Dissertation Defense Presentation

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


1

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)



2

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


3

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


4

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)



5

Properties of B Hadrons


Large semileptonic branching fraction


How often a B hadron decays to leptons+hadrons
B B l l X =



  Bl 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

% as quoted by PDG


6

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




7

k1

k2

1

2




Hadronization
k1

k2





Real example

8

Large Hadron Collider

Image courtesy of LHC@home, http://lhcathome.web.cern.ch/LHCathome/LHC/lhc.shtml, 2013.



9

Compact Muon Solenoid (CMS)
CMS Collaboration, Lucas Talyor, “CMS detector design,”
http://cms.web.cern/ch/news/cms-detector-design, 2013.



10

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.



11

2

Previous bb Angular Correlation
Measurements - Tevatron
DZero

 s=1.8 TeV, L = 6.5 ± 0.4 pb-1

Left: DØ Collaboration, Phys. Letters B, 487 (2000), p. 264-272.
Right: CDF Collaboration, CDF note 8939, 2007.



12

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



13

Previous BB Angular Correlation
Measurements – LHC, CMS

CMS Collaboration, JHEP03(2011)136.




BB production cross section



Overall uncertainty of 47% common to all data points


14

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



15

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



16

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



17

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


18

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



CMS Collaboration, CMS PAS PFT-10-001, 2010.

19

Particle-Flow Jet




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



20

Muon


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



21

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



22

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



23

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



24

Event Selection


Online selection



Offline selection





Preselection
B-Tagging

Final event sample



25

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



26

Online Efficiency



85.5±1.1 stat.3.9  syst. %
Online efficiency at plateau,
−1.5


27

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)


28

Preselection: Jet Kinematics



29

Preselection: Muon Kinematics

Electroweak Contamination


30

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)


31

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%).



32

B-Tagging Selection

TCHEM

TCHPT



TCHEM (N = 2) operating point: TCHE > 3.3



TCHPT (N = 3) operating point: TCHP > 3.41


33

Final Selection: Jet Kinematics



34

Final Selection: Muon Kinematics

EWK contamination does not survive b-tagging selection


35

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



36

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



37

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 }


Yields
Vector

}

B-tagging efficiencies
Ratios of dijet efficiency to single
jet efficiency


38

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)



39

bb Dijet Signal Purity in Data



Overall bb dijet signal purity in data: 93.3 ± 1.7 (stat.) %


40

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%


41

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%


42

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


43

Differential bb Dijet Production
Cross Section



44

Comparison to Previous CMS
Results




Red: previous
CMS Results
Black: work
presented here



45

Comparison with Theoretical
Preidctions of Perturbative QCD

All
Val
in n ues
b

e
lut ion
bso ect
A
S
ss
Cro


46

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


47

Back – Up



48

bb Production Mechanisms


Three primary
production
mechanisms



NLO – Flavor Excitation





LO – Flavor Creation
NLO – Gluon Splitting

Additional
mechanisms


NLO – Gluon Radiation



NLO Interference terms



Virtual emission
Loop diagrams


Image courtesy of D. Acosta et al., Phys. Rev. D71, 092001 (2005).


49



Real example



50

Previous BB Angular Correlation
Measurements – LHC, CMS





BB production cross section



Overall uncertainty of 47% common to all data points


51

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)



52

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 =


53

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



54

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



55

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


56

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



57

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



58

TCHEM B-Tagging Efficiency
Scale Factor





Note SFb = SFc with
twice the uncertainty

59

TCHPT B-Tagging Efficiency
Scale Factor





Note SFb = SFc with
twice the uncertainty

60

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



61

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


62


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


63

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



64

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%



65

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



66



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.


