Jet Physics at the Tevatron

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Jet Physics at the Tevatron

• Sally Seidel
• University of New Mexico
• XXXVII Rencontres de Moriond
• For the CDF and D0
• Collaborations

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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)
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• Jet distributions at colliders can
• signal new particles interactions
• test QCD predictions
• improve parton distribution functions

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• CDF (D0) data quality and reconstruction
  requirements
• zvertex lt 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)
• lt (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.
  

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• 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 gt 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.

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The Inclusive Jet Cross Section, Ed3?/dp3 CDF

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

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The CDF result for unsmeared data
(88.8 pb-1) (20.0 pb-1)
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• 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.

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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
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Begin with nt0 nominal prediction by theory t.
Smear prediction separately for each systematic
uncertainty k to get smeared prediction ntk. The
systematic uncertainty in bin i is then
Predicted jets in bin i is
Use this nt(i) to calculate (uncorrelated)
statistical uncertainty. The sk are chosen to
minimize total ?2 using MINUIT.
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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.
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• 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 PDFs.
• 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.
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Results, for 33 dof CTEQ4HJ 10 CL MRST 7 CL
(relatively high value because normalization
systematic is cancelled by shape
systematics). All other PDFs lt 5 CL CTEQ4M
1.4 CL, change in agreement with data above 250
GeV cannot be accounted for.
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• 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 PDFs. CDF is also
  consistent with D0.

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The Inclusive Jet Cross Section versus
Pseudorapidity and ET D0

• Extends the kinematic range beyond previous
  measurements

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D0 result, with cone algorithm, for 95
pb-1 at 1800 GeV
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?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.
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Conclusions PDF ?2/dof Probability CTEQ4HJ 0.6
6 0.99 MRSTg? 0.95 0.63 CTEQ4M 1.03 0.41 MRST
1.26 0.05
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Measurement of ?s from Inclusive Jet Production
CDF
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).
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• 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).

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• Result, for 87 pb-1, with CTEQ4M
• Average of results is ?s
• ?s evolution verified for 40 lt ET lt 250 GeV
• 27 values of ?s(MZ) are
  ET-independent.

ET (GeV)
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Theoretical uncertainties due to ET/2 lt ? lt
2ET PDF 5 (extracted ?s
values are consistent with those in PDFs.) 1.3 lt
Rsep lt 2.0 2-3
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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.

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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.
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• 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).

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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,
?lt0.5, statistical errors only
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Theory below data by 50 at low pT, by
(10 - 20) for pT gt 200 GeV/c. NLO predictions
with kT and cone are within 1. Cross section
measured with kT is 37 higher than with cone.
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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.
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• 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.

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Result, for 10 pb-1
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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.

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Subjet Multiplicity of Gluon and Quark Jets
Reconstructed with the kT Algorithm
D0

• This study examines
• pT and direction of kT jets
• event-by-event comparison of kT and cone
• multiplicity structure of quark and gluon jets

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Calibration of jet momentum
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.
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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.
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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.
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Comparison of kT and cone jet reconstruction for
2 leading jets in 69k Run 1b events 99.94 of
jets reconstructed within ?R lt 0.5.
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systematically higher than
by 3-6
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Subjets Reapply kT algorithm to each jet, using
its preclusters, until all remaining objects have

• These are subjets, defined by fractional pT and
  separation in space. Multiplicity M depends on
• color factor (gluon gt quark)
• ycut ycut 0 ? M preclusters
• ycut 1 ? M 1
• Choose ycut 10-3.

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• 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.

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

• Identify reconstructed jets with type of nearest
  parton. Gluon jet fractions for 55 lt pT lt
  100 GeV/c
• f1800 0.59
• f630 0.33

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Multiplicity M measured in the data is related to
gluon jet multiplicity Mg and quark jet
multiplicity Mq by
For Mg, Mq independent of ,

• 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,

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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.

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• The data
• minimum bias (one interaction each with forward
  backward beam-beam counters) and charged jets
  with ?lt1, 50 GeV/c gt pT gt 0.5 GeV/c.
• measured in the central tracker
  ?pT/pT2 ? 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).

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• The models
• pthard gt 3 GeV/c, to guarantee ?2?2 ?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...

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• 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.

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• 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 ? lt 1.

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• 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.

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To study the underlying event, global observables
ltcharged multiplicitygt and lt
gt are correlated with angle ? relative to axis of
leading jet. Region transverse to leading jet
(normal to the plane of the 2?2 parton hard
scatter) is most sensitive to beam-beam fragments
and initial state radiation.
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Observation ltcharged multiplicitygt and lt
gt grow rapidly with pTleading, then plateau at
pTleading gt 5 GeV/c.
Plateau height in transverse direction is half
height in direction of leading jet.
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PYTHIA 6.115 best model for ltcharged
multiplicitygt in tranverse region but
over-estimates in direction of leading jet.
ISAJET shows right activity but wrong pT
dependence
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ISAJET uses independent fragmentation (too many
soft hadrons when partons overlap) and leading
log picture without color coherence (no angle
ordering within the shower)
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HERWIG PYTHIA model hard scatter (esp. initial
state radiation) component of underlying event
best
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HERWIG lacks adequate
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• 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!