Dijet Transverse Thrust cross sections at DØ

Veronica Sorin

University of Buenos Aires

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Outline

• Introduction:– Overview– The KT algorithm– Definition of the observable

• Dijet Transverse Thrust cross section• Systematic uncertainties• Comparison with theory• Conclusions

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Theoretical IntroductionQuantum Chromodynamics: describe the interaction between quarks and gluons, which carry color charge, conventionally called: blue, red and green.

Main QCD characteristics:

Confinement: quarks and gluons cannot be seen as isolated particles, partons (q and g) are bound together into hadrons.

Fundamental Vertices

Asymptotic freedom: as the energy of the interaction increases, the strength of the coupling get smaller, allowing the aplication of perturbative techniques (pQCD).

Jet Physics

s ss

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Jet Physics

q

calo

rim

eter

jet

Tim

e

q g

K

part

on je

t par

ticle

jet

hadrons

CH

FH

EM

p

p

q

q

At the final state of an hadronic collision, QCD predicts the appareance of highly collimated sprays of particles, which are called Jets .

At the DØ experiment using the Fermilab Laboratory Tevatron collider, we study pp collisions at a c.m. energy of 1.8 TeV. The bunch crossing occurs every 3.5 µs. By identifying these jets, experimental measurements can be compared with pQCD predictions.

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Panoramic view of the Fermilab Laboratory

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Event ShapesEvent shapes have been extensively studied at e+e- and ep experiments to:• study spatial distribution of hadronic final states• test perturbative QCD predictions• extract a precise value of s

• recently to test QCD developments like resummation calculations and non-perturbative corrections

Resummations: needed at small values of the shape variable where fixed-order perturbative calculations are expected to fail.

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Thrust

: direction which maximizes T n̂

The sum is done over all partons/particles/ detector elements/jets in the event

T : Pencil-likeness of the event

2 partons in final state

N partons in final state

T=[1/2,1](N...NLO)

T=1

Jet production rate: s2 is LO

s3 is NLO

Thrust (T ≠ 1): s3 is LO

s4 is NLO

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T in hadron collidersBusy environment: underlying event, pile-up, multiple interactions and noise

particles jets

We have derived a correction to eliminateon average the energy contributions from sources other than the hard interaction itself.

Thrust is not invariant under z boosts Transverse Thrust

The pp c.m system is not the parton-parton c.m.–

By replacing momenta with transverse momenta

Lorentz invariant quantity 3D 2DTT

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The DØ Calorimeters

• Liquid argon active medium and uranium absorber

• Hermetic with full coverage

< 4.2 int

total)

• Transverse segmentation (towers)

x x

E / E = 15% /for electrons

E / E = 45% /for pions

2tanln

x

Z

y

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Jet Algorithms•Parton jet: q and g (before hadronization)

• Particle jet: final state particles (after hadronization)

• Calorimeter jet: measured object (after calorimeter shower)

Iterative

Fixed cone of radius R

Overlapping cones: arbitrary criteria to resolve ambiguities

Sensitivity to soft radiation

Requires ad-hoc parameter for the theory

Recombination

Distance parameter D

Infrared and collinear safe

Same algorithm in theory and experiment

Fixed Cone (RunI) KT (Ellis-Soper)

q

calo

rim

eter

jet

Tim

e

q g

K

part

on je

tpa

rtic

le je

t

hadrons

CH

FH

EM

p

p

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RunI DØ Analyses using the KT algorithm

• “Subjet Multiplicity of Gluon and Quark Jets”

Phys. Rev. D 65, 052008 (2002)

• “The Inclusive Jet Cross Section” Phys. Lett. B 525, 211 (2002)

• “Dijet Transverse Thrust Cross Sections”paper in preparation

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KT Algorithm at DØ (RunI)

Cone jetKT jet

2

22,

2, ),min(

D

RPPd ij

jTiTij

(Ellis-Soper PRD 48 3160)

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KT Algorithm at DØ (RunI)

For each particle or pair of particles :

jiij

jiij

EEE

ppp

• Produce list of jets

Is lessthan ?

