Malina Kirn's 2011-09-06 University of Maryland Scientific Computation dissertation defense. Using neural networks and grid computing to measure top quark pair production cross section at the Compact Muon Solenoid detector at the Large Hadron Collider.
5. The Standard Model
Sep 6 2011
5
๏จ Describes the interactions of
matter via 3 of the 4
fundamental forces.
๏จ Matter (and anti-matter):
๏ค Three generations
๏ค Leptons
๏ค Quarks (observed as jets)
๏จ Forces:
๏ค Electromagnetic (๐พ)
๏ค Weak nuclear (๐, ๐)
๏ค Strong nuclear (๐)
๏ค Does not include gravity Image source: LiveScience
7. Jets
Sep 6 2011
7
๏จ The strong force regulates particles with โcolorโ charge.
๏จ The strong force carrier, the gluon, possesses color charge.
๏จ Therefore, the strong force does not decrease with distance.
๏จ As quarks and gluons propagate further apart, it becomes energetically
favorable to create color neutral hadrons by pulling quark-antiquark pairs
from the vacuum.
๏จ Upshot: Quarks and gluons are never observed directly in particle
detectors. They shower into a โjetโ 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
๏จ The electron-volt (eV) is our unit of energy. 1 eV is the energy
required to move a single electron โupโ a one volt potential โhill.โ
๏จ Einsteinโs ๐ธ = ๐พ๐๐2
can be written as ๐ธ2
= ๐2
๐2
+ ๐2
๐4
, where
๐ธ=energy, ๐=rest mass, and ๐=momentum.
๏จ We use ๐ = 1, so ๐ฌ ๐
= ๐ ๐
+ ๐ ๐
.
๏จ Energy, mass, and momentum are therefore all in units of eV.
๏จ Protons at the LHC are collided with a total energy (center of mass
energy) of 7 TeV, or 7x1012 eV.
๏จ Most particles have mass much less than 7 TeV.
๏จ 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
๐
๐
๐
๐
๐
๐
๐
๐
๐
๐
๐ ๐
Top pair production:
70% gluon induced in
7 TeV pp collisions
Top quark decay lifetime:
โ
๐
๐ ๐
๐
, ๐ ๐๐โ๐๐
๐ฌ๐๐
Tops decay before they hadronize:
๐ โ ๐พ๐, ๐พ โ ๐๐ ๐๐ ๐๐
hadronic
44%
di-
lepton
(not ฯ)
5%
ยต+jets
15%
ฯ+x
21%
e+jets
15%
all jets
44%
10. Production cross section
Sep 6 2011
10
๏จ Related to the probability that an event will occur.
๏จ Units of area, barn: 1b=10-24 cm2
๏ค Hydrogen atom has cross section of ๐ช(10-20) cm2
๏ค Hydrogen nucleus has cross section of ๐ช(10-26) cm2
๏จ ๐ก๐ก production cross section in 7 TeV pp collisions should be 157 pb
according to a Standard Model calculation.
๏จ Luminosity is related to the โbrightnessโ of the particle source (the
LHC), measured in units of inverse area per second: cm-2s-1.
๏จ This analysis uses 36 pb-1 integrated luminosity, โ๐๐ก.
๏จ ๐ = ๐ด๐๐ โ๐๐ก
๏ค ๐ด๐=acceptance*efficiency
๏ค ๐=cross section
๏ค โ=luminosity, or instantaneous luminosity
18. Services
18
๏จ 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.
๏จ Sites publish availability and specs to grid database, BDII.
๏จ CMS tracks dataset metadata and location in DBS/DLS.
CMS
19. Software
19
๏จ User data analysis jobs are sent to the site hosting the dataset via CRAB.
CRAB supports several schedulers, including gLite-UI and Condor-glideIn.
๏จ Physics requests for simulations are regularly compiled and selected for
production. Several ProdAgent instances manage all production at a group of
sites.
