Download Z+Jet Center of Momentum Angular Distribution using the Compact

Z+Jet Center of Momentum Angular
Distribution using the Compact Muon Solenoid
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Luis Lebolo
Florida International University
SESAPS 2011
Motivation for the Angular Distribution
✦
Analysis is a measurement of the Z+jet partonic angular distribution (cosθ*) decoupled from the
parton distribution functions (^ and * signify the variable is in CM frame)
• Can be seen as a measurement of the partonic matrix element weighted by parton luminosity
✦
Good test of pQCD; can look for signatures of new physics
✦
First measurement of Z+jet angular distribution (as opposed to W+jet or dijet)
• Analogous to ɣ+jet analysis, with the advantage of negligible background
✦
CMS allows for a high reach in cosθ* (CM energy and rapidity)
d 3σ
d 3σ
1
fi (x1 ) f j (x2 ) dσ̂ ij
E  →
∝ ∑
* 2
*
dp
d( p ) dyB d cosθ
S i, j x1
x2 d cosθ *
✦
Luis Lebolo
SESAPS October 2011
2
Related Measurements (CDF) [1]
Dijet ~ (1 - cosθ*)-2
Z0 ~ (1 - cosθ*)-1
Luis Lebolo
SESAPS October 2011
3
Compact Muon Solenoid
Analysis uses a particle flow algorithm that combines information from all subdetectors to reconstruct stable particles
Luis Lebolo
SESAPS October 2011
4
PF Jet and Muon Momentum Resolution
Most candidate jets and
muons in this analysis have
pT < 70 GeV
|η| < 2.0
*pT = Transverse Momentum
Luis Lebolo
SESAPS October 2011
5
Center of Momentum Kinematics
✦
Angular distribution is predicted in CM frame - perform Lorentz boosts on Z0 and
jet four-momentum vectors (measured in lab)
• Boosted system = Z0 + jet 4-vector (gives boost β-vector)
• Boost the Z0 and jet into CM frame and calculate cosθ*
• Can also derive CM kinematics explicitly
y = yB + y *
E = mT cosh y
*
P = mT sinh y
*
z
mT ≡
*
pT2 + M 2
tanh y* = β * cosθ *
Luis Lebolo
Z0/ɣ*
*
jet
SESAPS October 2011
6
Datasets
✦ Processed
LHC collision data taken between May-Nov 2010, corresponding
to Lint ~ 36 pb-1 (√S = 7 TeV)
• Only looking at the Z0 muon decay (experimentally clean signature)
✦ Using
a NLO generator (MadGraph) as pQCD prediction/simulation
• Background is W+jet, ttbar+jet and QCD multijet events
Luis Lebolo
SESAPS October 2011
7
Particle Identification
✦ Events
must pass low pT muon triggers
✦ Apply
a standard CMS particle
identification selection criteria*
• Muon pT > 20 GeV
• Jet pT > 20 GeV (Anti-kT, R = 0.5)
• 60 < Mμμ < 120 GeV
✦ Muon
relative isolation (R = 0.4), Irel < 15%
• “A muon is considered isolated if the
energy in a surrounding hollow cone is
less than 15% of its momentum”
• Removes QCD multijet background
I rel
(p
∑
=
track
T
+E
ECAL
T
µ
T
+E
HCAL
T
)
p
*using Inclusive W and Z Cross Section [2] muon selections with V+Jet Ratio [3] isolation modifications (see backup slides)
Luis Lebolo
SESAPS October 2011
8
Candidate Z0 and Jet Distributions
Jet Multiplicity (Z " µµ, 60 < MZ < 120, Jet pT > 20 GeV)
Events
Work in Progress
#
4
10
Z Jets
-1
L = 36.00 pb
103
QCD Mu
TT-Jets
Z-Jets
W-Jets
Data
102
10
Work in Progress
Jet Multiplicity
! 0 jet(s)
! 1 jet(s)
! 2 jet(s)
Z
! 3 jet(s)
! 4 jet(s)
! 5 jet(s)
Events
1
Mass (Z " µµ, 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
Z Jets
T
# L = 36.00 pb
-1
103
QCD Mu
TT-Jets
Z-Jets
W-Jets
Data
102
Generator-level
10
MZ > 50 GeV
selection
0
Luis Lebolo
Z Mass
1
SESAPS October 2011
20
40
60
80
100
120
140
160
180 200
M (GeV)
9
Corrections and Sources of Uncertainty
✦ Trigger
