PhD dissertation defense proposal. This presentation details my research work with the Compact Muon Solenoid (CMS) Collaboration of the European Organization for Nuclear Research's (CERN) Large Hadron Collider (LHC). Specifically, my investigations of the behavior the strong nuclear force by studying the production rate of beauty and antibeauty quark pairs are presented, and a comparison with leading theoretical models is shown.
Disha NEET Physics Guide for classes 11 and 12.pdf
Dissertation Defense Presentation
1. Measurement of Angular Correlation in b Quark Pair
Production at the LHC as a Test of Perturbative QCD
Dissertation Defense
Brian L. Dorney
Florida Institute of Technology
Dissertation Committee:
Marc Baarmand (advisor)
Ugur Abdulla (outside)
Daniel Batcheldor
Marcus Hohlmann
Ming Zhang
Brian L. Dorney 07/03/13
Dissertation Defense
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2. The Standard Model...
...of Particle Physics
Describes interactions of
fermions and bosons
Image courtesy of MissMJ, “Standard Model of Elementary Particles,” Wikipedia, 2013.
Fermions: half-integer spin,
i.e. quarks and leptons
Bosons: integer spin, i.e. γ, g,
Z0, W±, and H
Incorporates “two” theories
Quantum Chromodynamics
Electroweak Theory
Quantum Electrodynamics
Quantum Flavordynamics
(i.e. weak interactions)
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3. Quantum Chromodynamics
Renormalizable nonabelian gauge
theory that describes interactions of
quarks and gluons
Anticharge screening
At high energies quarks and gluons
behave as free particles
Color confinement
As distance between quarks and gluons
increases their color charge increases
Asymptotic freedom
J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012).
All searches for free quarks since 1977
have yielded negative results
Quarks form color singlet bound states
Perturbation Theory
Observables described by perturbative
series in terms of αS
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4. bb Production Mechanisms
Left image courtesy of D. Acosta et al., Phys. Rev. D71,092001 (2005).
Right image courtsey of M. Baarmand et al., CMS-AN-2010/022.
FCR gives rise to a back-to-back topology for the bb pair
In FEX a bb pair is created within the parent proton
Angle in transverse plane between the b and b is ~π radians
Only one member of the bb pair is involved in collision causing a wide range of
angular separations between the b and b
In GSP, a gluon splits into a bb pair
The b and b are roughly collinear w/small angular separation in the transverse plane
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5. Properties of B Hadrons
Daughters generally have
high impact parameters
Perpendicular distance
between particle trajectory
and primary vertex
Generally decay into
several charged
secondary particles
Makes it possible to find
the location of the B
hadron's decay
(i.e. secondary vertex)
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6. Properties of B Hadrons
Large semileptonic branching fraction
How often a B hadron decays to leptons+hadrons
B B l l X =
Bl l X
B Y
At LO, decay proceeds via emission of virtual W
boson and a charm quark
νμ
μ+
0.29
−0.25
B( B → μ νμ X) = 10.95
Brian L. Dorney 07/03/13
% as quoted by PDG
Dissertation Defense
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7. Proton-Proton Collision
Underlying
Event
Spectator Partons
f k x1
h1 P 1
1
qk x1 P 1
1
1
k
k
q1 q 2 y
1
q
h2 P 2
k2
2
x2 P 2
2
FSR Included
Y
Jets
f k x2
2
Underlying
Event
ISR
Protons
Approach
Hard
Scattering
1
Parton
Shower
1
Decays
h1 h2 Y =∫0 dx 1∫0 dx2 ∑ ∑ f k x 1 f k x 2 q1 x1 P 1 q 2 x 2 P 2 y
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k1
k2
1
2
Dissertation Defense
Hadronization
k1
k2
9. Large Hadron Collider
Image courtesy of LHC@home, http://lhcathome.web.cern.ch/LHCathome/LHC/lhc.shtml, 2013.
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10. Compact Muon Solenoid (CMS)
CMS Collaboration, Lucas Talyor, “CMS detector design,”
http://cms.web.cern/ch/news/cms-detector-design, 2013.
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11. CMS Coordinate System
+y
+y
+z
+x
x-axis points out of page
z-axis points into page
yz-plane
xy-plane
= −ln tan / 2
= 2 − 1
R =
p x p y
= 2 − 1
A = or R
pT =
2
2
2
CMS Collaboration, Detector Drawings, CMS-PHO-GEN-2012-002.
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2
13. Previous bb Angular Correlation
Measurements – LHC, ATLAS
Right: bb dijet production
cross section
ATLAS Collaboration. Eur. Phys. J. C, 71 (1846), 2011.
Disagreement at low Δφ
Full range of Δφ was not
studied
Cross section with
respect to ΔR has not
been presented
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14. Previous BB Angular Correlation
Measurements – LHC, CMS
CMS Collaboration, JHEP03(2011)136.
CMS Collaboration, JHEP03(2011)136.
BB production cross section
Overall uncertainty of 47% common to all data points
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15. Motivation
Why perform another bb angular correlation
measurement at LHC energy levels?
Large uncertainty on absolute cross section of previous
CMS results
Limited Δφ range covered in ATLAS study
Propose a new bb angular correlation measurement
to address these two concerns
Complimentary measurement using different
experimental technique and in differing phase-space
Angular correlations measured w.r.t. b-tagged jets
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16. Overview
b-jet
Two b-tagged jets
p
Experimental Signature
One of which has a muon
μ
Strategy
Select high purity sample of bb dijet events
X
Signal purity determined in data via System4
p
b-jet
Selection efficiency
Calculated from simulated PYTHIA events
Weighted by data trigger efficiency
Corrected by data-over-simulation scale factors (muon
reconstruction, jet energy resolution, b-tagging, etc...)
