Jets Physics at CDF Sally Seidel University of New Mexico Ninth Adriatic Meeting 8 September 2003...

Jets Physics at CDF

Sally SeidelUniversity of New Mexico

Ninth Adriatic Meeting

8 September 2003

for the CDF Collaboration

1. Jets at CDF

2. The Inclusive Jet Cross Section versus ET

3. The Dijet Mass Spectrum

4. Jet Shapes

5. Jet Algorithms

The motivation:

Jet distributions at colliders can:

• signal new particles + interactions

• test QCD predictions

• constrain parton distribution functions

What’s new in Run 2?

•Energy increase:

•Bunch spacing decrease: to 396 ns

Consequences:

•more precision, better statistics, more jets: the jet cross section is higher

•shorter distance scales probed: the energy reach per jet is greater

GeV 19601800: s

New:

•tracking system (silicon vertex SVXII, intermediate silicon layers ISL, central outer tracker COT)

•scintillating tile end plug calorimeter

•intermediate muon detectors

•scintillator time of flight system

•front end electronics

•pipelined trigger system

•DAQ

Central muon detectors and calorimeters are unchanged.

All detectors inside the solenoid are new. Compare...

COT

0

.5

1.0

1.5

2.0

0 .5 1.0 1.5 2.0 2.5 3.0

END WALL HADRON CAL.

30

300

SOLENOID

= 1.0

= 2.0n

EN

D P

LUG

EM

CA

LOR

IMETER

EN

D P

LUG

HA

DR

ON

CA

LOR

IMETER

= 3.0n

n

m

m

Run 1

Run 2, inside solenoid

CDF jet energy calibration corrects for:

•calorimeter response

•multiple interactions

•neutrinos + muons

•underlying event

Corrections are based on

•Monte Carlo tuned on test beam (for 10 GeV Ebeam 227 GeV).

•Drift chamber tracks w/ 400 MeV/c pT 10 GeV/c.

MC fragmentation parameters tuned to match observed particle momenta + numbers.

Calorimeter resolution: = 0.1ET + 1GeV.

Forward + plug calorimeter response calibrated by balancing dijets in which 1 jet of the pair is central.

Reconstruction:

CDF reconstructs jets using an iterative cone algorithm with cone radius

7.0)()( 22 R

A typical jet crosses 40 calorimeter cells.

The algorithm is based on the Snowmass one, which says: if i indexes all towers within cone radius R,

jetT

ii

iT

jet

jetT

ii

iT

jet

i

iT

jetT

EE

EE

EE

The CDF iterative cone algorithm:

•Examine all towers with ET > 1 GeV.

•Form preclusters from continuous groups of towers with monotonically decreasing ET.

•If a tower is outside a window of 7 x 7 towers from the seed of its cluster, start a new precluster with it.

•For each precluster, find the ET-weighted centroid for all towers with ET > 100 MeV within R = 0.7.

•Define the centroid to be the new cluster axis.

•Iterate until the tower list is stable.

If 2 jets overlap –

Merge them if 75% of the smaller jet’s ET is in the overlap region; otherwise assign overlap energy to the nearest jet.

Recalculate (,).

i

iz

i

iy

i

ix

jet

E

EE22

1tan

, where

….the CDF jets have mass.

jetjetT EE sin

The Inclusive Jet Cross Section, E·d3/dp3

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

• For massless jets + 2 acceptance in ,

This is what we measure.

ddE

d

Edp

dE

TT

2

3

3

2

1

LE

N

T

Data quality requirements:• |zvertex | < 60 cm to maintain projective

geometry of calorimeter towers.

• 0.1 |detector| 0.7 for full containment of energy in central barrel.

• Etotal < 2000 to reject accelerator loss events.

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

Apply EM/HA + jet shape cuts to reject noise fakes.

. thresholdon trigger depending

,GeV )7 to5.3( 1/2

all

T

T

E

ETE

Next correct for

•Pre-scaling of triggers.

•Detection efficiencies (typically 94 –100%).

•underlying event + multiple interactions.

•Run 2-Run 1 jet energy scale (5%).

•“Smearing”: energy mismeasurement + detector resolution.

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

The CDF Unsmearing Procedure:

Simultaneous correction for detector response + resolution produces a result that is indepen-dent of binning but preserves the statistical uncertainty on the measured cross section.