momentum thresholds in the lab impose a CM phase space bias
• Will have to limit CM phase space
✦ Source
of uncertainty
• Only worry about systematics that have an angular dependence
• Largest source is the jet energy scale
- Measured jet energy is different from the true particle energy due to the non-linearity
of calorimeters
- Therefore the jet energy is scaled by a correction factor (with an uncertainty)
- Relative uncertainty of < 4%
✦ Other
sources (not discussed)
• Muon resolution negligible compared to jet uncertainty
• Jet pT and η resolution is accounted for by unfolding
• Summarized in conclusion slide
Luis Lebolo
SESAPS October 2011
10
Phase Space Bias
Z
Entries
Mean
T
T
400
8
350
Work in Progress
Z
RMS
41.75
Underflow
0
Overflow 0.08693
10
0.6
6
4
300
400
150
200
250
300
350
400
*
P (GeV)
Z
0.5
300
0.4
250
jetCMPVsRapProf
Entries
895872
Mean
0.004302
Mean y
61.56
RMS
0.9201
RMS y
43.78
Underflow
0
Overflow
0
0.3
T
400
350
0.2
300
100
250
200
1.5
50
0.5
0
-5
0.1
150
Z
T
jetCMRap
3 150
-4
-3
-2
-3
-1
0
-2
1
2
-1
3
4
*
0
5
50
0
-5
100
150
200
250
300
350
400
*
P (GeV)
1.094
0
0
Z
0.3
jetCMPVsRapProf
Entries
492534
Mean
0.007731
Mean y
85.26
RMS
1.094
RMS y
46.2
Underflow
0
Overflow
0
T
400
0.2
350
300
2.5
100
250
0.1
200
1.5
50
150
100
1
-4
2
-3
-2
3
-1
0
4
1
2
y
jet
3
5
4
y*
0
5
*
y
0
-5
0
-5
-4
-4
-3
Fixed minimum pT ➞ loss of
acceptance that increases with y*
-2
-3
-1
0
-2
1
2
-1
3
4
*
0
5
50
0
-5
1
-4
2
-3
-2
3
-1
0
y
jet
4
1
2
3
5
4
y*
0
5
*
y
p* ≥ pT ,min cosh y*
> 20 GeV
*
45 ≥ 20 cosh y*
p = pT cosh y*
y* ≤ cosh −1 (2.25) ≈ 1.45
dσ̂
* −1
~
(1
−
cos
θ
)
*
d cosθ
Luis Lebolo
50
Jet CoM Momentum vs. Rapidity (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
492534
0.007731
RMS
Underflow
Overflow
3.5
0.5
-4
0.4
p* > 45 GeV
Entries
Mean
100
0
-5
0.5
0
0
200
1
1
12
43.1
0
0.1521
4
Jet CoM Rapidity (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
2
2.5
2
492534
84.62
RMS
Underflow
Overflow
6
*
0.9201
0
0
3.5
3
100
Jet CoM Momentum vs. Rapidity (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
895872
0.004302
RMS
Underflow
Overflow
150
50
Jet p* vs y*
jetCMRap
Entries
Mean
T
8
350
P (GeV)
4
T
*
4.5
Z
P (GeV)
200
Entries
Mean
T
2
0
0
Jet CoM Rapidity (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
Z
10
2
250
jetCMP
Jet CoM Momentum (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
Jet CoM Momentum vs. Rapidity (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
895872
61.17
P* (GeV)
Work in Progress
Z
P* (GeV)
jetCMP
Jet CoM Momentum (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
Jet CoM Momentum vs. Rapidity (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
cosθ * ≤ tanh(1.76) ≈ 0.90
SESAPS October 2011
11
Results and Conclusions
*
dN/dcos! (Normalized)
Work in Progress
5
"
#2/ndf = 7.80 / 9 = 0.87
Probability 0.554
-1
L = 36.00 pb
✦ First
measurement of Z+jet
angular distribution shown
with LHC 2010 collision data
QCD Mu
TT-Jets
Z-Jets
W-Jets
Data
4
• Good agreement with
3
pQCD (NLO)
2
0
✦ Some
|cosθ*|
1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
|cos! |
Data / MC
*
• Plan to use full 2011 data
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
Luis Lebolo
systematic
uncertainties are limited by
MC statistics
(~3 fb-1) for more precise
evaluation
SESAPS October 2011
12
Backup Slides
Luis Lebolo
SESAPS October 2011
13
References
[1] pCDF Collaboration. W Boson + Jet Angular Distribution in pp Collsions at sqrt(S) = 1.8 TeV. Phys. Rev. Lett.,
73:2296-2300, Oct 1994.