Data
SF =
Sim.
Measurement of differential cross section w.r.t. Δφ and ΔR
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17. Simulated Samples &
Monte-Carlo Event Generators
PYTHIA
Muon-enriched hard QCD process
Passed through Geant4 CMS detector simulation
MadGraph
CASCADE
Hard scattering: p p b b j for j = 0, 1, & 2 additional partons
Hard scattering: g g Q Q for Q = b
MadGraph and CASCADE passed to PYTHIA for parton
shower and hadronization
Not passed through Geant4 CMS detector simulation
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18. Data Samples
Proton-proton collision events collected in 2010 at
s=7 TeV with recorded integrated luminosity 3 pb-1
Two independent samples collected
Low-pT single-muon trigger, referred to as HLT_Mu7
Single-jet and multijet triggers
Use of muon triggers are a natural choice to select
bb data sample online
Jet triggers collect statistically independent sample
for measuring online selection efficiency Online
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19. Particle-Flow Event
Reconstruction in CMS
“Global event description”
Hits in CMS detector channels used to
form elements
Elements are linked together to form
blocks
Tracks, calorimeter clusters
Charged tracks linked to calorimeter clusters
Calorimeter clusters linked to calorimeter
clusters
Tracks linked to tracks
Blocks identified as particle-flow
candidates
Block formed from a charged track linked to a
HCAL cluster forms a particle-flow hadron
Brian L. Dorney 07/03/13
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CMS Collaboration, CMS PAS PFT-10-001, 2010.
19
20. Particle-Flow Jet
Reconstruction in CMS
Jets are clustered by the infrared and collinear safe
anti-kT particle-flow algorithm
Iterative clustering algorithm
Collection of particle-flow candidates used as input
Clusters particles into jets if the particles are within a
given distance parameter djet of the jet axis
Characterized by two resolution variables:
d kB = p
2a
Tk
d kl =min p , p
2a
Tk
Beam Resolution
2a
Tl
R
d
Cluster Resolution
2
kl
2
jet
For a = 1 (a = -1), kT (anti-kT) clustering algorithm
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21. Muon
Reconstruction in CMS
Global Muon reconstruction, i.e. “outside-in”
Standalone-muon track: reconstructed in muon detector
Standalone-muon track extrapolated to inner tracking
detector and required to match a tracker track
Global-muon track: track formed from combined fit of hits in
the standalone-muon and tracker track
Tracker Muon reconstruction, i.e. “inside-out”
Track reconstructed by inner tracking detector is extrapolated
to muon detector
Tracker-muon track: If this extrapolated track matches a
muon segment the tracker track is called a tracker-muon
Muon segment: track stub made of drift tube or cathode-strip
chamber hits
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22. Physics Object Matching
Objects are said to be matched if they are
within some parametric distance of each other
Example of matching
A generator-level jet and a reconstructed jet are
considered to be matched if the ΔR between them
is less than 0.25
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23. Physics Object Selection
Anti-kT particle-flow jets
Loose PF Jet ID
Distance parameter, djet = 0.5
pT > 30 GeV & |η| < 2.4
Muons
Tight Muon Selection
pT > 8 GeV & |η| < 2.1
This pT cut corresponds to plateau in online efficiency
Referred to as tight muons
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24. Muon Association
Tight muon found within a
jet referred to as the jet's
associated muon
Association uses a jet's
particle-flow constituents
If two or more tight muons
found the tight muon with
Rel
pT to jet axis
the highest
is taken
p jet p
∣ ×∣
p =
p
∣∣
Rel
T
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26. Online Selection
Data has at least one “offline” reconstructed tight muon
with HLT_Mu7 trigger object match
HLT_Mu7 trigger object is a muon (i.e. track) reconstructed by
the HLT_Mu7 trigger algorithm
ΔR matching, with ΔR < 0.5
The tight muon must be associated to a jet
Simulated PYTHIA events are weighted with Online
Simulated trigger information not used
Event weighting determined from η of highest pT tight muon
associated to a jet
Shown to be equivalent to a data-over-simulated efficiency
scale factor weighting
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28. Offline Preselection
At least one jet having an associated tight muon
with trigger-matched (ΔR < 0.5) object
No trigger-matched object criterion for simulation
At least one jet w/o an associated tight muon
The highest TCHE mu-jet and the highest TCHP
non-mu-jet must have ΔR > 0.6
Jets with (without) associated tight muons are
referred to as mu-jets (non-mu-jets)
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31. B-Tagging
Identification of jets arising from
the hadronization and decay of b
quarks
Signed impact parameter
significance (SIP)
Referred to as b jets
CMS Collaboration, CMS PAS BTV_07_002, 2008.
Impact parameter significance given by IP / IP
Impact parameter inherits the sign of the scalar product between the
IP and jet axis, tracks from B hadron decays favor positive SIP values
Track counting algo. orders a jet's tracks by decreasing SIP
Numeric discriminator formed by taking the SIP of the Nth track
Two versions, high eff. (TCHE, N = 2) and high purity (TCHP, N = 3)
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32. B-Tagging Selection
For TC discriminator values > X, the light (u, d, s, and g) jet
misidentification probability is Y
Form “operating points” which give specific values of Y
Loose (L), Y = 10%; Medium (M), Y = 1%; Tight (T), Y = 0.1%;
In each event highest TCHE mu-jet and highest TCHP non-mujet taken as a dijet pair
Event is finally selected if mu-jet (non-mu-jet) passes TCHEM
(TCHPT) operating point
TCHEM: TCHE > 3.30; TCHPT: TCHP > 3.41
Event is rejected if two or more mu-jets (non-mu-jets) pass TCHEM
(TCHPT), fraction of events rejected in data (sim.) is 0.7% (0.7%).
