 6 2011
36
 Apply 𝑆𝐹 𝑏 = 0.9 and 𝑆𝐹𝑙 = 1.06 − 1.32.
 Line = nominal simulation. Fill = corrected.
Single top
Neural network output
Fractionofevents
Neural network output
Fractionofevents
𝒕𝒕

37. QCD (jet only events)
Sep 6 2011
37
 Simulation is
difficult due to
parton showering.
 Events with muon
𝑅𝑒𝑙𝐼𝑠𝑜 > 0.1 are
dominated by
QCD (97%).
Signalregion
Data driven region

38. QCD data driven inputs
Sep 6 2011
38
QCD events passing nominal selection
(𝑅𝑒𝑙𝐼𝑠𝑜 < 0.05) have similar NN input
distributions as events with reversed
muon isolation (𝑅𝑒𝑙𝐼𝑠𝑜 > 0.1).

39. 𝑉+jets
Sep 6 2011
39
 Heavy flavor
content in 𝑉+jets
subject to same
uncertainties as in
QCD.
 Events with a
muon and exactly
two jets are
dominated by
𝑉+jets (87%).
Signal region
Data
driven
region

40. 𝑉+jets data driven inputs
Sep 6 2011
40
𝑉+jets events passing nominal selection
(≥ 3 jets) have similar NN input
distributions as events with =2 jets.

41. Final fit templates
Sep 6 2011
41
 Lines=original nominal
simulations.
 Histos=final data
corrected/replaced fit
templates.
 The templates will be
fit to the discriminant
calculated from data
to determine 𝑡𝑡 yield.
Neural network outputNeural network output
Neural network output Neural network output
FractionofeventsFractionofevents
FractionofeventsFractionofevents
Corrected 𝒕𝒕
simulations
2 jet data (𝑽+jets)
Corrected single
top simulations
𝑹𝒆𝒍𝑰𝒔𝒐 > 𝟎. 𝟏
data (QCD)

42. Measuring cross section42
How many collisions are from top quarks? What is the
uncertainty of this number?

43. Maximum likelihood fit
Sep 6 2011
43
 We assume the observed 𝑁 𝑑𝑎𝑡𝑎 data events are composed of 𝑁 𝑡𝑡
from 𝑡𝑡, 𝑁𝑡 from single top, 𝑁 𝑉 from 𝑉+jets, and 𝑁 𝑄𝐶𝐷 from QCD,
where each 𝑁 is unknown: 𝑁 𝑑𝑎𝑡𝑎 = 𝑁 𝑡𝑡 + 𝑁𝑡 + 𝑁 𝑉 + 𝑁 𝑄𝐶𝐷.
 Given each probability density function, 𝑃(𝑥), over measureable 𝑥,
this assumption yields: 𝑁 𝑑𝑎𝑡𝑎 𝑃 𝑥 = 𝑁 𝑡𝑡 𝑃 𝑡𝑡 𝑥 + 𝑁𝑡 𝑃𝑡 𝑥 +
𝑁 𝑉 𝑃𝑉 𝑥 + 𝑁 𝑄𝐶𝐷 𝑃𝑄𝐶𝐷 𝑥 .
 We use the output from the NN as our 𝑥.
 Likelihood function: 𝐿 𝜃|𝑥 = 𝑃 𝑥𝑖|𝜃
𝑁 𝑑𝑎𝑡𝑎
𝑖=1 .
 We determine 𝜃 = 𝑁 𝑡𝑡, 𝑁𝑡, 𝑁 𝑉, 𝑁 𝑄𝐶𝐷 by maximizing 𝐿.
 Using 𝑁 = 𝐴𝜖𝜎 ℒ𝑑𝑡, we convert 𝑁 𝑡𝑡 into the 𝑡𝑡 cross section, 𝜎 𝑡𝑡.

44. Uncertainty
Sep 6 2011
44
 𝑁 = 𝐴𝜖𝜎 ℒ𝑑𝑡 is a statement of the average number of
events we expect to observe.
 Any given experiment is not expected to measure exactly
𝑁 events, due to:
 Quantum Mechanics (particle interactions are statistical!)
 Experimental measurement uncertainties
 Underlying assumptions that could be wrong
 We use pseudo-experiments to calculate how much our
measurement of 𝜎 changes in various scenarios. This is our
uncertainty.

45. Pseudo-experiments
Sep 6 2011
45
 Randomly sample the NN templates from simulations.
 The number of times each template is sampled varies in each pseudo-experiment.
It is Poisson varying about the expected number of events for each.
 Fit the NN templates to the randomly sampled pseudo-data.
𝒕𝒕 simulations 𝑽+jets simulations
Single top
simulations
QCD simulations

46. Pseudo-results
Sep 6 2011
46
 We perform 10,000
pseudo-experiments.
 Indicate presence of
-3% intrinsic bias
(measure 375 𝑡𝑡
events on average,
expect 387).
 Due to using data to
form the fit templates
for QCD and 𝑉+jets.
 Final measurement is
corrected for bias.
 Statistical uncertainty
of 10%.
𝒕𝒕 signal yield
Pseudo-experiments

47. Systematic uncertainty
Sep 6 2011
47
 We relate photon counts in calorimeters to particle
energy.
 What if this conversion factor is high or low?
 Measured jet energies would be systematically higher
or lower than the true energy of the particle.
 Change the simulations to experience a systematic
increase or decrease in jet energy.
 The change in measured cross section in a systematic
scenario is the “systematic uncertainty”.