67

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


68

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



69

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


70

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


71

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



72

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



73

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



74

Online Efficiency

Online Efficiency




Black: nominal distribution



Red: increased selection beyond Tight Muon Selection


75

Online Efficiency

Online Efficiency







Blue: jet passes TCHPT operating point


76

Online Efficiency

Online Efficiency







Green: muon's track determines jet's TCHE value


77





Red: increased
selection beyond
w/b-tagging
Blue: increased
selection beyond
w/o b-tagging


Online Efficiency

Purple: using tight
muon selection w/o
b-tagging

Online Efficiency



Black: nominal
distribution

Online Efficiency



Online Efficiency



78



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.



 syst.%

79

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



80

Preselection: Mu-jet Kinematics



81

Preselection: Non-mu-jet
Kinematics



82

Track Counting Discriminators
TCHE
N=2



TCHP
N=3

83

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



84

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



85

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


86

System4

Flavor
Vector

Efficiency Matrix

Dijet Tagging Efficiencies
TCHEM

 ij =  i

Description
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


nl
all

Yields
Vector

Sim.


all l

Efficiency to tag a non-b jet

nc n l


87

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




Yields
Vector

Description
Ratio of dijet efficiency to single jet
efficiency
Description
As above
Define κIJ = {αIJ, βIJ, γIJ}

As above


88

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


Yields
Vector

Ratio of dijet efficiency to single jet
efficiency
Description
Example dijet efficiency, similarly
for other two cases


89

System4

Flavor
Vector

Efficiency Matrix

Purity Definition

P BB =   BB  BB f BB  / f


Yields
Vector

Description
Both

mu-jet (non-mu-jet), i, j = B or X.


90

System4 –  IJ Factors, Δφ



91

System4 –  IJ Factors, ΔR



92

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


93

System4 –  IJ Factors,
Binned by Mu-Jet pT


Approximately
uniform shape
over all pT bins



94

System4 –  IJ Factors,
Binned by Jet pT


Approximately
uniform shape
over all pT bins



95

System4 –  IJ Factors,
Binned by Non-Mu-Jet pT


Approximately
uniform shape
over all pT bins



96

System4 –  IJ Factors,
Binned by Jet |η|


Uniform shape
over all |η| bins



97

System4 –  IJ Factors,
Binned by Jet |η|


Uniform shape
over all |η| bins



98

System4 –  IJ Factors,
Binned by Jet |η|


Uniform shape
over all |η| bins



99

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



100

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


101

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


102

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


103

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


104

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



105

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



106

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



107

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


108

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



109

System4 – Closure Test, ΔR




Better
agreement
using κIJ
Behavior of
attributed to
small statistics
of XB dijet case



110





With GSP
events
reweighted by
factor of ½
Behavior of
attributed to
small statistics
of XB dijet case



111





With GSP
events
reweighted by
factor of 2
Behavior of
attributed to
small statistics
of XB dijet case



112

System4 – Closure Test, Δφ




Better
agreement
using κIJ
Behavior of
attributed to
small statistics
of XB dijet case



113





With GSP
events
reweighted by
factor of ½
Behavior of
attributed to
small statistics
of XB dijet case



114





With GSP
events
reweighted by
factor of 2
Behavior of
attributed to
small statistics
of XB dijet case



115

System4 – Results From Data, ΔR


Behavior of fXB
attributed to
small statistics
of XB dijet case



116

System4 – Results From Data, Δφ


Behavior of fXB
attributed to
small statistics
of XB dijet case


Δφ

Δφ


Δφ

Δφ

117

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



118

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



3
 
4

Highest pT Jet

119

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



3
 
4

Lowest pT Jet

120

Binned by ΔR

0.6 R1.4

1.4 R2.3

2.3 R3.2

Leading Jet pT

Leading Jet pT

Leading Jet pT

3.2 R4.1



Highest pT
jet in bb dijet
candidate

Leading Jet pT


4.1 R5.0

Leading Jet pT

121

Binned by ΔR

0.6 R1.4

1.4 R2.3

2.3 R3.2

Leading Jet pT

Leading Jet pT

Leading Jet pT

3.2 R4.1



Lowest pT jet
in bb dijet
candidate

Leading Jet pT


4.1 R5.0

Leading Jet pT

122

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



123







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



124



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



125







Prime
Sel

  〈 pT 〉 Sim. 









=  Sel⋅ 1

  〈 pT 〉 Data  −  〈 pT 〉 Sim. 

{ [0,2.4),[0.0.9),[0.9,2.4)}

dijet candidate





126







Prime
Sel

  〈 pT 〉 Sim. 









=  Sel⋅ 1

  〈 pT 〉 Data  −  〈 pT 〉 Sim. 

{ [0,2.4),[0.0.9),[0.9,2.4)}

dijet candidate





127







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


128







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


129

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



130

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



131

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


132

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



133

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


134

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%



135

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


2

2


136



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


2


2

137

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



138

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