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34. Final Selection: Jet Kinematics
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35. Final Selection: Muon Kinematics
EWK contamination does not survive b-tagging selection
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36. Detector Response
ΔRReco
From true flavor bb dijets and their matched (ΔR < 0.25)
generator-level jets from final selected simulated events
ΔφReco
ΔφGen
ΔRGen
Off diagonal elements are an order of magnitude smaller
than their main diagonal counterparts
Bin-to-bin migration taken as negligible
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37. Purity Correction with System4
System of 4 equations in 4 unknowns, System4
Solves an “S x = b” system for each bin of ΔA
Designed to determine bin-by-bin bb signal purity in data
S = efficiency matrix; x = flavor vector; b = yields vector
Breaks analysis into four classes of cuts
TCHPT applied to non-mu-jet
TCHEM applied to mu-jet
Preselection
Both discriminators applied to both jets
Unknowns are the flavor content of preselected events
Transformed to purity of final selected events
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38. System4
Flavor
Vector
Efficiency Matrix
Unknowns
Description
Contents of preselected events by flavor.
First (second) letter is the flavor of the
mu-jet (non-mu-jet), X = non-b.
{ f BB , f BX , f XB , f XX }
Knowns
{f
TCHPT
{ B
TCHPT
,f
TCHPT
TCHEM
Description
,f
TCHEM
Both
Fraction of events passing cuts
}
TCHEM
, X
, B
, X
{ BB , BX , XB , XX }
{ BB , BX , XB , XX }
{ BB , BX , XB , XX }
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Yields
Vector
}
B-tagging efficiencies
Ratios of dijet efficiency to single
jet efficiency
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39. System4 Toy MC
Use 100k pseudo-experiments for each bin of ΔA
Vary elements of yields vector & efficiency matrix by their
uncertainties
Solves “S x = b” via non-negative least squares algorithm
C. L. Lawson, R. H. Hanson, “Solving Least Squares Problems,”
Prentice-Hall, Inc., 1974.
Distributions of flavor vector elements and purity are
formed from all pseudo-experiments
Purity given as P IJ = IJ IJ f IJ / f Both
Fit with a Gaussian, mean (standard deviation) is set to the
central value (statistical uncertainty)
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40. bb Dijet Signal Purity in Data
Overall bb dijet signal purity in data: 93.3 ± 1.7 (stat.) %
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41. Online plus Offline Selection
Efficiency
H Sel
Sel =
H Gen
Taken from simulation as ratio of reconstructed bb
dijet to generated bb dijet ΔA distributions
Overall online plus offline efficiency Sel =17.1%
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42. Systematic Uncertainties
Calculated bin-by-bin in ΔA:
Signal purity
Muon reconstruction and identification efficiency scale factor
B-tagging efficiency scale factors
Jet energy correction (JEC)
Jet energy resolution (JER)
Fragmentation
Shape of online plus offline efficiency
Proton distributions functions
Taken as a flat value across all bins of ΔA:
Online efficiency
Recored integrated luminosity
Total syst. uncert. on absolute cross section +13.1/-9.8%
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43. Differential bb Dijet Production
Cross Section
Experimental cross section for ith bin of ΔA
N Data P bb
d
=
d A i
L A bin Sel
i
NData → raw number of final selected events
Pbb → bb dijet signal purity
L → recorded integrated luminosity
ΔAbin → bin width in ΔA
Sel → online plus offline selection efficiency
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44. Differential bb Dijet Production
Cross Section
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45. Comparison to Previous CMS
Results
Red: previous
CMS Results
Black: work
presented here
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46. Comparison with Theoretical
Preidctions of Perturbative QCD
All
Val
in n ues
b
e
lut ion
bso ect
A
S
ss
Cro
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47. Suggestions for Future Work
Extend study to full CMS pp collision dataset
Compare results with a complete NLO MC
event generator
Determine the fractions of bb pairs produced
by the FCR, FEX, and GSP mechanisms
Determine the double differential bb dijet
2
production cross section d / d A d E
Detemine the cross section as a function of ΔA
with n additional light jets in final state
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51. Previous BB Angular Correlation
Measurements – LHC, CMS
CMS Collaboration, JHEP03(2011)136.
CMS Collaboration, JHEP03(2011)136.
