A measurement of the Ratio of Tree over Two Jet Cross Sections with CMS at 7TeV P.Kokkas, I.Papadopoulos, C.Fountas, I.Evangelou, N.Manthos University

A measurement of the Ratio of Tree over Two Jet Cross Sections with CMS at 7TeV

P.Kokkas, I.Papadopoulos, C.Fountas, I.Evangelou, N.ManthosUniversity of Ioannina, Greece

Senior Editor for PAS : James RohlfBoston University, USA

P.Kokkas, Univ. of Ioannina 2

Outline

• Motivation• Monte Carlo studies

• Studies on rapidity• Leading jets pT response and resolution

• HT resolution

• MC prediction for ratio R32

• Data analysis• Data and MC samples• Online Selection and Trigger studies• Offline Selection• Extraction of ratio R32 from data• Studies on Systematics

• Summary


Motivation• Motivation: Measure the ratio R32

and compare with pQCD predictions with goals:• Extend the phase space of the measurement in a regime

that goes above the Tevatron.• Measure S: Comparisons of the measured ratio at hadron

level with the predictions of pQCD (parton level), after accounting for hadronisation corrections uncertainty, will measure the QCD coupling constant S at a scale never measured before.

• We measure the ratio because we expect that certain systematic uncertainties will cancel:• The dominant sources of systematic uncertainties in the

measurement of jet inclusive cross sections are the Luminosity and the Jet Energy Scale (JES).

• We expect the ratio to be less sensitive than absolute cross section measurements to these uncertainties.

• The pQCD predictions for the ratio may be less sensitive to uncertainties due to the renormalization and factorization scales which hamper the absolute cross section predictions particularly at low Jet-pT scales.

D0 PRL 86, p1955 (2001)

jetTpTH vs

2n X; jetsn ppσ

3n X; jetsn ppσ

2σ3σ

32R

4

Monte Carlo models and studies

• MC samples• PYTHIA : /QCDDiJet_Ptxxtoxx/Spring10-START3X_V26_S09-v1/GEN-SIM-RECO• Madgraph : /QCD_Ptxxtoxx-madgraph/Spring10-START3X_V26_S09-v2/GEN-SIM-RECO

PYTHIA6 Madgraph

LO processes LO matrix element 2→2 hard process

Tree Level helicity amplitudes +Parton shower (PS) modelHigher order

processesParton shower (PS) model

Hadronization Lund string model Lund string model

Parton Distribution(PDF) Model

CTEQ6L1 CTEQ6L1

• Jets were reconstructed using the antikt (D=0.5) clustering algorithm.• CaloJets : using antkt5 on calorimeter energy depositions• GenJets : using antikt5 on MC stable particles.

• Calo jets were corrected for energy loss and effects due to non-linear response of calorimeter• Relative (corrects for η dependence)• Absolute (corrects for the pT dependence)

P.Kokkas, Univ. of Ioannina

5

Plot the difference

• For various bins of GenJet pT

• Distributions flat for |y|≤2.5

(Barrel + EndCap regions)• Reasonable cut: |y|≤2.5

Studies on rapidity

GenCaloGen y vsyy

60-100 GeV

100-150 GeV

150-200 GeV


Contour Plot Profile Y Projection

PYTHIA

PYTHIA

PYTHIA

z

z

pE

pEln

2

1yRapidity


Leading Jets pT Response

Fitting above distribution to aGaussian, we extract pT

Response and Resolution.

The pT Response of leading jets is uniform for jet pT even below 50 GeV.

Calo jet corrections work very well.

T

TTT p

ppp

GenJet

CaloJet GenJet Resolution

7

pT Resolution

For jet pT about 50 GeV the resolutionis ≈15% dropping to ≈10% at 200 GeV.

For our analysis we apply a cuton Jet pT≥50 GeV.

With this cut we can compare our results with Tevatron for a region of HT between 300-600 GeV


Resolution on HT

By accepting all jets with• rapidity |y|≤2.5• and pT≥50 GeV

We construct in the case of • number of Jets ≥ 2• number of jets ≥ 3

HT resolution studies are important to define the binning for the ratio R32.

jetTpTH

T

TT

T HGenJet

HCaloJet HGenJet Resolution H

nJets≥2 nJets≥3

HT resolution: ≈10% at 200 GeV dropping to ≈5% at 1000 GeV

PYTHIA

MC predictions for R32

9

• The ratio R32 starts at 150 GeV, rises fast ad reach to a plato at ≈800 to 1000 GeV.

• Madgraph is systematically lower than PYTHIA by as much as 30% in the lower HT bins. This difference decreases to ≈10% around 400 GeV and becomes smaller than 5% at higher HT bins.

• The cross section predicted by Madgraph is consistently ≈30% lower than PYTHIA’s.