๏จ 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
24. Muon reconstruction
๏จ Particle track reconstruction:
๏ค hypothesis = helix
๏ฎ radius, ๐(๐ ๐)
๏ฎ displacement from the origin, ๐0
๏ฎ โcoil separationโ, ๐(๐ ๐ง)
๏ค data = tracking โhitsโ
๏ฎ location of particle in layers of tracker
๏ฎ uncertainty is partially a function of sensor
size
๏ค seed (first hypothesis)
๏ฎ inner tracker: three hits or two
hits+beamspot
๏ฎ muon chambers: hits that form track
segments in a large chamber
๏จ Muon:
๏ค global
๏ฎ start with track in muon chambers
๏ฎ search for matching inner track
๏ฎ efficient at high ๐ ๐
๏ค tracker
๏ฎ start with inner track
๏ฎ search for matching hits in muon
chambers
๏ฎ efficient at low ๐ ๐
24
Kalman filter: iteratively update a hypothesis
using data with measured uncertainties
๐๐
๐
25. Jet reconstruction
๏จ Particle flow:
๏ค Creates the partons to be used in
the jet cone algorithm
๏ค inner tracks:
๏ฎ repeatedly reconstruct inner tracks
๏ฎ remove associated hits each time
๏ฎ progressively loosen quality criteria
๏ค calorimeter clusters:
๏ฎ seed = calorimeter cells with
energy above some threshold
๏ฎ add cells with energy above
another threshold to cluster if cell is
geometrically adjacent to cluster
๏ฎ adjust cluster energy and position
by fractionally sharing cell energy
across clusters
๏จ Jet from Anti-๐ ๐ algorithm:
๏ค distance metric:
๐๐๐
2
= ๐๐๐ ๐ ๐,๐
โ2
, ๐ ๐,๐
โ2
โ๐ ๐๐
2
/๐ 2
๏ค We use ๐ = 0.5
๏ค Make a jet when its ๐ ๐
โ2
is smaller
than any ๐๐๐.
๏ค infrared and collinear safe
25
Jet cone: iteratively add partons to jets with smallest distance metric,
create jet when distance too large
๐๐
๐
26. ๐ tags
Sep 6 2011
26
๏จ The ๐ quark hadronizes into a ๐ต
meson, which has a lifetime of
๐ช(10โ12
) seconds.
๏จ The decay of the ๐ต meson occurs within
the beampipe, but a resolvable
distance from the interaction point.
๏จ Jets from ๐ quarks can be โtaggedโ by
the presence of displaced tracks.
๏จ We require the impact parameter
significance of the 2nd track be larger
than 3.3.
๏จ Efficiency of 55% to 74% and light
fake rate of 1% to 6% (varies with jet
๐ ๐ and ๐).
27. โฅ4 jets
๐ฝ+jets
37%
Single top
2%
QCD
2%
โฅ3 jets
๐ฝ+jets
57%
Single top
3%
QCD
4%
Event selection
27
๐๐
๏จ Canโt observe ๐ก๐ก directly.
๏จ We choose to search for ๐ก๐ก โ ๐+jets:
๐ก๐ก โ ๐+
๐ ๐โ
๐ โ ๐๐๐ ๐๐๐๐
๏จ Require exactly one isolated ๐:
๏ค ๐ ๐ > 20 GeV
๏ค |๐| < 2.1
๏ค ฮ๐ ๐, ๐ > 0.3
๏ค ๐ ๐๐๐ผ๐ ๐ < 0.05
๐ ๐๐๐ผ๐ ๐=(๐ธ ๐ near ๐)/(๐ ๐ ๐)
๏จ Veto on an electron
๏จ Expect โฅ4 jets, require โฅ3:
๏ค ๐ ๐ > 30 GeV
๏ค |๐| < 2.4
๏จ We need to discriminate between ๐ก๐ก
and ๐+jets (๐ = ๐/๐).
29. Neural network
Sep 6 2011
29
๏จ Given measureables as inputs (e.g., muon ๐ or jet ๐ ๐).
๏จ Combines the inputs using nested sums of functions:
๐ฆ =
๐ ๐ + ๐1 ๐ ๐ + ๐1 ๐ โฆ + ๐2 ๐ โฆ + โฏ + ๐2 ๐ โฆ + โฏ
๏จ Outputs the discriminant, ๐ฆ, which takes values near 0 for
background and near 1 for signal.
๏จ Learning algorithm finds the parameters that yield the
desired ๐ฆ values.
๏จ We use sigmoid function for ๐: ๐ ๐ฅ =
1
1+๐โ๐ฅ
30. Neuron
Sep 6 2011
30
๏จ Takes as input either the:
๏ค physical measureables
๏ค output from other
neurons
๏จ Calculates ๐ฃ, a shifted
sum of weighted inputs.