48. Summary of systematics
Sep 6 2011
48
Source Uncertainty (%)
Jet energy scale +9.7/-5.1
Jet energy resolution ±3.3
b tag efficiency +16.1/-14.7
V+b k factor +5.2/-5.6
V+c k factor +4.4/-1.8
ISR/FSR ±5.0
Q2 +6.8/-3.5
ME to PS matching +6.0/-3.0
PDF +0.6/-1.8
Combined +22.8/-18.4
 Largest from b-tag
efficiency uncertainty
(𝑆𝐹 𝑏=0.900±0.135)
 This uncertainty
already reduced by
half for 2011 data.

49. Summary
Sep 6 2011
49
The cross section for 𝑝𝑝 → 𝑡𝑡 production at a center of
mass energy of 7 TeV is measured using a data sample
with integrated luminosity 36.1 pb-1 collected by the
CMS detector at the LHC. The analysis is performed on
a computing grid. Events with an isolated muon and
three hadronic jets are analyzed using a multivariate
machine learning algorithm. Kinematic variables and b
tags are provided as input to the algorithm; output from
the algorithm is used in a maximum likelihood fit to
determine 𝑡𝑡 event yield. The measured cross section is
𝟏𝟓𝟏 ± 𝟏𝟓 𝒔𝒕𝒂𝒕. −𝟐𝟖
+𝟑𝟓
(𝒔𝒚𝒔𝒕. ) ± 𝟔(𝒍𝒖𝒎𝒊. ) pb.
This is in agreement with the theory predicted cross
section of 157 pb.

50. Outlook
Sep 6 2011
50
 Submitted to Physics Review
D for publication.
 Available statistics going
up, though measurement is
systematics limited.
 Systematic uncertainties are
going down, especially with
respect to 𝑏 tags.

51. I received a lot of help from some really wonderful
people. You know who you are.
Sean, words can‟t express, so I shall just lamely say:
thank you.
Dedication
Sep 6 2011
51

52. Backup material
Sep 6 2011
52

53. LHC beam
53
 Design specs listed above
 2010 data taking at
3.5 TeV beam energy
 2010 luminosity
𝒪(1029-1032) cm-2s-1
 This analysis uses 36 pb-1
integrated luminosity, ℒ𝑑𝑡
Sep 6 2011

54. The CMS collaboration
Sep 6 2011
54
 39 Countries
 181 institutions (49 in US)
 2001 authors (641 graduate students)

55. Accelerator chain
Sep 6 2011
55

56. Sample cross sections
Sep 6 2011
56

57. Simulated sample statistics
Sep 6 2011
57

58. Event yields
Sep 6 2011
58
Selection
Simulated sample
Sim total Data
𝒕𝒕 𝑽+jets QCD Top
Good 𝜇 672 172871 10293 173 184009 181911
e veto 584 172317 10205 168 183274 181270
≥ 1 jet 579 22113 3007 150 25848 28011
≥ 2 jets 532 3726 316 84 4658 5535
≥ 3 jets 387 613 41 27 1068 1271
≥ 4 jets 189 119 7 7 321 344

59. Simulation
Sep 6 2011
59
 MadGraph: matrix element
 Particle interactions are fundamentally statistical.
 Matrix element is related to probability that particles with given
kinematics will be produced in collision.
 Physicist specifies desired initial and final particles, including +jets.
 Matrix element includes all possible intermediate „paths‟.
Image source: Scholarpedia
 Pythia:
 Colored particles like gluons and
quarks never observed in isolation
 Particle shower pulls new partons
from vacuum
 Beam remnant (leftover from collided
protons)
 Multiple interactions from data

60. Monte Carlo (MC) simulations
Sep 6 2011
60
 Integrate a function from
𝑥1 to 𝑥2.
 The analytical form is unknown,
but the value can be calculated.
 The minimum, 𝑦1, and maximum,
𝑦2, values of the function in the
range [𝑥1, 𝑥2] are known or can
be approximated.
 Throw random points (𝑥, 𝑦) in
the region (𝑥1, 𝑦1) → (𝑥2, 𝑦2).
 Calculate the fraction, 𝐹, with
𝑦 < 𝑓(𝑥).
 The integral is then
𝐹(𝑥2 − 𝑥1)(𝑦2 − 𝑦1). 𝑥1 𝑥2
𝑦1
𝑦2