[2] CMS Collaboration. Measurement of the Inclusive W and Z Production Cross Sections in pp Collisions at sqrt(s) = 7
TeV. arXiv e-prints, 2011.
[3] CMS Collaboration. Rates of jets produced in association with w and z bosons. CMS Physics Analysis Summary, CMSPAS-EWK-10-012, 2011.
[4] CMS Collaboration. Determination of Jet Energy Calibration and Transverse Momentum Resolution in CMS. arXiv eprints, 2011.
[5] S. Alekhin et al. The PDF4LHC Working Group Interim Report. ArXiv e-prints, January 2011.
[6] G. Cowens. A survey of unfolding methods for particle physics. In Proc. Advanced Statistical Techniques in Particle
Physics, Durham, 2002.
[7] T. Adye. Unfolding algorithms and tests using RooUnfold. ArXiv e-prints, May 2011.
Luis Lebolo
SESAPS October 2011
14
Particle Identification Details
Luis Lebolo
SESAPS October 2011
15
Post-Selection Z0 and Jet Distributions
Z Jets
T
Events
Z
#
QCD Mu
TT-Jets
Z-Jets
W-Jets
Data
-1
L = 36.00 pb
102
Z Rapidity (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
Z
Events
Z Transverse Momentum (Z " µ µ , 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
Z Jets
T
#
102
-1
L = 36.00 pb
QCD Mu
TT-Jets
Z-Jets
W-Jets
Data
10
10
Z pT
Z Rapidity
1
1
20
40
60
80
100
120
140
160
Z Jets
Work
in
Events
Jet Transverse Momentum (Z " µµ, 60 < MZ < 120, ! 1 Jet(s) w/ pT > 20 GeV)
103
#
180 200
PT (GeV)
-1
L = 36.00 pb
QCD Mu
TT-Jets
Z-Jets
W-Jets
Data
-3
-2
Progress
-1
0
1
2
Jet Rapidity (Z " µµ, 60 < M < 120, ! 1 Jet(s) w/ p > 20 GeV)
Events
0
Z
Z Jets
T
#
2
10
3
y
-1
L = 36.00 pb
QCD Mu
TT-Jets
Z-Jets
W-Jets
Data
102
10
10
1
0
Luis Lebolo
Jet pT
50
100
Jet Rapidity
1
150
200
250
300
350
400
PT (GeV)
-3
SESAPS October 2011
-2
-1
0
1
2
3
y
16
Effect of JES Uncertainty
Jet energy affects cosθ* measurement through the Lorentz boost (lab-to-CM)
pz γ ( pz − β E) cosθ − β
cosθ =
=
=
p γ (E − β pz ) 1 − β cosθ
*
pzZ + pzj
pzZ + pTj cot θ
β≈
=
EZ + E j EZ + pTj 1 + cot 2 θ
JES Uncertainty (%)
Work in Progress
!2 / ndf
p0
p1
p2
1.256 / 36
1.057
1.984
2.478 ± 0.03535
0.03192
77.14
76.81 ± 0.991
1.041
0 ± 1.562
1.522
0.00 < |"| < 1.30
1.30 < |"| < 3.00
14
12
Use uncertainty to smear
jet pT then recalculate
cosθ*
10
8
6
4
2
0
Luis Lebolo
10
102
103
Jet pT (GeV)
SESAPS October 2011
17
JES Uncertainty Results
Z CoM Work
Cosine -in
After
(Z # µµ, 60 < M < 120, " 1 Jet(s) w/ p > 20 GeV)
Progress
% of Events
Z
22
T
Before
Gaussian
Down
Up
20
18
16
14
12
10
8
Smeared / Orig
6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
|cos!*|
1.06
1.04
1.02
1
0.98
0.96
0.94
Luis Lebolo