๏จ Outputs ๐(๐ฃ).
๐ค๐0
๐
โ
f
๐ฃ๐
๐
๐ฆ๐
๐๐ฆ ๐
๐โ1 k
๐ค๐๐
๐
32. Inputs
Sep 6 2011
32
๏จ Presence of a ๐-tagged jet
๏จ Angular separation of two
leading jets, ฮ๐ 12
๏จ Position |ฮท| of the muon
33. Neural network outputNeural network output
Neural network output Neural network output
FractionofeventsFractionofevents
FractionofeventsFractionofevents
๐๐ simulations ๐ฝ+jets simulations
Single top
simulations
QCD simulations
Output
Sep 6 2011
33
๏จ Two peak structure
due to ๐ tag boolean
๏จ We form fit
templates for signal
and background.
34. Correcting or replacing simulations using data34
Some simulations arenโt as good as others. How do we correct or
replace them using data?
35. ๐ tag efficiency
Sep 6 2011
35
๏จ The ๐ tag boolean is an important input to the NN.
๏จ The shape is dependent on the efficiency and fake rate of
tagging jets.
๏ค Jets in selected events have ๐ tag efficiency of 55% to 74% and
light fake rate of 1% to 6% according to simulations.
๏ค Simulations arenโt perfect.
๏จ The tag efficiency and fake rate are measured from
(nearly) independent data samples.
๏จ ๐๐น ๐ =
๐ ๐,๐๐๐ก๐
๐ ๐,๐๐ถ
= 0.9 and ๐๐น๐ =
๐ ๐,๐๐๐ก๐
๐ ๐,๐๐ถ
= 1.06 โ 1.32.
36. ๐ก๐ก and single top
data corrected templates
Sep 6 2011
36
๏จ Apply ๐๐น ๐ = 0.9 and ๐๐น๐ = 1.06 โ 1.32.
๏จ Line = nominal simulation. Fill = corrected.
Single top
Neural network output
Fractionofevents
Neural network output
Fractionofevents
๐๐
37. QCD (jet only events)
Sep 6 2011
37
๏จ Simulation is
difficult due to
parton showering.
๏จ Events with muon
๐ ๐๐๐ผ๐ ๐ > 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
(๐ ๐๐๐ผ๐ ๐ < 0.05) have similar NN input
distributions as events with reversed
muon isolation (๐ ๐๐๐ผ๐ ๐ > 0.1).
39. ๐+jets
Sep 6 2011
39
๏จ Heavy flavor
content in ๐+jets
subject to same
uncertainties as in
QCD.
๏จ Events with a
muon and exactly
two jets are
dominated by
๐+jets (87%).
Signal region
Data
driven
region
40. ๐+jets data driven inputs
Sep 6 2011
40
๐+jets events passing nominal selection
(โฅ 3 jets) have similar NN input
distributions as events with =2 jets.
41. Final fit templates
Sep 6 2011
41
๏จ Lines=original nominal
simulations.
๏จ Histos=final data
corrected/replaced fit
templates.
๏จ The templates will be
fit to the discriminant
calculated from data
to determine ๐ก๐ก yield.
Neural network outputNeural network output
Neural network output Neural network output
FractionofeventsFractionofevents
FractionofeventsFractionofevents
Corrected ๐๐
simulations
2 jet data (๐ฝ+jets)
Corrected single
top simulations
๐น๐๐๐ฐ๐๐ > ๐. ๐
data (QCD)
43. Maximum likelihood fit
Sep 6 2011
43
๏จ We assume the observed ๐ ๐๐๐ก๐ data events are composed of ๐ ๐ก๐ก
from ๐ก๐ก, ๐๐ก from single top, ๐ ๐ from ๐+jets, and ๐ ๐๐ถ๐ท from QCD,
where each ๐ is unknown: ๐ ๐๐๐ก๐ = ๐ ๐ก๐ก + ๐๐ก + ๐ ๐ + ๐ ๐๐ถ๐ท.