BB production cross section
Overall uncertainty of 47% common to all data points
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52. Corrections Made to Simulated
PYTHIA Sample
The analysis takes the online plus offline efficiency with
respect to ΔA from the simulated PYTHIA sample
Simulation has been weighted/corrected by:
Data-driven jet energy resolution scale factors jet-by-jet (CMS
PAS JME-10-011)
Semileptonic branching fraction scale factors for direct B
hadron to muon decays jet-by-jet (presented herein)
Data trigger efficiency event-by-event (presented herein)
Data-driven muon reco. and ID efficiency scale factor, muonby-muon and mu-jet-by-mu-jet (CMS PAS MUO-10-004)
Beauty, charm, and light b-tagging efficiency scale factors for
TCHEM and TCHPT jet-by-jet (Official CMS SFs)
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53. Jet Energy Resolution Scale
Factor
Corrects the JER in simulated samples to what is
observed in data
p
prime
T
=p
Gen
T
SF JER⋅ p
Reco
T
−p
Gen
T
SFJER reported in CMS PAS JME-10-011
JM
E10
-
01
1
SFJER =
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54. Branching Fraction Scale Factor
PDG branching fraction:
0.0029
B B X PDG = 0.10956−0.0025
PYTHIA branching fraction:
−3
B B X PYTHIA = 0.1048±1.663⋅10
Measurements made from B+, B0, B0s, b-baryons, Bc,
and charge conjugates
For both PDG and PYTHIA numbers given above
Cascade b → c → μX decays are not considered in
above PDG or PYTHIA numbers
They are not direct decays
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55. Branching Fraction Scale Factor
For true flavor b jets w/direct b to mu decays
SF BF =
B
PDG
B
PYTHIA
0.027
= 1.044− 0.024
For true flavor b jets w/o direct b to mu decays
non−
SF BF
=
1 − B PDG
1 − B PYTHIA
0.0032
= 0.9948−0.0028
Use the hadron ancestry chain method to identify which
case generator-level true flavor b jets belong to
Reconstructed true flavor b jets use their matched generator-level
jets to determine which case they belong to
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56. Muon Reconstruction and
Identification Efficiency Scale Factor
Efficiency to reconstruct and identify muons in CMS
detector presented in CMS PAS MUO-10-004
For both data and simulated samples
M
U
O
-1
000
4
Observables obtained from tight muons (or the jets they
are found w/in) are weighted by muon-by-muon (jet-by-jet)
with the muon reconstruction and identification efficiency
scale factor
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57. B-Tagging Efficiency Scale
Factors
Two sets of functions, { SF b , SF c , SF l }
Note SFc = SFb with double the quoted uncertainty
Separate functions for light, charm, and beauty jets
One set for each TCHEM and TCHPT
Parameterized in terms of jet pT
Scale factor functions are used jet-by-jet in simulated events
Randomly upgrades (degrades) tagged (untagged) jets in
simulation
Ensures b-tagging efficiencies in simulated events agree with
what is observed in data
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58. B-Tagging Efficiency Scale
Factors
Jet with transverse momentum pT and flavor i will
SF i = SF i pT and Sim. = Sim. pT
have
i
i
Obtain a uniformly distributed random number R such
that R ∈ [ 0, 1 ]
For SF i 1 & jet is untagged, calculate
1− SF i
f=
SF i
1− Sim.
i
If R < f, tag the jet (i.e. upgrade)
This is the fraction of jets we need to tag in simulation
For SF i 1 & jet is tagged
If R > SF i untag the jet (i.e. downgrade)
This is the fraction of jets we fail to tag in data
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59. TCHEM B-Tagging Efficiency
Scale Factor
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Note SFb = SFc with
twice the uncertainty
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60. TCHPT B-Tagging Efficiency
Scale Factor
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Note SFb = SFc with
twice the uncertainty
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61. B-Tagging Efficiency Scale
Factors, Factorizable at Low ΔR?
Study conducted by D. Bloch
at my request
Looked at b-tagging efficiency
scale factors in dijet events
D. Bloch, b tag meeting, 12th Dec. 2012
Mu-jet tagged by TCHEM
Non-mu-jet (“away- jet”) tagged
by TCHPT
Conclude scale factors are
factorizable at low ΔR
D. Bloch, b tag meeting, 12th Dec. 2012
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62. PYTHIA Hard QCD Process
All hard scattering processes of the form:
qi qi q j q j
qi qi g g
qi g qi g
g g qi qi
q i q j qi q j
gg gg
Where q is any flavor quark (top excluded) and
g is a gluon
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63.
p T in PYTHIA
Mandelstam Variables
Where pi are 4-vectors
s = p A p B
t = p A − pC
2
u = p A− p D
2
2
pC
pD
time
pA
pB
Form pT
1
pT =
t u − m3 m4
s
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64. Infrared & Collinear Safe Jet
Algorithms
Jet definition is insensitive to “infrared and
collinear divergences”
What does this Mean?
Theoretical predictions of the inclusive jet cross
section must be finite at all orders
Experimentally the jet definition does not
drastically change in the presence of additionally
emitted collinear or soft particles
i.e. Event topology/jet multiplicity is relatively constant
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65. Jet Matching
Before the Selection record the ΔR
of all possible reconstructed and
generator-level jet pairings
For conservative measure apply ΔR
matching criterion of 0.25
For reco jets with pT > 10 GeV
First inflection point at ΔR ≈ 0.3
1.19% remain unmatched
0.01% have two possible matches, no
jet with three possible matches
Fraction of unmatched reco jets
with pT > 30 GeV is ≈0.1%
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66. Assignment of True Flavor to
Jets in Simulated Samples
True flavor of a generator-level jet is determined from the jet's
three highest generator-level constituents
Heaviest-flavor hadron ancestor in the decay chain of these
three particles is assigned as the generator-level jet's flavor
Occurrence of a generator-level particle having more than one
mother in a decay chain was found to be negligible (≈0.03%)
True flavor of a reconstructed jet is taken from its matched
generator-level jet
True flavor of unmatched reconstructed jets assigned as light
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67. Tight Muon Selection
Muon is both a global muon and a tracker muon.
Global track
Global track has at least one muon chamber hit.
2
Tracker track required to be matched to muon
segments in at least two muon stations.
Tracker track has nhits ≥ 10.
fit's / n.D.o.F. 10.
At least one of these hits is in the pixel detector
Transverse impact parameter w.r.t. PV
∣d xy∣ 2 mm.