•A smooth function is proposed representing a trial “pre-detector” cross section. This is called the “physics function.” For the inclusive cross section, the physics function has the form:

.parameters fitted are the GeVin is

,/2

,)][ln()(

:where

,10)1()(

5

1

)(0

6

itrueT

trueTT

i

i i

EFPTtrue

T

trueT

PE

sEx

xPxF

xPdE

Ed trueT

•The physics function is convoluted with measured ET-loss and resolution functions and binned in ET. The response functions have long tails due to uninstrumented regions. The response function is parameterized by an exponential combined with a Gaussian and depends on the choice of cone opening angle. The response function requires

•Gaussian mean M = C1ET3 + C2ET

+ C3ET2

+ C4ET + C5ET + C6,

•Gaussian standard deviation = C7(ET + C8) - C10, and

•Exponential decay constant S = C11ET + C12 (where C11 and C12 depend upon the ET range).

9C

The Ci are determined by comparing measured calorimeter jet response to jets in Monte Carlo simulation. The Monte Carlo is based on single particle response from test beam data and isolated tracks from minimum bias events.

•The result of the convolution is compared with the measured cross section.

•The parameters of the physics function are iterated to obtain the best match between the convoluted function and the data.

•The ratio of (data):(physics function) for each ET bin is tabulated. The correction factors (typically 10%) are subsequently applied to data to obtain the “unsmeared physics cross section.”

Title:R2CTEQ6NLO.epsCreator:ROOT Version 3.04/02Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

The CDF inclusive jet cross section result for

GeV... 1960s

Systematic uncertainties (all uncorrelated)

on inclusive jet cross section measurement:

i. Calorimeter response to high-pT charged hadrons (+3.2% -2.2%)

ii. Calorimeter response to low-pT charged hadrons (5%)

iii. Energy scale stability (±5%)

iv. Jet fragmentation model used in the simulation

v. Energy of the underlying event in the jet cone (±30%)

vi. Calorimeter response to electrons + photons (2%)

vii. Modelling of the jet energy resolution function (10%)

viii. Normalization (6%)

Title:SysErr-1.epsCDFCreator:ROOT Version 3.04/02Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

Theoretical choices

•Calculation of PDF systematic:

•CTEQ6.1M includes error info for all its Drell-Yan, DIS, and jet datasets.

•20 free parameters used in fit.

•20x20 Hessian error matrix computed and diagonalized. Eigenvectors are 20 independent directions in PDF space.

•Small (large) eigenvalues = directions poorly (well) determined. Direction associated with gluon PDF dominates.

•Vary each eigenvalue until the 2 for the global fit increases by 100 (= 90% CL).

•renormalization and factorization scales chosen at ET

jet/2. Scale uncertainty small.

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Conclusions and status...

•Good agreement between data and theory

•Data are below theory at low ET, above theory at high ET---this was also true for CDF Run 1.

•Study of systematics is ongoing to quantify the effect.

The Dijet Mass SpectrumA search for new particles

Many classes of new particles have a larger branching fraction to just 2 partons than to lepton or Z/W modes. These new particles’ masses could appear as resonances in the spectrum.

Search for:

•Axigluons arise if SU(3) is replaced by SU(3)LSU(3)R

•Excited quarks arise in compositeness models

•Extended Technicolor Coloron

•Supersymmetry-inspired E6 Scalar Diquarks

qqA

qgq *

qqC

udDduD c and

Theoretical sources

AXIGLUONS

P. Frampton and S. Glashow, Phys. Lett. B 190 (1987) 157.

EXCITED QUARKS

U. Baur, I. Hinchliffe, and D. Zeppenfeld, IJMP A2 (1987) 1285.

TECHNICOLOR

E. Eichten and K. Lane, Phys. Lett. B 327 (1994) 129.

E6 DIQUARKS

J. Hewitt and T. Rizzo, Phys. Rep. 183 (1989) 193.

Set mass cuts where jet triggers are 100% efficient:

• trigger inefficiency < statistical uncertainty

• lost events are low mass

Plot:

Fit:

LEffAccm

N

vtxz

xs

mp

s

m

m

p

s

mp

s

m

m

p

dm

d

p

p

i

p

p

high at falloff PDF is )1(

andelement matrix QCD theis 1

,parameters are thewhere

,)1(

2

3

2

3

2

1

2

10

•Fit probability 0.66 is good

•bin width is mass resolution: new particle signal would appear in 2-4 bins

•No evidence for new particles

Title:DijetMassFit.epsDisplay of Dijet MassCreator:ROOT Version 3.03/07Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

To set limits on cross section for new particle production as a function of mass:

•Assume measured mass spectrum comes from resonance + QCD bkg

•Predict signal Nisig in bin i:

•Calculate signal d/dm using line shape for an excited quark (Gaussian + radiative tails) generated by PYTHIA, smeared by CDF detector simulation

•Normalize cross section with theory

•Predict background Nibkg in bin i:

•Assume QCD spectrum

•Float signal normalization: multiply by

•Predict total events i in bin i:

i = Nisig + Ni

bkg

•Poisson probability to observe ni when i are expected:

•Likelihood function L for making this observation over all bins in the mass spectrum:

•Use MINUIT to minimize -ln L for each M in range (200 - 1150) GeV/c2, in 50 GeV/c2 steps. Fit to signal normalization , bkg normalization p0, and shape (p1-p3).