Move i to list of jets

Anyleft?

No

No

Yes

Yes

Merge i+jijd

iid

2

22,

2, ),min(

D

RPPd ij

jTiTij

2,iTii Pd

Beam

Beam

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Jet Momentum Scale Correction

jet

measjetptcl

jet R

OPP

• Offset (O): Ur noise, pileup, multiple interactions,

underlying event (ue)

• Response (Rjet): Pmeas / Ptrue

(using transverse momentum balance in -jet events)

Calorimeter jet

Particle jet

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Offset Correction

MC Jets MC+Noise

O = UE + N Ur noise, pileup, multiple interactions

Underlying Event

The offset contribution is obtained as the momentum difference between jets.

MC events + detector simulation + noise data

Noise data can be:

• Zero bias: random crossing (N)

• Minimum bias: crossing with a pp interaction (UE)

_

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O = UE + NOffset CorrectionLuminosity dependent (L in cm-2 s-1)

.

..

MC + Overlayed to crossing withinelastic interaction

MC + Overlayed to random crossing

UE

(GeV

)

N(G

eV)

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Rjet = a + b ln(Pjet) + c ln2(Pjet)

Rjet Correction Monte Carlo Closure

D=1 (KT jets)

Pptcl (GeV)

Pm

eas /

Pp

tcl

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Dijet TransverseThrust

• Sum done over jets• Jets have been reconstructed with the KT algorithm with D=1

Jet Momentum scale correction does not eliminate low energy jets ( high probability to originate 100% from background) distort the shape of the physical distributions

Observable selected to reduce detector effects and maximize the signal in a hadron collider.

Only the two leading jets will be used to calculate Thrust

The spatial configuration of the two leading jets inherits the information of the other jets in the event

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Effects of noise and luminosity on TT

The addition of randomly oriented noise jets renders the event more isotropic

Use only the 2 leading jets

Selection of the observable

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Selection of the observableThe event energy scale

Look for a variable correlated with Q2 and with low sensitivity to noise

HT at parton level: measure of Q2

HT3 (scalar sum of the transverse momentum of the three leading jets)

HT3 vs HTNoise jets ET3 spectrum

Data

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Brief Recapitulation

• Measurement of cross section as a function of HT3

• Using jets for which we have derived a correction that eliminates on average the contributions not related with the hard interaction.

• Test quality of QCD predictions• Study significance of resummation calculations

TT2

12/2 2 TT

O(s3) calculations can not cover the whole physical range:

for , the LO calculation is O(s4)2/32/2 2 TT

120o

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• Observed Dijet Transverse Thrust Cross Sections• Systematic Uncertainties:

– Momentum Scale Correction– Energy and Angular resolutions– Unfolding

• Final results and Comparison with Theory• Conclusions

Coming up now….

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Dijet Transverse Thrust cross section

188,8.1, pbLTeVs1996)-(1994 IbRun

KT algorithm (parameter D = 1)

Event Selection:

• Vertex cut (| z | < 50 cm, e ~ 90 %)• Cut on missing ET (ET/pT

lj < 0.7, e ~ 99.8 %)

• Jet quality cuts (e ~ 99.5 % )( 0.05 < EMF < 0.95, CHF < 0.4 )

• Kinematic cuts: |1,2| < 1

Jet Selection:

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It is presented in four HT3 ranges

HT3 : scalar sum of the transverse momentum of the three leading jets.

( use 3rd jet only when | 3 | < 3)

Four single jet triggers are used for different HT3 ranges where they are fully efficient.

HT3 distributions

Jet Trigger HT3 range (GeV)

Jet30 160-260

Jet50 260-360

Jet85 360-430

JetMax 430-700

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Observed cross sectionsT2T

Distributions still distorted due to finite detector resolutions

)1log( 2TT

TT

Td

dT

22 )1(

eLT

N

Td

dTT

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LO O(s4)Resummations ?