PYTHIA Madgraph

10

Data Analysis

• Data Samples• /MinimumBias/Commissioning10-SD_JetMETTau-v9/RECO• /JetMETTau/Run2010A-May27thRereso_v1/RECO• JSON file

• CMS official JSON file : Cert_132440-136297_7TeV_StreamExpress_Collisions10_JSON.txt• But for Runs > 134630 (Trigger scheme 6)• Total Integ.Lumi = 10.8 nb-1 (Evaluated from crab)

• Trigger Samples• /MinimumBias/Commissioning10-SD_JetMETTauMonitoring-v9/RECO• /JetMETTauMonitoring/Run2010A-May27thRereso_v1/RECO• /MinimumBias/Commissioning10-May27thReReco_v1/RECO (MinBias Studies)

• MC Samples• PYTHIA: QCDDiJet_Ptxxtoxx/Spring10-START3X_V26_S09-v1/GEN-SIM-RECO• Madgraph: QCD_Ptxxtoxx-madgraph/Spring10-START3X_V26_S09-v1/GEN-SIM-RECO

• On line Selection:• Require BPTX Technical bit 0, to select events with consistent timing

with LHC bunch crossing• None of the BSC beam halo triggers (Technical bits 36,37,38,39)• Select events with HLT Jet15U


11

Online Selection - Trigger

HLT Jet Trigger L1 Prerequisite Prescaled

HLT L1Jet6U L1 SingleJet6U yes

HLT Jet15U L1 SingleJet6U no



Main HLT Jet Triggers

• Trigger efficiencies vs HLT MinBiasBSC.• HLT L1Jet6U turn on point well in advance, can be used

for calculating efficiencies .

HLT Jet15U Trigger efficiency with HLT L1Jet6U and HLT MinBiasBSC – complete agreement,




• Safe to use HLT Jet15U for our analysis • Turn on points for simulation is systematically

higher.

12

HLT Jet Trigger Turn on points (GeV)Leading Jet

HLT Jet15U 37HLT Jet30U 62HLT Jet50U 87

Data PYTHIA



HLT Jet Trigger

HT nJets≥2 (GeV)

HT nJets≥3 (GeV)

HLT Jet15U 100 150

HLT Jet30U 120 150

HLT Jet50U 230 230

• HLT Jet15U : R32 can be measured for HT≥150GeV .• HLT Jet30U : Practically the same as above• HLT Jet50U : R32 can be measured for HT≥230GeV.• The “kink” appearing to HLT Jet50U at ≈150GeV (left

plots), is due to events with three jets of almost equal pT which do not pass the trigger HLT Jet50U.

nJets ≥2 Data

nJets ≥2 PYTHIA

nJets ≥3 Data

nJets ≥2 PYTHIA

14

Off Line Selection and Data Stability• Off line Selection:

• Removal of “monster” events• Primary Vertex: |PVz| < 15 cm, nDof > 4• Jet selection: pT ≥ 50 GeV and |y|≤2.5• “Loose” Jet ID :

• EMF > 0.01 OR |η|>2.6, • n90Hits > 1 , • FHPD < 0.98

Selection Events

Trigger, Data quality &PV 1508800

After pT≥50GeV, |y|≤2.5 & ‘’Loose” JetID

At least 2 jets 24823

At least 3 jets 1418

• Data stability : Flat distributions of number of events normalized with run lumi vs run number.• Run Numbers 135537, 135573, 136080 ,136098 and 136119 (marked with the arrows) represent to

a small amount of Lumi ≈0.14 nb-1 .

nJets ≥2 nJets ≥3



Data Stability

15

• Data stability : Flat distribution of ratio Number of events with (njets≥3 )/(njets ≥2) vs run number.• Run Numbers 135537, 135573, 136080, 136098 and 136119 (marked with the arrows) represent to a

small amount of Lumi ≈0.14 nb-1 .• We also tried to normalize the last runs with a MinBias trigger (eg. HLT_L1_BscMinBiasOR_BptxPlusOR

Minus) but was not possible from point of statistics since these runs are very small.


All jets: Data over PYTHIA

Good agreement with simulation.

Small differences in shape for fHPD and N90Hits, not important for our analysis.

PYTHIA MC normalized to the total number of inclusive DiJet events.

The effect of the “loose” JetID selection is ≈0.3%.

17

Leading Jets: Data over PYTHIA

PAS

PAS

PAS

PAS

PAS

PAS

PYTHIA MC normalized to the total number of inclusive DiJet events.

%3.197935

1532CaloR

%7.168485

1416CaloR

GeV 800 H 150

PYTHIA32

Data32

T

%2.624819

1532CaloR

%7.524821

1416CaloR

GeV 800 H 100

PYTHIA32

Data32

T

PYTHIA describes well the shape of the data distributions


All jets: Data over Madgraph

Good agreement with simulation.

