Jet Physics at the Tevatron

Sally SeidelUniversity of New Mexico

XXXVII Rencontres de Moriond

For the CDF and D0

Collaborations

An overview of selected jet studies by CDF and D0 in 2001-2.

1. Jets at CDF and D0

2. Inclusive Jet Production (CDF)

3. Inclusive Jet and ET Dependence (D0)

4. s from Inclusive Jet Production (CDF)

5. Inclusive Jet Cross Section using the kT Algorithm (D0)

6. Ratios of Multijet Cross Sections (D0)

7. Subjet Multiplicity of g and q Jets using the kT Algorithm (D0)

8. Charged Jet Evolution and the Underlying Event (CDF)

Jet distributions at colliders can:

• signal new particles + interactions

• test QCD predictions

• improve parton distribution functions

CDF (D0) data quality and reconstruction requirements:• |zvertex | < 60 (50) cm to maintain projective

geometry of calorimeter towers.

• 0.1 (0.0) |detector| 0.7 (0.5) for full containment of energy in central barrel.

• To reject cosmic rays + misvertexed events, define = missing ET. Require

(CDF)

< (30 GeV or 0.3ETleading jet,

whichever is larger). (D0)• Reconstruct jets using a cone algorithm with

cone radius • Apply EM/HA + jet shape cuts to reject noise

fakes.

6

all

T

T

E

E

TE

TE

7.022 R

Next correct for

•Pre-scaling of triggers.

•Detection efficiencies (typically 94 –100%).

•underlying event + multiple interactions.

•“smearing” of the data: the effects of detector response and resolution.

•If > 1 primary vertex:

•choose vertex with 2 highest ET jets. (CDF).

•choose 2 vertices with max track multiplicity, then choose the one with minimum . (D0)

No correction is made for jet energy deposited outside the cone by the fragmentation process, as this is included in the NLO calculations to which the data are compared.

jetE

The Inclusive Jet Cross Section, E·d3/dp3 CDF

• For jet transverse energies achievable at the Tevatron, this probes distances down to 10-17 cm.

•

This is what’s measured.

ddE

d

Edp

dE

TT

2

3

3

2

1

LE

N

T

(88.8 pb-1)(20.0 pb-1)

GeV 1800s

The CDF result for unsmeared data:

New in this analysis: compare raw data to smeared theory. This uncouples the systematic shift in the cross section associated with smearing from the statistical uncertainty on the data.

•Consider only uncorrelated uncertainties first.

•Develop a 2 fitting technique that includes experimental uncertainties, to quantify the degree to which each theory reproduces the data.

Define

where:

nd = observed # jets in bin i

nt = predicted # jets in bin i

t = uncertainty on prediction

sk,t= shift in kth systematic for tth theoretical prediction

Term 1: uncorrelated scatter of points about a smooth curve

Term 2: 2 penalty from systematic uncertainties

8

1

2,

12

22 ))()((

ktk

nbin

i t

tdt s

inin

Begin with nt0: nominal prediction by

theory t. Smear prediction separately for each systematic uncertainty k to get smeared prediction nt

k. The systematic

uncertainty in bin i is then

)()()( 0 ininif tkt

kt

Predicted # jets in bin i is

)()(8

1,

0 ifsnin kt

ktktt

Use this nt(i) to calculate (uncorrelated) statistical uncertainty. The sk are chosen to minimize total 2 using MINUIT.

Example resulting 2 values:

CTEQ4M: 63.4

CTEQ4HJ: 46.8

MRST: 49.5

This suggests that CTEQ4HJ best describes the data. But combinations of the 8 systematics can cancel. To study this, redo the fit separately for every combination of systematics. For:

NO systematics: 2 = 94.2

4 systematics: best 2 = 47.6

8 systematics: best 2 = 46.8

The normalization systematic can be cancelled by shape systematics.

To extract confidence levels:

•Generate fake raw data (“pseudo-experiments”) using CTEQ4HJ. Predict nominal # entries for each of the 33 bins. Vary each prediction with 33 (statistical) + 8 (systematic) random numbers. Assume systematics are gaussian but ET dependent. Repeat for other PDF’s.