Theoretical Predictions:Jetrad : QCD event generator O(s

3).NLOJET++ : NLO 3 jets generator O(s

4).

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Momentum scale correction

Uncertainty on the Jet Momentum calibration propagates to the thrust via two mechanisms: errors between 10-25%

T value changes

Migration of eventsbetween HT3 bins

Dominant Effect

Low energy jets : 2-5% uncertainty to take into account reconstruction efficiencies and contamination.

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Effect smaller than 5%

Affects T via two mechanisms: T value

changes

Event migration between HT3 ranges

Deconvolution

Average Momentum (P1T + P2

T)/2 (GeV)

0 100 200 300

σ(P T

)/P T

0.02

0.06

1

Measured using PT balance in data, in the limit of no soft radiation.

Fractional ResolutionMeasured in two jet events, assuming:

21TT pp

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Energy Resolutions

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Resolutions

Important effect in the limit T 1MC smeared

2),(

E

C

E

BAE

Calculated from positiondifference between calorimeterand particle MC jets:

MC

10-6 10-4 10-2

1-T10-6

10-4

10-2

1-T

sme

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Unfolding

Smear MC at particle level by energy and angular resolutions

MC

Conservative way:let the contents on each bin vary freely

Correlation Matrix1-T

Uncertainty:

Correction factor extractedfrom MC as : generated / smeared

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Correction factors

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Only statistical errors are shown.

DØ preliminary DØ preliminary

DØ preliminary DØ preliminary

CTEQ4HJ, µF = µR = PTmax/2

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Only statistical errors are shown.

DØ preliminary

DØ preliminary DØ preliminary

DØ preliminary

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Sources of systematic uncertainties

(2nd Bin)

99.5

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Sources of systematic uncertainties

)( ijC

ijjjijii TDCTD )()( 12

Using the full covariance matrix

(2nd Bin)

9 9.5

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Strong point to point correlations in the uncertainty

DØ preliminary

DØ preliminary

DØ preliminary

2/2 3toupJetrad TT

Thrust Range (1-T) 2 ndof Prob (%)

0. – 0.1 10.19 10 42.40

0. – 0.12 12.98 11 29.46

0. – 0.14 41.52 12 0.004

Thrust Range (1-T) 2 ndof Prob (%)

10-2.4 – 10-1.2 2.69 5 74.76

10-3 – 10-1.2 3.76 6 70.9

10-4 – 10-1.2 95.08 7 0.

Thrust range 10-4-10-1.2

HT3 2

160-260 95.08

260-360 81.68

360-430 62.15

430-700 27.69

Comparison with theory(s3)

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Thrust Range (1-T) 2 ndof Prob (%)

10-2.4 – 10-1.2 3.19 5 67.0

10-3 – 10-1.2 6.26 6 39.5

10-4 – 10-1.2 28.86 7 0.01

Thrust range 10-4-10-1.2

HT3 2

160-260 28.86

260-360 8.25

360-430 3.89

430-700 4.54

430<HT3<700

Comparison with theory(s4)

DØ preliminary

DØ preliminaryDØ preliminaryDØ preliminary

Thrust Range (1-T) 2 ndof Prob (%)

0.01. – 0.12 6.10 10 80.67 0.01 – 0.14 6.78 11 81.66 0.01 – 0.28 15.15 16 51.36

DØ preliminary

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Conclusions

The first precise measurement of an event shape distribution such as d/dT in a hadron collider.

The prediction s3 (Jetrad) agrees with data except for high T

values, 1-T < 10-3 and in the low region 1-T > 0.12 .Resummation calculations needed in the limit T 1.

Between the LO prediction is O(s4).

Excellent opportunity to test the recently developed NLO 3-jet generators.This prediction (NLOJET++) agrees with data over the whole T range (T ≠ 1), except in the limit T 1 for low HT3, where higher order corrections are still important.

2/32/2 2 TT