61. Anti-kT algorithm
Sep 6 2011
61

62. Finding network weights
 „Train‟ on simulated datasets.
 Signal events are given a
training target of 1,
background events given
training target of 0.
 Training goal is to minimize a
cost function. If 𝑖 = 1 … 𝑁
training events have target
𝑦(𝑖) =
0, 𝑖 = 𝑏𝑘𝑔
1, 𝑖 = 𝑠𝑖𝑔
and 𝑦(𝑖)
is the network output for
event 𝑖, then cost, 𝐶, is:
𝐶 =
1
2
𝑦 𝑖 − 𝑦(𝑖) 2𝑁
𝑖=1 .
 „Propagate‟ the cost, calculated
for the network output, back in the
network by weighting the cost by
the weight between the neurons.
 Minimize using steepest descent.
62
Network weights are found that tend to yield a final network output
value near 1 for signal events and near 0 for background events.
𝐶
𝑤

63. 𝑆𝐹 𝑏
Sep 6 2011
63
 The 𝐵 meson decay includes a muon in 11% of 𝑏
jets, or in 20% of 𝑏 jets including 𝑏 → 𝑐.
 Select events with Δ𝑅 𝜇, 𝑗𝑒𝑡 < 0.4.
 Jets with muons inside are from a 𝑏 or from jet
fakes (pion decay or muon chamber punch-
through).
 To get efficiency of tagging 𝑏 jets in data, the
fraction of tagged jets with muons is adjusted by
the fraction of jets with fake muons.
 Done by fitting the 𝑝 𝑇
𝑟𝑒𝑙
distribution.
 𝑆𝐹 𝑏 uncertainty primarily from 𝑝 𝑇
𝑟𝑒𝑙
shape and
fraction of jets with fake muons.

64. 𝑆𝐹𝑙
Sep 6 2011
64
 Jets with tracks that have negative impact
parameters are nearly all from light quarks.
 Change the tag algorithm to sort tracks in
opposite order (smallest impact parameter
significance first), label negative tag.
 The negative tag distribution is not symmetrical
with respect to the normal tag distribution.
 Calculate the ratio between the tag rate of light
jets and negative tag rate of all jets: 𝑅𝑙 =
𝑒𝑙
𝑀𝐶
𝑒−
𝑀𝐶
 Fake rate in data is then 𝑒𝑙
𝑑𝑎𝑡𝑎
= 𝑒−
𝑑𝑎𝑡𝑎 𝑅𝑙
 𝑆𝐹𝑙 uncertainty primarily due to 𝑅𝑙.

65. Likelihood
Sep 6 2011
65
Binned
likelihood
Unbinned
likelihood
Gaussian
constraints

66. Systematic uncertainty
Sep 6 2011
66
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67. Higgs, top, and W
Sep 6 2011
67
Image source: Epiphany
2011, Krzysztof Sliwa,
“Tevatron collider program
physics, results, future?”

68. Kalman filter (Wikipedia)
Sep 6 2011
68

69. Kalman filter (Wikipedia)
Sep 6 2011
69

70. CMS performance:
leptons
Sep 6 2011
70
EWK-10-002
updatedfor35pb-1

71. CMS performance:
jets & MET
Sep 6 2011
71
JME-10-005JME-10-010

72. CMS performance:
b-tagging
Sep 6 2011
72
BTV-10-001 TOP-10-001
 Track counting: impact parameter of tracks inside jet
 Secondary vertex: secondary vertex from tracks inside jet
 Muon-in-jet: soft muon track inside jet

73. Not for consumption, just objects needed or
previously used to create the presentation.
Testing slides
Sep 6 2011
73

74. My slide!74
A picture is worth 29,658 words…
High energy physics
Why measure the rate at which top quarks are produced?
Experimental apparatus
Where do we make top quarks and how do we observe them?
Grid computing
What computing facilities are required?
Event simulation, reconstruction, and selection
How do we know what to expect from top quarks?
How do we recognize different types of particles?
Discrimination
Can we differentiate between top quarks and other particles?
Correcting or replacing simulations
Some simulations aren‟t as good as others. How do we correct or
replace them using data?
Measuring cross section
How many collisions are from top quarks? What is the
uncertainty of this number?

75. Recipe for a particle physics plot
(ingredients to taste)
 High energy physics
 Why measure the rate at which
top quarks are produced?
 Experimental apparatus
 Where do we make top quarks
and how do we observe them?
 Grid computing
 What computing facilities are
required?
 Event simulations, reconstruction,
and selection
 How do we know what to
expect from top quarks?
 How do we recognize different
types of particles?
 Discrimination
 Can we differentiate between
top quarks and other particles?
 Correcting or replacing
simulations
 Some simulations aren‟t as
good as others. How do we
correct or replace them using
data?
 Measuring cross section
 How many collisions are from
top quarks?
 What is the uncertainty of
this number?
Sep 6 2011
75

76. Sep 6 2011
change
Systematic uncertainty
Grades
0 100
Students
90807060
Grades
0 10090807060
Average professor Nice professor
Average student grade
Professors
0 10090807060
Averageprofessors
Niceprofessors

77. Sep 6 201177
Signal
27%
Background
64%
Signal
59%
Background
41%
Data sources
for event
selection
graphics

78. Irregular crop for histo