•Fit each pseudo-experiment to the nominal PDF prediction using 2.

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Calculate 2 between data and smeared theory. Integral of the distribution above this 2 is the CL.

Results, for 33 dof:

CTEQ4HJ: 10% CL

MRST: 7% CL (relatively high value because normalization systematic is cancelled by shape systematics).

All other PDF’s: < 5% CL

CTEQ4M: 1.4% CL, change in agreement with data above 250 GeV cannot be accounted for.

CDF conclusion on inclusive jet cross section measurement:

•predictions using CTEQ4HJ have best agreement with data in both shape and normalization before considering systematics.

•when systematics are included, some combinations cancel out to produce only small changes in the spectrum shape. CTEQ4HJ provides the best prediction, followed by MRST.

•CDF Run Ib data are consistent with Run Ia and with NLO QCD given the flexibility allowed by current knowledge of PDF’s. CDF is also consistent with D0.

The Inclusive Jet Cross Section versus

Pseudorapidity and ET

D0Extends the kinematic range

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D0 result, with cone algorithm, for 95 pb-1 at 1800 GeV:

2 Comparison of D0 data and theory:

i.) Define

ii.) Construct the Cij by analyzing the correlation of uncertainties between each pair of bins. (Bin-to-bin correlations for representative bins are ~ 40% + positive.)

iii.) There are 90 -ET bins.

matrix covariancey uncertaint

theoryby the predicted jets ofnumber

data in the observed jets ofnumber

#bin

where, 1

,

2

C

T

D

i

TDCTD jjijji

ii

Conclusions:

PDF 2/dof Probability

CTEQ4HJ 0.66 0.99

MRSTg 0.95 0.63

CTEQ4M 1.03 0.41

MRST 1.26 0.05

Measurement of s from Inclusive Jet Production

CDF

),,()(1

),(ˆ

1

)0(2

TFRRs

TFsT

Ek

EXdE

d

The cross section and s are related at NLO by:

In the Tevatron ET regime, non-perturbative contributions are negligible.1

1S.D. Ellis et al., PRL 69, 3615 (1992).

Procedure:

•The and k1 are calculated with JETRAD1 for given2 matrix elements, in the scheme. Clustering and cuts are applied directly to the partons.

•The 33 ET bins provide independent measurements at 33 values of R = F.

•Evolve the measured s values:

1W. Giele et al., PRL 73, 2019 (1994) and Nucl. Phys. B403, 633 (1993)2R.K. Ellis and J. Sexton, Nucl. Phys. B 269, 445 (1986).

)0(X̂

SM

21

0

10

24

38306

,6

233

)/ln())()((1)(

f

f

ZRRsRs

sZa

nb

nb

MbbM

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•Result, for 87 pb-1, with CTEQ4M :•Average of results is s =

s evolution verified for 40 < ET < 250 GeV :

27 values of s(MZ) are ET-independent.

syst.). (exp. (stat) 1000.01178.0 0.00810095.0

ET (GeV)

Theoretical uncertainties due to:

ET/2 < < 2ET:

PDF: 5% (extracted s values are consistent with those in PDF’s.)

1.3 < Rsep < 2.0: 2-3%

%6%4

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The Inclusive Jet Cross Section using the kT

Algorithm D0

The kT algorithm differs from the cone algorithm because

•Particles with overlapping calorimeter clusters are assigned to jets unambiguously.

•Same jet definitions at parton and detector levels: no Rsep parameter needed.

•NNLO predictions remain infrared safe.

The kT algorithm successively merges pairs of nearby objects (partons, particles, towers) in order of increasing relative pT.

Parameter D controls the end of merging, characterizes jet size.

Every object is uniquely assigned to one jet.

Infrared + collinear safe to all orders.

D0 kT Algorithm1:

1) For each object i with pTi, define dii = (pTi)2

2) For each object pair i, j, define

•(Rij)2 = (ij)2 + (ij)2

•dij = min[(pTi)2,(pTj)2]·(Rij)2/D2

3) If the min of all dii and dij is a dij, i and j are combined; otherwise i is defined as a jet.