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68. Loose PFJetID
Neutral hadron energy fraction < 0.99
Neutral EM energy fraction < 0.99
Number of pfConstituents > 1
Charged hadron energy fraction > 0
Charged EM energy fraction < 0.99
Charged multiplicity > 0
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69. Trigger Muon Object Matching
Offline tight muons are matched to HLT_Mu7 trigger
objects
Matching Criteria
Only HLT_Mu7 trigger objects
ΔR between the tight muon and trigger object is less than 0.5
Matching is one-to-one
i.e. trigger objects matched to one tight muon are not considered for
other matches, and vice versa
Trigger object match candidates ordered by increasing ΔR
Tight muon-trigger object match with lowest ΔR is taken as the
matched pair
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70. Online Efficiency
SFOnline
SFOnline
Online Efficiency
Trigger Efficiency Weighting
Comparison
Online efficiency scale factor SFOnline flat for muon pT > 8 GeV
Noticeable variation w.r.t. muon η
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71. Trigger Efficiency Weighting
Comparison
Performed analysis using simulated trigger information
Event-by-event weighting: SF Online high
high is from the highest p muon, having a HLT_Mu7 trigger matched object,
associated to a jet
T
Observe that data trigger efficiency weighting is equivalent to online
efficiency scale factor weighting
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71
72. Determination of Online
Efficiency
Data collected by single-jet and mutlijet triggers provides
statistically independent sample for online efficiency
measurement
Event Selection
Only one offline reconstructed muon present
Muon is associated to a jet
Association uses the jet's particle-flow constituents
Jet passes TCHEM operating point (i.e. TCHE > 3.3)
Object Selection
Jet with muon must have pT > 30 GeV
Muon must pass the Tight Muon Selection with |η| < 2.1
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72
73. Determination of Online
Efficiency – Results
Efficiency defined as Online = N matched / N all
Nmatched → # of tight muons in a given p or bin, associated to a b-tagged jet,
T
matched with an HLT_Mu7 trigger object
Nall → # of tight muons in a given pT or bin that are associated to a b-tagged jet
Online efficiency Online = 85.5±1.1 stat.−1.5 syst. %
3.9
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73
74. Determination of Online
Efficiency – Systematic Uncertainties
Methodology taken from CMS PAS-MUO-10-004
Independently varied the following
Increased selection beyond Tight Muon Selection
Jet b-tagging operating point changed to TCHPT
Muon's track was required to be the track that
determined the jet's TCHE value
With and w/o the b-tagging requirement under both
the Tight Muon Selection and the more stringent
muon selection
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74
75. Online Efficiency
Online Efficiency
Determination of Online
Efficiency – Systematic Uncertainties
Black: nominal distribution
Red: increased selection beyond Tight Muon Selection
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75
76. Online Efficiency
Online Efficiency
Determination of Online
Efficiency – Systematic Uncertainties
Black: nominal distribution
Blue: jet passes TCHPT operating point
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76
77. Online Efficiency
Online Efficiency
Determination of Online
Efficiency – Systematic Uncertainties
Black: nominal distribution
Green: muon's track determines jet's TCHE value
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77
79. Determination of Online
Efficiency – Systematic Uncertainties
Effect on online efficiency
With & w/o B-tagging
under Normal &
Increased Selection
0.00%
Increase B-Tagging
-0.1%
0.00%
Increased Muon Sel
0.0%
+3.9%
Muon's track
determines TCHE
0.0%
+0.6%
Total
-1.5%
-1.5%
+3.9%
3.9
−1.5
Online efficiency Online = 85.5±1.1 stat.
Brian L. Dorney 07/03/13
Dissertation Defense
syst.%
79
80. Online Efficiency Cross Check
Efficiency of a different
low-pT single-muon
trigger published in
CMS PAS MUO-10-004
Referred to as HLT_Mu9
Measured efficiency of
HLT_Mu9 using my
technique
Find agreement with
published values
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80
84. Summary of Event Selection
Number of events passing each stage of the
event selection
Fraction of events remaining after each stage
of event selection w.r.t. previous stage allows
for direct comparison of data and simulation
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84
85. Δφ & ΔR Resolution
For all true flavor bb dijet pairs record A Reco− AGen
ΔA represents Δφ or ΔR
RMS of this distribution taken as resolution on ΔA
Brian L. Dorney 07/03/13
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85
86. Detector Response – Revisited
Decrease Δφ detector response matrix bin size by 2
Bin size now approximately five times Δφ resolution
Observe off diagonal elements in “larger” bin size are actually
part of main diagonal
Conclusion: bin-to-bin migration is negligible
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86
87. System4
Flavor
Vector
Efficiency Matrix
Dijet Tagging Efficiencies
TCHEM
ij = i
Description
First (second) letter is the flavor of the
mu-jet (non-mu-jet), i, j = B or X.
TCHPT
j
Non-b Tagging Efficiencies
all
X=
nc
all
Description
all
Sim.
all c
nc n l
Brian L. Dorney 07/03/13
nl
all
Yields
Vector
Sim.
all l
Efficiency to tag a non-b jet
nc n l
Dissertation Defense
87
88. System4
Flavor
Vector
Efficiency Matrix
Beta Factors
Both Tag
IJ =
IJ
TCHEM
I
TCHPT
J
Alpha & Gamma Factors
IJ =
IJ =
Mu Tag
IJ
TCHEM
I
Non Mu Tag
IJ
TCHPT
J
Brian L. Dorney 07/03/13
Yields
Vector
Description
Ratio of dijet efficiency to single jet
efficiency
Description
As above
Define κIJ = {αIJ, βIJ, γIJ}
As above
Dissertation Defense
88
89. System4
Flavor
Vector
Efficiency Matrix
Beta Factors
Description
Both Tag
IJ =
IJ
TCHEM
I
TCHPT
J
Dijet Efficiency Example
Tag
Both Tag
IJ
=
N IJ
Tag
Tag
N IJ N IJ
Brian L. Dorney 07/03/13
Yields
Vector
Ratio of dijet efficiency to single jet
efficiency
Description
Example dijet efficiency, similarly
for other two cases
Dissertation Defense
89
90. System4
Flavor
Vector
Efficiency Matrix
Purity Definition
P BB = BB BB f BB / f
Brian L. Dorney 07/03/13
Yields
Vector
Description
Both
First (second) letter is the flavor of the
mu-jet (non-mu-jet), i, j = B or X.