๏จ Given each probability density function, ๐(๐ฅ), over measureable ๐ฅ,
this assumption yields: ๐ ๐๐๐ก๐ ๐ ๐ฅ = ๐ ๐ก๐ก ๐ ๐ก๐ก ๐ฅ + ๐๐ก ๐๐ก ๐ฅ +
๐ ๐ ๐๐ ๐ฅ + ๐ ๐๐ถ๐ท ๐๐๐ถ๐ท ๐ฅ .
๏จ We use the output from the NN as our ๐ฅ.
๏จ Likelihood function: ๐ฟ ๐|๐ฅ = ๐ ๐ฅ๐|๐
๐ ๐๐๐ก๐
๐=1 .
๏จ We determine ๐ = ๐ ๐ก๐ก, ๐๐ก, ๐ ๐, ๐ ๐๐ถ๐ท by maximizing ๐ฟ.
๏จ Using ๐ = ๐ด๐๐ โ๐๐ก, we convert ๐ ๐ก๐ก into the ๐ก๐ก cross section, ๐ ๐ก๐ก.
44. Uncertainty
Sep 6 2011
44
๏จ ๐ = ๐ด๐๐ โ๐๐ก is a statement of the average number of
events we expect to observe.
๏จ Any given experiment is not expected to measure exactly
๐ events, due to:
๏ค Quantum Mechanics (particle interactions are statistical!)
๏ค Experimental measurement uncertainties
๏ค Underlying assumptions that could be wrong
๏จ We use pseudo-experiments to calculate how much our
measurement of ๐ changes in various scenarios. This is our
uncertainty.
45. Pseudo-experiments
Sep 6 2011
45
๏จ Randomly sample the NN templates from simulations.
๏จ 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.
๏จ Fit the NN templates to the randomly sampled pseudo-data.
๐๐ simulations ๐ฝ+jets simulations
Single top
simulations
QCD simulations
46. Pseudo-results
Sep 6 2011
46
๏จ We perform 10,000
pseudo-experiments.
๏จ Indicate presence of
-3% intrinsic bias
(measure 375 ๐ก๐ก
events on average,
expect 387).
๏จ Due to using data to
form the fit templates
for QCD and ๐+jets.
๏จ Final measurement is
corrected for bias.
๏จ Statistical uncertainty
of 10%.
๐๐ signal yield
Pseudo-experiments
47. Systematic uncertainty
Sep 6 2011
47
๏จ We relate photon counts in calorimeters to particle
energy.
๏จ What if this conversion factor is high or low?
๏จ Measured jet energies would be systematically higher
or lower than the true energy of the particle.
๏จ Change the simulations to experience a systematic
increase or decrease in jet energy.
๏จ The change in measured cross section in a systematic
scenario is the โsystematic uncertaintyโ.
48. Summary of systematics
Sep 6 2011
48
Source Uncertainty (%)
Jet energy scale +9.7/-5.1
Jet energy resolution ยฑ3.3
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 ยฑ5.0
Q2 +6.8/-3.5
ME to PS matching +6.0/-3.0
PDF +0.6/-1.8
Combined +22.8/-18.4
๏จ Largest from b-tag
efficiency uncertainty
(๐๐น ๐=0.900ยฑ0.135)
๏จ This uncertainty
already reduced by
half for 2011 data.
49. Summary
Sep 6 2011
49
The cross section for ๐๐ โ ๐ก๐ก 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 ๐ก๐ก event yield. The measured cross section is
๐๐๐ ยฑ ๐๐ ๐๐๐๐. โ๐๐
+๐๐
(๐๐๐๐. ) ยฑ ๐(๐๐๐๐. ) pb.
This is in agreement with the theory predicted cross
section of 157 pb.
50. Outlook
Sep 6 2011
50
๏จ Submitted to Physics Review
D for publication.
๏จ Available statistics going
up, though measurement is
systematics limited.
๏จ Systematic uncertainties are
going down, especially with
respect to ๐ tags.
51. I received a lot of help from some really wonderful
people. You know who you are.
Sean, words canโt express, so I shall just lamely say:
thank you.
Dedication
Sep 6 2011
51
59. Simulation
Sep 6 2011
59
๏จ MadGraph: matrix element
๏ค Particle interactions are fundamentally statistical.
๏ค Matrix element is related to probability that particles with given
kinematics will be produced in collision.
๏ค Physicist specifies desired initial and final particles, including +jets.