4) Continue until all objects are combined into jets.

5) Choose D = 1.0 to obtain NLO prediction identical to that for R = 0.7 cone.1Based on S.D. Ellis and D. Soper, PRD 48. 3160 (1993).

kT jets do not have to include all objects in a cone of radius D, and may include objects outside cone.

D0 result for 87 pb-1, unsmeared data, ||<0.5, statistical errors only:

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Theory below data by 50% at low pT, by (10 - 20)% for pT > 200 GeV/c.

NLO predictions with kT and cone are within 1%.

Cross section measured with kT is 37% higher than with cone.

Effect of final state hadronization studied with HERWIG:

For 24 d.o.f., 2 calculated with covariance technique:

PDF 2/dof Prob.

MRST + hadr. 1.00 0.46 CTEQ4HJ + hadr. 1.01 0.44 MRST 1.12 0.31 MRSTg 1.17 0.25 CTEQ4M 1.30 0.15 MRSTg 1.38 0.10

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Ratios of Multijet Cross Sections

D0

This study measures

as a function of . Compare to JETRAD with CTEQ4M for several choices of renormalization scale using a 2 covariance technique.

)2 X; jets (

)3 X; jets (32

mmpp

nnppR

jetTT EH

Recall F controls infrared divergences; R controls ultraviolet. Assume R= F.

Test four options:

R = for leading 2 jets and

(a) R = also for third jet.

(b) R = ET for third jet.

(c) R = 2ET for third jet.

R = 0.6 ETmax for all 3 jets.

jetTE

jetTE

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•No prediction accurately describes the data throughout the full kinematic region.

•A single R assumption is adequate: introduction of additional scales does not improve agreement with data.

• R = 0.3 is consistent with the data.

jetTE

Subjet Multiplicity of Gluon and Quark Jets Reconstructed with the kT Algorithm

D0This study examines

•pT and direction of kT jets

•event-by-event comparison of kT and cone

•multiplicity structure of quark and gluon jets

Calibration of jet momentum:

responsedetector

where

),(

),,(

R

ppp

pR

pLppp

environunderlyingoffset

jetjet

jetT

jetoffset

measjettrue

jet

To find penviron (from U noise, multiple interactions, pile-up) : overlay HERWIG events with zero-bias (random crossing) events at various luminosities.

Observation: penviron for (D = 1.0) kT is 50-75% higher (i.e., 1 GeV/jet) than for (R = 0.7) cone.

To find punderlying:

(1) overlay HERWIG events with minimum-bias (coincidence in hodoscopes) data at low luminosity (negligible environment)

(2) overlay HERWIG events with zero-bias events at low luminosity

(3) subtract: (1) - (2).

Observation: punderlying for (D = 1.0) kT is 30% higher than for (R = 0.7) cone.

To find R:

(1) calibrate EM energy scale with Z, J, 0 decays

(2) require pT conservation in -jet events:

R consistent for kT and cone jets.

T

TTrcalorimete p

nER

ˆ1

Comparison of kT and cone jet reconstruction for 2 leading jets in 69k Run 1b events:

99.94% of jets reconstructed within R < 0.5.

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systematically higher than by 3-6%:

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jetkT

Tp jetconeTE

Subjets

Reapply kT algorithm to each jet, using its preclusters, until all remaining objects have

)(),min( 22

22

,2

, jetpyD

Rppd tcut

ijjTiTij

These are subjets, defined by fractional pT and separation in space. Multiplicity M depends on:

•color factor (gluon > quark)

•

•ycut: ycut = 0 M = # preclusters

ycut = 1 M = 1

Choose ycut = 10-3.

s

Select gluon-enriched and quark-enriched data samples:

PDF data show that fraction of gluon jets decreases with x pT/ .

•Select jets with same pT at = 630 GeV and = 1800 GeV for 2-jet events.

s

s s

•Use HERWIG with CTEQ4M to predict gluon jet fraction f. LO calculation is algorithm-independent.