SESAPS October 2011
18
Correcting for Pileup
✦ Following
recommendations of JEC
group for 42X
• Followed JEC Workbook
✦
In short,
• PU subtraction via L1FastJet (jet area
and energy density calculation “ρ”)
• Also using PF charged hadron
subtraction
- i.e. charged hadrons from
secondary vertices are removed
• See JME-10-011 for details [4]
Luis Lebolo
SESAPS October 2011
19
Theoretical (PDF) Uncertainties
pdfMeanRatio
Mean Ratio of Varied PDF Eigenvectors
i
Ratio (e / e0)
Work in Progress
Entries
530
Mean
0.45
Mean y
1.001
RMS
0.2872
RMS y 0.01556
1.04
PDFs w.r.t nominal set
✦ Analysis
was done for a photon
+jet cross section
0.98
• However, the Z+jet shape is
Black bar = RMS/spread
Red bar = error in mean
0.96
0
is to vary sets of PDFs [5]
• Then take the ratios of the new
1.02
1
Hessian Uncertainty (Ratio)
✦ Idea
0.1
0.2
0.3
0.4
0.5
0.6
0.7
analogous
0.8
0.9
1
cos!*
1.2
1.15
✦ Correct
way to determine errors is
through a Hessian approach
• Hessian inflated by lack of MC
1.1
statistics
1.05
1
• Conservative relative
0.95
uncertainty of 5%
0.9
0.85
0.8
0
Luis Lebolo
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
cos!*
SESAPS October 2011
20
Jet Resolution - Reco vs. Gen
Z
T
Reco cos!*
1
16
0.9
14
0.8
12
0.7
0.6
10
0.5
8
0.4
Reco CoM Cosine (Z # µ µ , 60 < M < 120, " 1 Jet(s) w/ p > 20 GeV)
Z
% of Events
Reco vs Gen CoM Cosine (Z # µ µ , 60 < M < 120, " 1 Jet(s) w/ p > 20 GeV)
6
14
10
4
0.2
8
2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0
Gen cos!*
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Reco cos!*
Work in Progress
Gen CoM Cosine (Z # µ µ , 60 < M < 120, " 1 Jet(s) w/ p > 20 GeV)
Reco vs Gen CoM Cosine (Z # µµ, 60 < MZ < 120, " 1 Jet(s) w/ pT > 20 GeV)
T
Reco cos!*
Z
% of Events
16
12
0.3
0
0
T
16
14
1
0.9
0.8
0.7
Distributions are
almost identical
0.6
12
0.5
0.4
10
0.3
0.2
8
0.1
0
Luis Lebolo
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Gen cos!*
0
0
0.1
SESAPS October 2011
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Gen cos!*
21
Jet Resolution - Reco / Gen
dN/dcos!* (Normalized)
Work in Progress
2.4
2.2
Gen
Reco
2
1.8
1.6
1.4
1.2
1
Reco / Gen
0
Luis Lebolo
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
cos!*
1.04
1.02
1
0.98
0.96
SESAPS October 2011
22
Jet Resolution Unfolding (Bayesian) [6]
Z
Work
in Progress
CMS
Preliminary
% of Events
CoM Cosine (Z $ µµ, 60 < M < 120, # 1 Jet(s) w/ p > 20 GeV)
T
Data
Bayes Unfolding
20
15
10
Using RooUnfold
package [7]
Unfolded / Data
5
0
1.20
0.1
0.2
-1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
cos!