๏ค Matrix element includes all possible intermediate โpathsโ.
Image source: Scholarpedia
๏จ Pythia:
๏ค Colored particles like gluons and
quarks never observed in isolation
๏ค Particle shower pulls new partons
from vacuum
๏ค Beam remnant (leftover from collided
protons)
๏จ Multiple interactions from data
60. Monte Carlo (MC) simulations
Sep 6 2011
60
๏จ Integrate a function from
๐ฅ1 to ๐ฅ2.
๏จ The analytical form is unknown,
but the value can be calculated.
๏จ The minimum, ๐ฆ1, and maximum,
๐ฆ2, values of the function in the
range [๐ฅ1, ๐ฅ2] are known or can
be approximated.
๏จ Throw random points (๐ฅ, ๐ฆ) in
the region (๐ฅ1, ๐ฆ1) โ (๐ฅ2, ๐ฆ2).
๏จ Calculate the fraction, ๐น, with
๐ฆ < ๐(๐ฅ).
๏จ The integral is then
๐น(๐ฅ2 โ ๐ฅ1)(๐ฆ2 โ ๐ฆ1). ๐ฅ1 ๐ฅ2
๐ฆ1
๐ฆ2
62. Finding network weights
๏จ โTrainโ on simulated datasets.
๏จ Signal events are given a
training target of 1,
background events given
training target of 0.
๏จ Training goal is to minimize a
cost function. If ๐ = 1 โฆ ๐
training events have target
๐ฆ(๐) =
0, ๐ = ๐๐๐
1, ๐ = ๐ ๐๐
and ๐ฆ(๐)
is the network output for
event ๐, then cost, ๐ถ, is:
๐ถ =
1
2
๐ฆ ๐ โ ๐ฆ(๐) 2๐
๐=1 .
๏จ โPropagateโ the cost, calculated
for the network output, back in the
network by weighting the cost by
the weight between the neurons.
๏จ 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.
๐ถ
๐ค
63. ๐๐น ๐
Sep 6 2011
63
๏จ The ๐ต meson decay includes a muon in 11% of ๐
jets, or in 20% of ๐ jets including ๐ โ ๐.
๏จ Select events with ฮ๐ ๐, ๐๐๐ก < 0.4.
๏จ Jets with muons inside are from a ๐ or from jet
fakes (pion decay or muon chamber punch-
through).
๏จ To get efficiency of tagging ๐ jets in data, the
fraction of tagged jets with muons is adjusted by
the fraction of jets with fake muons.
๏จ Done by fitting the ๐ ๐
๐๐๐
distribution.
๏จ ๐๐น ๐ uncertainty primarily from ๐ ๐
๐๐๐
shape and
fraction of jets with fake muons.
64. ๐๐น๐
Sep 6 2011
64
๏จ Jets with tracks that have negative impact
parameters are nearly all from light quarks.
๏จ Change the tag algorithm to sort tracks in
opposite order (smallest impact parameter
significance first), label negative tag.
๏จ The negative tag distribution is not symmetrical
with respect to the normal tag distribution.
๏จ Calculate the ratio between the tag rate of light
jets and negative tag rate of all jets: ๐ ๐ =
๐๐
๐๐ถ
๐โ
๐๐ถ
๏จ Fake rate in data is then ๐๐
๐๐๐ก๐
= ๐โ
๐๐๐ก๐ ๐ ๐
๏จ ๐๐น๐ uncertainty primarily due to ๐ ๐.
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 wordsโฆ
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 arenโt 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)
๏จ High energy physics
๏ค Why measure the rate at which
top quarks are produced?
๏จ Experimental apparatus
๏ค Where do we make top quarks
and how do we observe them?
๏จ Grid computing
๏ค What computing facilities are
required?
๏จ Event simulations, reconstruction,
and selection
๏ค How do we know what to
expect from top quarks?
๏ค How do we recognize different
types of particles?
๏จ Discrimination
๏ค Can we differentiate between
top quarks and other particles?
๏จ Correcting or replacing
simulations
๏ค Some simulations arenโt as
good as others. How do we
correct or replace them using
data?
๏จ Measuring cross section
๏ค How many collisions are from
top quarks?
๏ค What is the uncertainty of
this number?
Sep 6 2011
75
76. Sep 6 2011
change
Systematic uncertainty
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