Small differences in shape for fHPD and N90Hits, not important for our analysis.

Madgraph MC normalized to the total number of inclusive DiJet events.

19

Leading Jets: Data over Madgraph

PAS

PAS

PAS

PAS

PAS

PAS

Madgraph MC normalized to the total number of inclusive DiJet events.

Madgraph describes well the shape of the data distributions

%7.424819

1172CaloR

%7.524821

1416CaloR

GeV 800 H 100

Madgraph32

Data32

T

%2.148282

1172CaloR

%7.168485

1416CaloR

GeV 800 H 150

Madgraph32

Data32

T

20

Number of Jets (Not in the PAS but requested)

PYTHIA and Madgraph MC normalized to the total number of inclusive DiJet events.

%7.424819

1172CaloR

%2.624819

1532CaloR

%7.524821

1416CaloR

GeV 800 H 100

Madgraph32

PYTHIA32

Data32

T


%2.148282

1172CaloR

%3.197935

1532CaloR

%7.168485

1416CaloR

GeV 800 H 150

Madgraph32

PYTHIA32

Data32

T


Method of extracting R32

T

CaloSmear

T ΔH

jetsN

ε

C

dH

dσ

L

Inclusive jetcross section

sizebin H the: ΔH

bin ain counted events ofnumber : jetsN

ibin in eventsGen ofNumber

ibin at eventsGen from events Calo tedreconstruc ofNumber ε

cuts survived eventsfor efficiency the: ε

luminocity integrated the:

ibin in events Calo tedreconstruc ofNumber

ibin at eventsGen from events Calo tedreconstruc ofNumber C

correction smearing : C

TT

Calo

Smear

Smear

L

Smear2

2

3

Smear3

T

CaloT

Calo

T

Calo

2

Smear2

T

Calo

3

Smear3

T

2

T

3

C

ε

ε

C

ΔH

2Jetsn N

ΔH

3Jetsn N

ΔH

2Jetsn N

ε

C

ΔH

3Jetsn N

ε

C

dH

dσdH

dσ

32R

L

LRatio R32

A Bmeasurement

• The factor AxB has been used to correct the Calo Level ratio to stable particle level (Hadron Level).


Method of extracting R32

3 jetsn N

3 jetsn N

3 jetsn N

3 jetsn NA

Calo

CaloPass

CaloPass

Gen

2 jetsn N

2 jetsn N

2 jetsn N

2 jetsn NB

Gen

CaloPass

CaloPass

Calo

H of ibin in eventsGen ofNumber : 2,3 jetsn N TGen

TCalo H of ibin in events Calo tedreconstruc ofNumber : 2,3 jetsn N

bin any appear to and cuts survived events

Calo tedreconstruc allH of ibin of eventsGen For : 2,3 jetsn N TCaloPass

1/ε3 (1/efficiency)nJets≥3

CSmear3

Smearing correctionnJets≥3

ε2 (efficiency)nJets≥2

1/CSmear2

Smearing correctionnJets≥2

With

• This MC driven method of extracting R32 from the data does not depend upon the absolute predictions of the MC programs .

• It does depend on how well the MC distributions describe the shape of the data distributions.

• As we have seen in the previous slides both PYTHIA and Madgraph describe well the shapes of the data distributions, hence we are entitle to use them to derive the AXB correction factors to the data.


Closure test

• PYTHIA MC events were considered as “data” (top left).• Madgraph MC events were considered as “MC” and used to evaluate factor AxB (bottom left). • Then with AxB from Madgraph, PYTHIA CaloJets were corrected and compared with GenJets from

PYTHIA (top right).• The corrected PYTHIA CaloJet ratio (with AxB from Madgraph) is within ±5% from the GenJet ratio

except the first bin which is off by ≈10%.

AxB from Madgraph

PYTHIA PYTHIA Corrected

24

Ratio R32 at Calo levelData over PYTHIA Data over Madgraph

High R32 bins merged to match statistics.

AxB factors evaluated with new binning.

AxB from PYTHIACaloJets



Ratio R32 at Hadron Level

• Measured ratio rises with HT in the range 150≤HT≤800 GeV in agreement with predictions of PYTHIA and Madgraph.

PAS


Studies on the Systematic uncertainties.

• Studies on Systematics

• Jet Energy Scale (JES) systematics• Absolute scale : flat 10% JES uncertainty• Relative scale : 2% for every unit of pseudorapidity

• Systematic uncertainty due to difference in shape between data and MC• Reweight the pT and HT spectra so that the shape of distributions changes and

repeat the analysis to compute systematic.

• Systematic uncertainty due to detector response• Smearing Calo Jets by 10% and 15% while leaving Hadron jets unchanged.