)!/()( inii neP ii

i

iPL

•Map out L(Nisig) by varying holding other

parameters constant.

•Let 95 = 95% CL upper limit on . This is the value of for which 95% of the area of the likelihood distribution is between 0 and 95 .

•Compute 95% CL upper limit on cross section for production and decay of par ticle M as (total expected cross section) 95. Title:

limit_color.epsCreator:HIGZ Version 1.22/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

Systematic uncertainties are under study on

•absolute jet energy scale

•background parameterization

•radiation

•jet energy resolution

•luminosity and efficiency

A study of the internal structure of jets.

Process dominated by multi-gluon emission, controlled by higher-order QCD.

Tests models of parton cascades.

Sensitive to:

Color structure of the hadronic final state + initial state radiation

Underlying event due to interactions between collision remnants

Jet Shapes

Define the differential jet shape,

the average fraction of the jet’s transverse energy that lies inside an annulus in the - plane of inner (outer) radius r-r/2 (r+r/2) concentric to the jet cone. Note (r = R) = 1.

jets T

T

jets RE

rrrrE

rNr

)(

)2/,2/(1)(

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Define the integrated jet shape,

the average fraction of the jet’s transverse energy that lies inside a cone of radius r concentric to the jet cone. Note

jets T

T

jets RE

rE

Nr

)(

)(1)(

R

rr0

1)(

Data selection:

•iterative cone jet clustering algorithm

•R = 0.7 and calorimeter towers with ET > 100 MeV

•dijet events:

2 jets with uncorrected ET > 30 GeV, |jet| < 2.3

•|zvtx| < 60 cm

•

Compare data to HERWIG and PYTHIA Monte Carlo simulations. Both are (22) including initial- and final-state gluon radiation and secondary interactions between remnants.

1/2GeV 2

all

T

T

E

E

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Typical result for the integrated distribution:

HERWIG produces jets narrower than data, especially in forward regions. HERWIG jet description improves with ET.

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Typical result for the differential distribution:

PYTHIA describes jet shapes fairly well but produces jets slightly narrower at low ET and in the range 1.4 < || < 2.3.

Jets narrow as ETjet increases: see the

integrated jet shape measured at fixed cone size r = 0.4...

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Algorithm:

A method for grouping collimated particle paths in a calorimeter.

Needed to provide a common, objective, and unambiguous definition for use by theorists and experimentalists.

Ideally should be infrared- and collinear-safe: cross section should not change if parton radiates a soft parton or splits into two collinear ones.

Jet direction should correspond with parent parton direction.

Run II Jet Algorithms

CDF has compared the cone and kT algorithms and applied both to the Inclusive Jet Cross Section measurement.

The kT algorithm successively merges pairs of nearby objects (partons, particles, towers) in order of increasing relative ET. Parameter D controls the end of merging, characterizes jet size.

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.

•kT jets can have more complicated boundaries than do the smooth cones; consequently less ET near their boundaries.

CDF kT Algorithm1:

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

2) For each object pair i, j, define

•(Rij)2 = (ij)2 + (ij)2

•dij = min[(ETi)2,(ETj)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) Consider various values for D. Show results here for D = 0.7 and 1.0.1Based on S.D. Ellis and D. Soper, PRD 48. 3160 (1993).

Analysis:

•The Inclusive Jet Cross Section analysis cuts were applied to 82 pb-1 of Run 2 data

•Jets were reconstructed with cone and kT and matches were sought: Define

1.022 TT kconekconeR

First results...

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The kT algorithm typically captures less ET:

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...and the difference in ET assignment depends upon the ET of the cone jet:


The relative ET captured by the two algorithms depends strongly on the choice of parameter D:


The uncorrected Inclusive Cross Section shape varies slightly with parameter D:

...different algorithms may have different corrections.

Summary

•Inclusive jet cross section shows good agreement with theory; slight disagreement that was present in the Run 1 data persists.

•New limits set on masses of axigluon, excited quark, coloron, and E6 scalar diquark.

•Evidence for jet narrowing with increasing ET; Herwig and Pythia provide adequate models of jet shapes but with typically slightly too narrow jets in some kinematic regions.

•Studies of kT algorithm implementation are underway.

Jets Physics at CDF Sally Seidel University of New Mexico Ninth Adriatic Meeting 8 September 2003...

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