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•Identify reconstructed jets with type of nearest parton. Gluon jet fractions for 55 < pT < 100 GeV/c:

f1800: 0.59

f630: 0.33

Multiplicity M measured in the data is related to gluon jet multiplicity Mg and quark jet multiplicity Mq by:

qg MffMM )1(

For Mg, Mq independent of , s

6301800

18006306301800

6301800

63018001800630

and

)1()1(

ff

MfMfM

ff

MfMfM

q

g

•Correct result for shower detection effects in calorimeter.

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Mean subjet multiplicities:

•gluon jets: 2.21 0.03

•quark jets: 1.69 0.04

after unsmearing,

22.018.015.084.1

1

1

q

g

M

Mr

Charged Jet Evolution and the Underlying Event

CDF

A two-part analysis: Data are compared to HERWIG, ISAJET, and PYTHIA for

• observables associated with the leading charged jet: the hard scatter.

•global observables used to study the behavior of the underlying event.

The data:

•minimum bias (one interaction each with forward + backward beam-beam counters) and charged jets with ||<1, 50 GeV/c > pT > 0.5 GeV/c.

•measured in the central tracker: pT/pT

2 0.002 (GeV/c)-1

•impact parameter cut, vertex cut, to ensure 1 primary vertex.

•no correction for track finding efficiency (92% correction applied to models).

The models:

•pthard > 3 GeV/c, to guarantee

22 ‹ total inelastic

•All assume superposition of

•the hard scatter

•the underlying event: beam-beam remnants, initial state radiation, and multiple parton scattering

•but different models for underlying event...

•HERWIG: soft collision between 2 beam “clusters.”

•ISAJET: “cut Pomeron” similar to soft min bias. Independent fragmentation allows tracing of particles to origin: beam-beam, initial state rad, hard scatter + final state rad.

•PYTHIA: non-radiating beam remnants + multiple parton interactions with different effective minimum pT options: 0, 1.4, and 1.9 GeV/c. No independent fragmentation: cannot distinguish initial from final state radiation but can distinguish beam-beam.

The standard CDF jet algorithm based on calorimeter towers is not directly applicable to charged particles. A naive jet algorithm is used because it can be applied at low pT:

•define jet as a circular region with radius

•Order all charged particles by pT.

•Start with particle with pTmax , include in

the jet all particles within R = 0.7. Recalculate centroid after each addition.

•Go to next highest pT particle and construct new jet around its R = 0.7.

•Continue until all particles are in a jet.

•Jet can extend beyond || < 1.

7.022 R

Results on the leading jet:

The QCD hard scattering models describe these observables for the leading (highest ) charged jet well:

•multiplicity of charged particles

•size

•radial distribution of charged particles and pT around jet direction

•momentum distribution of charged particles

Charged particle clusters evident in the minimum bias data above pT 2 GeV/c

a continuation of the high pT jets in the jet trigger samples.

Tp

To study the underlying event, global observables

<charged multiplicity> and

< >

are correlated with angle relative to axis of leading jet. Region transverse to leading jet (normal to the plane of the 22 parton hard scatter) is most sensitive to beam-beam fragments and initial state radiation.

Tp

Observation: <charged multiplicity> and < > grow rapidly with pT

leading, then plateau at pT

leading > 5 GeV/c. Tp

Plateau height in transverse direction is half height in direction of leading jet.

PYTHIA 6.115 best model for <charged multiplicity> in tranverse region but over-estimates in direction of leading jet. ISAJET shows right activity but wrong pT dependence:

ISAJET uses independent fragmentation (too many soft hadrons when partons overlap) and leading log picture without color coherence (no angle ordering within the shower):

HERWIG + PYTHIA model hard scatter (esp. initial state radiation) component of underlying event best:

HERWIG lacks adequate : Tp

Summary:

Many interesting and significant results from D0 and CDF in

•Inclusive jets

s

•kT algorithm

•Multijet production

•Particle evolution

•Underlying event

On to Run II!