1.1
1
0.9
0.8
0
Luis Lebolo
"
Ldt=36.1pb
0.1
0.2
0.3
0.4
0.5
0.6
SESAPS October 2011
0.7
0.8
0.9
1
cos!*
23
Boosted System pT
Boost Transverse Momentum (Z " µµ, 60 < MZ < 120, ! 1 Jet(s) w/ pT > 15 GeV)
Boost Transverse Momentum (Z " µµ, 60 < M < 120, ! 1 Jet(s) w/ p > 15 GeV)
% of Events
Work in Progress
Z
20
T
Entries
1401151
Mean
20.01
16.67
RMS
0
Underflow
0.1448
Overflow
18
20
16
14
18
12
10
16
sysPt
Entries
1401151
Mean
21.17
20.27
RMS
0
Underflow
Overflow 0.1448
sysPt
8
6
14
4
12
0
0
2
10
sysPt
Entries
1401151
Mean
21.17
20.27
RMS
0
Underflow
Overflow 0.1448
Boost Transverse Momentum (Z " µµ, 60 < MZ < 120, ! 1 Jet(s) w/ pT > 15 GeV)
20
18
16
14
12
10
8
0
0
80
100
120
140
160
180
200
pB (GeV)
T
sysPt
Entries
1401151
Mean
21.17
20.27
RMS
0
Underflow
Overflow 0.1448
Boost Transverse Momentum (Z " µµ, 60 < MZ < 120, ! 1 Jet(s) w/ pT > 15 GeV)
20
6
14
12
4
10
8
2
6
4
0
0
20
20
40
60
80
100
40
120
140
160
180
200
pB (GeV)
2
60
0
0
T
Luis Lebolo
Boosted
System pT
60
16
4
2
40
18
8
6
20
SESAPS October 2011
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20
40
60
80
100
120
100
160
180
200
pBT (GeV) p (GeV)
140
B
T
24
System vs CM Rapidity
Boost Rapidity (Z " µµ, 60 < M < 120, ! 1 Jet(s) w/ p > 15 GeV)
Boost vs. Jet CoM Rapidity (Z " µµ, 60 < M < 120, ! 1 Jet(s) w/ p > 15 GeV)
Z
Work in Progress
Z
T
4
B
2.5
y
T
3.5
0.14
3
2
2.5
0.12
2
1.5
1.5
1
1
0.1
0.5
0.5
0
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
y
0.08
B
0
Jet CoM Rapidity (Z " µµ, 60 < M < 120, ! 1 Jet(s) w/ pT > 15 GeV)
B
-0.5
y
4
Boost vs. Jet CoM Rapidity (Z " µµ, 60 < MZ < 120, ! 1 Jet(s) w/ pT > 15 GeV)
Z
1.5
-1
1.5
1
0.5
0
-5
0.5
-1.5
0
0.02
-0.5
-2
-1
-1.5
-2.5
-5
-4
-4
-3
-2
-3
-1
0
-2
1
2
-1
3
4
y
Luis Lebolo
0.04
1
2.5
2
0.06
2
3.5
3
2.5
*
0
5
-2
-2.5
-5
1
jet
SESAPS October 2011
2
-4
-3
3
-2
-1
4
0
1
2
0
5
3
*
y
Jet
4
y
*
5
Jet
25
Boosted System Rapidity
d 3σ
1
fi (x1 ) f j (x2 ) dσ̂ ij
∝ ∑
ˆ
dx1dx2 dt S i, j x1
x2 d cosθ *
Events
2 p * ± yB
xi, j =
e
S
250
Work in Progress
!
QCD Mu
TT-Jets
Z-Jets
W-Jets
Data
-1
L = 36.00 pb
200
150
100
yB
50
Data / MC
-2.5
Luis Lebolo
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
yB
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
SESAPS October 2011
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