Dissertation Defense
90
91. System4 – IJ Factors, Δφ
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Dissertation Defense
91
92. System4 – IJ Factors, ΔR
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92
93. System4 – IJ Factors,
Shape Investigation
Factors generally increase with decreasing
angular separation between two jets
Investigated whether factor behavior is due to
differing kinematic behavior
Investigated shape of factors in bins of jet
transverse momentum and absolute
pseudorapidity
Brian L. Dorney 07/03/13
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93
94. System4 – IJ Factors,
Binned by Mu-Jet pT
Approximately
uniform shape
over all pT bins
Brian L. Dorney 07/03/13
Dissertation Defense
94
95. System4 – IJ Factors,
Binned by Jet pT
Approximately
uniform shape
over all pT bins
Brian L. Dorney 07/03/13
Dissertation Defense
95
96. System4 – IJ Factors,
Binned by Non-Mu-Jet pT
Approximately
uniform shape
over all pT bins
Brian L. Dorney 07/03/13
Dissertation Defense
96
97. System4 – IJ Factors,
Binned by Jet |η|
Uniform shape
over all |η| bins
Brian L. Dorney 07/03/13
Dissertation Defense
97
98. System4 – IJ Factors,
Binned by Jet |η|
Uniform shape
over all |η| bins
Brian L. Dorney 07/03/13
Dissertation Defense
98
99. System4 – IJ Factors,
Binned by Jet |η|
Uniform shape
over all |η| bins
Brian L. Dorney 07/03/13
Dissertation Defense
99
100. System4 – IJ Factors,
Track Mismatching
Investigated possibility of track mismatching as a contributor to
shapes of κIJ factors
For each mu-jet (non-mu-jet) track that determines jet's TCHE
(TCHP) referred to as the b-tagging track
ΔR between parent mu-jet (non-mu-jet) and b-tagging track plotted
against the ΔR between the adjacent non-mu-jet (mu-jet) and the
b-tagging track
Symbolically referred to as trackTCHE (trackTCHP) for the mu-jet (non-mu-jet)
Here “adjacent” refers to the other member of the dijet object
In O(107) events, O(10) events have instances of track mismatching
i.e. Negligible, too rare to describe shapes of κIJ factors
Brian L. Dorney 07/03/13
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100
101. System4 – Track Mismatching
Mu-Jet Passes TCHEM, b-tagging = trackTCHE
Imagine y=x line
Entries falling
below line
indicate track
mismatching
i.e. mu-jet's
b-tagging track
is closer in
ηφ-plane to the
non-mu-jet
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101
102. System4 – Track Mismatching
Non-Mu-Jet Passes TCHPT, b-tagging = trackTCHP
Imagine y=x line
Entries falling
above line
indicate track
mismatching
i.e. non-mu-jet's
b-tagging track
is closer in
ηφ-plane to the
mu-jet
Brian L. Dorney 07/03/13
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102
103. System4 – Track Mismatching
Both Jets Pass Operating Pts, b-tagging = trackTCHE
Imagine y=x line
Entries falling
below line
indicate track
mismatching
i.e. mu-jet's
b-tagging track
is closer in
ηφ-plane to the
non-mu-jet
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103
104. System4 – Track Mismatching
Both Jets Pass Operating Pts, b-tagging = trackTCHP
Imagine y=x line
Entries falling
above line
indicate track
mismatching
i.e. non-mu-jet's
b-tagging track
is closer in
ηφ-plane to the
mu-jet
Brian L. Dorney 07/03/13
Dissertation Defense
104
105. System4 – Minimum ΔR
Separation
Spike in first bin of ΔR of κIJ factors
Could be caused by poorly reconstructed and/or
fake jets being used in System4 dijet pair
Investigated requiring minimum ΔR separation
between jets used in dijet pair
Brian L. Dorney 07/03/13
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105
106. System4 – Minimum ΔR
Separation
Reduction in spiking κIJ behavior when going from
ΔR > 0.5 to ΔR > 0.6
Values of κIJ don't vary substantially when moving
from ΔR > 0.6 to ΔR > 0.7
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106
107. System4 – Correlation of IJ Factors
Order pairs of κIJ's made from all bin of ΔA
i.e. { { (αIJ, βIJ) }, { (αIJ, γIJ) }, { (γIJ, βIJ) } }
Correlation coefficients ρ determined from
each set of ordered pairs
αIJ weakly correlated with βIJ and γIJ
βIJ and γIJ strongly correlated
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107
108. System4 – Event Rejection
Concerns
mu-jet multi.
Fraction of events that would be rejected for System4 is negligible
non-mu-jet multi.