Jet Energy Scale (JES) systematics : Absolute Scale

The pT≥50 GeV/c cut modulates the efficiency at low HT

Above 400 GeV we observe a rather flat distribution shifted by 50% to 80%

Absolute scale : flat 10% JES uncertainty


Jet Energy Scale (JES) systematics : Absolute Scale

Smearing effects dominate

• We observe a strong uncertainty cancellation (uncertainty less than 5%).• For the first two bins bellow 200 GeV systematics are of the order of 10%.

Absolute scale : flat 10% JES uncertainty


Jet Energy Scale (JES) systematics : Relative Scale

Relative scale : 2% for every unit of pseudorapidity

• This results to a systematic uncertainty which is significantly small than the previous.

)Jet(0.02 1 Jet Jet TT pp

Systematic uncertainty due to difference in shape between data and MC

onsDistributi Normal

No reweightnJets≥2

Pythia with harder pT spectrumnJets≥2

Pythia withsofter pT spectrumnJets≥2

No reweightnJets≥3

Pythia with harder pT spectrumnJets≥3

Pythia with softer pT spectrumnJets≥3

TGenJet1p0.71weightweight TGenJet1p0.11weightweight

• To see how sensitive we are to smearing corrections we assume that the detector response is correct in the MC and we change the underline physics by reweighting and we observe the change in the measured ratio due to different smearing effects.

• Reweight the pT and HT spectra so that the shape of distributions changes and repeat the analysis to compute systematic.

30


Systematic uncertainty due to difference in shape between data and MC

• This uncertainty, while probably over-estimated, is of the same order of the JES uncertainty.


Systematics due to detector response

Smearing Calo Jets by 10% or 15% while leaving Hadron jets unchanged.

TT

TT

pJet Second pJet Leading

pJet Second - pJet Leading

10% Smearing

15% Smearing

With 10% smearing MC shapedescribes data better.

We plot :

%2.624819

1532CaloR

%7.524821

1416CaloR

GeV 800 H 100

PYTHIA32

Data32

T


Systematics due to detector response : smearing by 10%

• Results consistent with previous studies. • Uncertainty ≈5% , except the first two bins bellow 200 GeV where uncertainty is of the order of 10%.

Smearing Calo Jets by 10% while leaving Hadron jets unchanged.


Systematics due to detector response : smearing by 15%

Smearing Calo Jets by 15% while leaving Hadron jets unchanged.

• Results consistent with previous studies. • Uncertainty ≈5% , except the first two bins bellow 200 GeV where uncertainty is of the order of 10%.


Summary

• Summary:• The ratio of the inclusive three-jet over two-jet cross sections as a function of the

total jet transverse energy, HT, has been measured with the CMS detector at the LHC for proton-proton center-of-mass energy 7 TeV using an integrated luminosity of 10.8 nb-1.

• Measurements have been performed for jets with pT ≥50 GeV in the rapidity range |y| ≤2.5.

• The measured ratio rises with HT in the range 150≤HT≤800 GeV.• The measured ratio is consistent with the predictions of PYTHIA and MadGraph.


Spare


Gen HT for PYTHIA and Madgraph

PYTHIA Madgraph

The cross section predicted by Madgraph is consistently ≈30% lower than PYTHIA’s


Predicted R32 with various pT – y cuts

Both Figures demonstrate theinfluence of the threshold cutson pT and y to the measurement.

39

Main HLT Jet Trigger efficiencies

HLT Jet Trigger

L1 Prerequisite Prescaled Turn on points (GeV)Raw pT

Turn on points (GeV)corrected pT

HLT L1Jet6U L1 SingleJet6U yes 13 28

HLT Jet15U L1 SingleJet6U no 16 37

HLT Jet30U L1 SingleJet6U no 32 60

HLT Jet50U L1 SingleJet6U no ≈53 >80

Main HLT Jet Triggers

Raw pT Corrected pT


Ratio R32 at Calo level

CaloJets


AxB from PYTHIA and Madgraph

• Correction factors AxB from PYTHIA and Madgraph agrees better than 5%. • Except the two first bins where disagreement is ≈10%.


Residual Corrections

According to JEC group a residualcorrection for η>1.5 is needed (on the top of the Default L2L3).

Selection Events Eventswith Residual Corrections

At least 2 jets 24823 23909


• The effect is ≈ 3%. • Small effect to the measurement.


Analysis without JetID selection

Selection EventsWith ‘’Loose”

JetID

EventsWithout

‘’Loose” JetID



The effect of the “loose” JetID selection is ≈ 0.3%.


Full resolution SystematicsMoving Calo pT cut by 15% (the pT resolution at 50 GeV) while leaving Hadron cut unchanged.

• Uncertainty probably over-estimated for the lower bins (HT < 400GeV)

Documents

A measurement of the Ratio of Tree over Two Jet Cross Sections with CMS at 7TeV P.Kokkas, I.Papadopoulos, C.Fountas, I.Evangelou, N.Manthos University