In data (sim.) for cut stage 2, TCHPT applied to non-mu-jet, have 0.8% (0.7%) events with
two or more non-mu-jets passing TCHPT
In data (sim.) for cut stage 3, TCHEM applied to mu-jet, have 0.14% (0.15%) events with
two or more mu-jets passing TCHEM
Note: the event rejection is not used for cut cases of System4
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108
109. System4 – Closure Test
Split Simulated PYTHIA sample into two statistically
independent datasets
Efficiency matrix taken from even events
Yields vector taken from odd events
System4 solution obtained from toy MC method in odd
events compared to the true solution in odd events
Four closure tests performed
Nominal
Using κIJ = 1
Reweighting gluon splitting events by factor of ½
Reweighting gluon splitting events by factor of 2
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109
110. System4 – Closure Test, ΔR
Better
agreement
using κIJ
Behavior of
attributed to
small statistics
of XB dijet case
Brian L. Dorney 07/03/13
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110
111. System4 – Closure Test, ΔR
With GSP
events
reweighted by
factor of ½
Behavior of
attributed to
small statistics
of XB dijet case
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Dissertation Defense
111
112. System4 – Closure Test, ΔR
With GSP
events
reweighted by
factor of 2
Behavior of
attributed to
small statistics
of XB dijet case
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Dissertation Defense
112
113. System4 – Closure Test, Δφ
Better
agreement
using κIJ
Behavior of
attributed to
small statistics
of XB dijet case
Brian L. Dorney 07/03/13
Dissertation Defense
113
114. System4 – Closure Test, Δφ
With GSP
events
reweighted by
factor of ½
Behavior of
attributed to
small statistics
of XB dijet case
Brian L. Dorney 07/03/13
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114
115. System4 – Closure Test, Δφ
With GSP
events
reweighted by
factor of 2
Behavior of
attributed to
small statistics
of XB dijet case
Brian L. Dorney 07/03/13
Dissertation Defense
115
116. System4 – Results From Data, ΔR
Behavior of fXB
attributed to
small statistics
of XB dijet case
Brian L. Dorney 07/03/13
Dissertation Defense
116
117. System4 – Results From Data, Δφ
Behavior of fXB
attributed to
small statistics
of XB dijet case
Dissertation Defense
Δφ
Δφ
Brian L. Dorney 07/03/13
Δφ
Δφ
117
118. B Jet Transverse Momentum
Residuals
Post Preselection
Post Final Selection
Post Final Selection
Reco
Gen
For true flavor b jets and their matched generator-level jets, studied: p T − pT
Means of distributions slightly positive with large RMS
Conclude that the residuals are consistent with zero within their statistical uncertainties
A small fraction of final selected true flavor b jets with pT > 30 GeV are matched
with generator-level jets with pT < 30 GeV
Vast majority of these cases are within one standard deviation of 30 GeV
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118
119. Shape of Jet pT in Final Event Sample,
Binned by Δφ
Highest pT jet in bb
dijet candidate
0
4
Highest pT Jet
4
2
Highest pT Jet
3
2
4
Highest pT Jet
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Dissertation Defense
3
4
Highest pT Jet
119
120. Shape of Jet pT in Final Event Sample,
Binned by Δφ
Lowest pT jet in bb
dijet candidate
0
4
Lowest pT Jet
4
2
Lowest pT Jet
3
2
4
Lowest pT Jet
Brian L. Dorney 07/03/13
Dissertation Defense
3
4
Lowest pT Jet
120
121. Shape of Jet pT in Final Event Sample,
Binned by ΔR
0.6 R1.4
1.4 R2.3
2.3 R3.2
Leading Jet pT
Leading Jet pT
Leading Jet pT
3.2 R4.1
Highest pT
jet in bb dijet
candidate
Brian L. Dorney 07/03/13
Leading Jet pT
Dissertation Defense
4.1 R5.0
Leading Jet pT
121
122. Shape of Jet pT in Final Event Sample,
Binned by ΔR
0.6 R1.4
1.4 R2.3
2.3 R3.2
Leading Jet pT
Leading Jet pT
Leading Jet pT
3.2 R4.1
Lowest pT jet
in bb dijet
candidate
Brian L. Dorney 07/03/13
Leading Jet pT
Dissertation Defense
4.1 R5.0
Leading Jet pT
122
123. Systematic Uncertainty,
Shape of Online Plus Offline Eff.
Differing kinematic behavior between data and
simulation could adversely affect cross section
Affect would be most pronounced in
uncertainties in the shape of the online plus
offline selection efficiency
Investigated in similar manner to what was
presented in JHEP03(2011)136.
However analysis performed in three jet |η| bins
Brian L. Dorney 07/03/13
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123
124. Systematic Uncertainty,
Shape of Online Plus Offline Eff.
Top: difference between data
and simulation in the average
pT of the highest pT jet in the
bb dijet candidate
Bottom: online plus offline
selection efficiency w.r.t. pT of
highest jet in bb dijet
candidate
All plots from final selected
events
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124
125. Systematic Uncertainty,
Shape of Online Plus Offline Eff.
Differences btw data and
sim. used to modify Sel via:
Prime
Sel
〈 pT 〉 Sim.
Performed in three |ηjet| bins
= Sel⋅ 1
〈 pT 〉 Data − 〈 pT 〉 Sim.
{ [0,2.4),[0.0.9),[0.9,2.4)}
Performed using highest
and lowest pT jet in the bb
dijet candidate
Six variations in total
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125
126. Systematic Uncertainty,
Shape of Online Plus Offline Eff.
Differences btw data and
sim. used to modify Sel via:
Prime
Sel
〈 pT 〉 Sim.
Performed in three |ηjet| bins
= Sel⋅ 1
〈 pT 〉 Data − 〈 pT 〉 Sim.
{ [0,2.4),[0.0.9),[0.9,2.4)}
Performed using highest
and lowest pT jet in the bb
dijet candidate
Six variations in total
Brian L. Dorney 07/03/13
Dissertation Defense
126
127. Systematic Uncertainty,
Shape of Online Plus Offline Eff.
Differences btw data and
sim. used to modify Sel via:
Prime
Sel
〈 pT 〉 Sim.
Performed in three |ηjet| bins
= Sel⋅ 1
〈 pT 〉 Data − 〈 pT 〉 Sim.
{ [0,2.4),[0.0.9),[0.9,2.4)}
Performed using highest
and lowest pT jet in the bb
dijet candidate
Six variations in total
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127
128. Systematic Uncertainty,
Shape of Online Plus Offline Eff.
Brian L. Dorney 07/03/13
Modified online plus offline
selection efficiencies used to
recompute the cross section
Maximum difference, for each
bin of ΔA, between nominal
cross section and the six new
cross sections taken as
systematic uncertainty
Dissertation Defense
128
129. Systematic Uncertainty,
Shape of Online Plus Offline Eff.
Brian L. Dorney 07/03/13
Modified online plus offline
selection efficiencies used to
recompute the cross section
Maximum difference, for each
bin of ΔA, between nominal
cross section and the six new
cross sections taken as
systematic uncertainty
Dissertation Defense
129
130. Systematic Uncertainty,
Signal Purity
Mismodeling of the shapes of kIJ factors
System4 was solved using varied αIJ and using simultaneously varied βIJ and γIJ
true
Closure
Difference f BB − f BB between System4 solution and the true solution
obtained in the nominal closure test
Varied shapes of efficiencies in the numerators of the kIJ equations in identical
fashion to what was done for the shape of the online plus offline selection
efficiency
prime
true
Closure
Solution in data modified by f BB = f BB f BB − f BB
prime
Purity in data recalculated using f BB
Possible differences in relative fraction of charm and light jets between
data and simulation
The value of n c n l is varied up and down by a factor of two while holding the
value n all n all of fixed.
l
c
all
all
Cross section recalculated for each of the above variations
Differences between nominal and varied cases are added in quadrature and
assigned as the systematic uncertainty for signal purity
Brian L. Dorney 07/03/13
Dissertation Defense
130
131. Systematic Uncertainty,
Muon Reco & ID Eff. Scale Factor
Muon reconstruction and identification scale factor
taken from CMS PAS MUO-10-004
Observables obtained from tight muons (or the jets
they are found w/in) are weighted muon-by-muon (jetby-jet) with the scale factor
For systematic uncertainty
Scale factor is varied up (down) by its total uncertainty
resulting in a -1.2% (+1.2%) change in the total cross section
Brian L. Dorney 07/03/13
Dissertation Defense
131
132. Systematic Uncertainty,
B-Tagging Eff. Scale Factors
B-tagging scale factors {SF b , SF c , SF l } for TCHEM
and TCHPT are varied up and down by their
uncertainties
Both scale factors changed at the same time in the
same direction
Beauty and charm scale factors are correlated,
varied simultaneously
Light scale factor uncorrelated, varied independently
Results of variations added in quadrature
Scale factor variations up (down) resulted in a
-3.2% (+6.7%) change in total cross section
Brian L. Dorney 07/03/13
Dissertation Defense
132
133. Systematic Uncertainty,
JEC and JER
The jet energy correction is varied up and down by its
uncertainty
The up (down) variations of the JEC resulted in a -5.6% (+9.1%)
change in the total cross section
The JER in the simulation is smeared jet-by-jet via
prime
Reco
p T = p Gen SF JER⋅ p T − p Gen
T
T
SFJER =
JM
E10
-0
11
SFJER variations resulted in a +1.7% change in the total cross
section
Brian L. Dorney 07/03/13
Dissertation Defense
133
134. Systematic Uncertainty,
Fragmentation
An additional PYTHIA sample was generated
using Peterson/SLAC fragmentation function
Generator-level jet pT distributions between
two PYTHIA samples are compared
Differences are used to modify the reco and
generator-level jet pT in the nominal case
Same is done for muons
Brian L. Dorney 07/03/13
Dissertation Defense
134
135. Systematic Uncertainty,
Fragmentation
The transverse momentum of reconstructed and
generator-level jets and muons modified via
p
prime
T
f Lund pT − f Peterson pT
= pT
m
Modifications are performed before the
selection is applied
Effect on total cross section found to be +0.4%
Brian L. Dorney 07/03/13
Dissertation Defense
135
136. Systematic Uncertainty,
Proton PDFs
Uncertainty due to proton PDFs assessed by
reweighting technique
Contribution of PDF to cross section can be
assigned a weight wi
1
1
k1
k2
h1 h2 Y =∫0 dx 1∫0 dx2 ∑ ∑ f k x 1 f k x 2 q1 x1 P 1 q 2 x 2 P 2 y
k1
1
1
k2
2
1
k
k
h1 h2 Y =∫0 dx 1∫0 dx2 ∑ ∑ f k x 1 f k x 2 w i q1 x1 P 1 q2 x 2 P 2 y
k1
k2
1
2
1
2
f k x1 ; Si f k x2 ; S i
Where wi given by: w i = f x ; S f x ; S
k
1
0
k
2
0
1
1
Brian L. Dorney 07/03/13
2
2
Dissertation Defense
136
137. Systematic Uncertainty,
Proton PDFs
In practice this means simulated events are
reweighted by wi
Three PDF sets were used in reweighting
Maximum deviation per bin of ΔA between the
nominal cross section and the reweighted cross
sections is taken as the systematic uncertainty
CTEQ66m, MSTW2008-nlo, NNPDF2.0
Effect on total cross section found to be -1.0%
wi=
f k x1 ; Si f k x2 ; S i
1
f k x1 ; S0 f k x2 ; S0
1
Brian L. Dorney 07/03/13
2
Dissertation Defense
2
137
138. Systematic Uncertainty,
Summary
Right: systematic uncertainties
on total cross section
Uncertainty sources listed
under the shape variations and
theory headings do not follow
standard “down/up” description
Down/upwards headings give
direction of parameter variation
while the sign of the value gives
effect on total cross section
Sign of the value again gives
effect on total cross section
Total systematic uncertainty on
total cross section +13.1/-9.8%
Dominat systematics are the JEC
and b-tagging scale factors
Brian L. Dorney 07/03/13
Dissertation Defense
138