Production and Evolution of High Energy Jets

1

• Production and Evolution of High Energy Jets
• Outline (both lectures)
• A look at the data
• Theoretical framework
• Inclusive Jet Cross sections
• Multijet Events
• Double Parton Scattering
• Underlying Event
• Clustering algorithms
• Structure inside jets
• Overall Theme Interplay of Theory and
  Measurements

Day 1
Day 2
2
Simple view of a proton - antiproton collision
jet
y
detector
x
?
p
p
z

• Pseudo-rapidity
• - ln tan ?/2
• Simple translation
• (additive) under
• longitudinal boosts

jet

• 2?2 scattering
• Two partons are produced from the collision of a
  
• parton in each of the incoming hadrons
• Initial partons have a fraction, x, of proton
  (antiprotion)
• longitudinal momentum and small 0 transverse
  momentum.
• Each outgoing parton forms one jet
• Events are characterized by x and Q2, where Q is
  the total momentum transfer ETjet

3
Jets at Fermilab Hadron Collider

• Fermilab Tevatron collides protons and
  antiprotons at
• vs 1.96 GeV
• (was 1.8 TeV in Run 1)
• These collisions produce the highest energy jets
  (ET500 GeV)
• Probes proton structure to smallest distance
  scales
• ? hc/Mc2
• 197MeVfm/500 GeV
• 4x10-17cm

p
Hadronic
Electromagnetic
Jet ET Sum of towers 415 GeV
p
4
Regions Covered by Different Measurements

• Tevatron data overlaps and extends reach of DIS
  (talks by Jose Repond)
• This talk concentrates on jet production at the
  Tevatron.

5
What is a Jet?

• Jets are the clusters of particles produced by
  the scattered partons
• Particles (mostly hadrons) are produced nearly
  collinear to parent parton
• Underlying Event Remnants of incoming hadrons
  leave some low energy particles too. These are
  randomly distributed, not in clusters
• Fundamental concept Sum up all the daughter
  particles and you approximate the properties of
  the scattered parton

6
End view of the two-jet event in CDF
Azimuthal angle
?
Tracks in magnetic field
Can measure momentum of charged particles in
tracking chambers. Neutral particles e.g (p0)
are measured only by the calorimeters
7
More complicated events three-jet event

• ET 328 GeV
• ? 0.21
• f 2.5o

ET 123 GeV ? 0.23 f 170.4o
ET 173 GeV ? -0.57 f 192.4o
8
A five-jet event
9
6 - jet events
10
From Partons to Jets
Leading Log Approximation (LLA) sum leading
contributions to all orders (from collinear
radiation of quarks and gluons around original
parton)
Leading Order Theory Uses 2?2 matrix elements
Parton Shower
Only two jets in final state Only one parton/jet
11
From Partons to Jets Cont.

• Hadronization Each parton in the shower is
  converted into colorless hadrons
• The hadrons are measured in the tracking chambers
  and calorimeters
• Sum of the momentum and energy of all the
  particles in a cluster
• ? particle level jet
• scattered parton

Clustering (or Jet) algorithms Rules for
combining measured energy into Jets
12
Comparisons between Data and Theory

• Overall rate of jet production ( cross sections)
• Valid over full ET range (Jet ET 20 GeV 500
  GeV)?
• Match data for different vs ?
• Look for something new and unexpected which
  increases the rate of jet production over the
  predicted rates
• rate of multi( 3, 4, 5...) jet events, can QCD
  predict these higher order processes?
• Details of event structure
• Jet shapes
• Structure inside jets
• Multiple parton interactions
• Use Monte Carlo programs (e.g. ISAJET) to
  generate hadrons from LO predictions, and a
  detector simulation to derive corrections to data
• Compare corrected data to pQCD parton level
  predictions
• Theory no dependence on empirical parton shower
  or hadronization models
• Data can minimize and quantify dependence of
  corrections on modeling

13
Theoretical predictions at the parton level
fa/A(xa ,?F) Parton Momentum Distributions
(PDF) probability to find parton of type a in
hadron A with momentum fraction xa ?F
4-momentum transfer or factorization scale of
interation

• partonic level
• cross section

?
14
Rapidity and Pseudo-rapidity
y
scattered parton
x
?
z
antiproton
proton
Rapidity (y)
bcosq tanh y where b p/E
Pseudorapidity (?) high energy limit (mpT, ß ?
1)
Rapidity and Pseudo-rapidity are simply additive
under longitudinal boosts
15
Parton momentum fractions

• x1 (e?1 e?2) ET/vs
• x2 (e-?1 e-?2) ET/vs

x1 and x2 can not exceed unity ? -ln tan ?/2
xT 2ET/?s and xT2 ltx1x2lt1 As xT ? 1, x1
and x2 are tightly constrained
??boost ½ (??1 ?2) ?? ½ (??1 - ?2) ??Lab
?? ?boost
??1
??1
CM
Lab
?
?2
?2
16
Kinematic Variables

• Transverse Energy ET
• ET m2 px2 py2 Esin?
• E2- pz2

• Energy E
• E2 m2 p2
• ET cosh ?

• Momentum p
• p2 px2 py2 pz2
• Longitudinal momentum
• pz E tanh ?
• ET sinh ?

• Transverse Momentum pT
• pT px2 py2 psin?

• Invariant Mass for di-jet event
• M122 (p1 p2)2
• m12 m22 2(E1E2-p1p2)
• For m1, m2 ? 0
• M122 ? 2ET1ET2(cosh?? cos?f)

17
Phase Space Boundaries for 2 ?2 Scattering
?s 2 TeV and Jet ET 100, 200 and 400 GeV
?2

• phase space shrinks
• as ET increases
• for??1 -?2 , ??boost ? 0
• for??1 ?2 , M122 4ET2

??1
18
Leading Order Two-Jet Cross Section
At leading order ET1 ET2 ET

• where,
• fi(x,?F) (i g, q, q) is the PDF
• Mij is lowest order matrix element for ij?2
  partons
• summed and averaged over initial and
  final states
• ?s(?R) is the strong coupling constant
• ?F is the factorization scale
• ?R is the renormalization scale

Usually assume ?F ?R ? ET/2
Many processes contribute
19
Lowest order matrix elements

• Matrix elements for

Averaged (summed) over initial (final) state
colors and spins
where s (p1 p2)2, t (p1 - p3)2 and u (
p2-p3)2 are the Mandelstam variables
20
Quark and Gluon contributions to cross section
Solid ?s 2 TeV Dashed ?s 14 TeV

• Lowest ET jets from
• Tevatron are 20 GeV
• or xT 0.02
• gluon initial states
• dominate
• Highest ET jets are
• 500 GeV or xT 0.5
• ??qq dominates,
• but qg still 20 of total

Fraction of total

• xT 2ET/?s

21
The single effective subprocess approximation

• All the matrix elements have similar shape
• Can approximate the parton momentum distributions
  fi(x,?F) (i g, q, q) as a single effective
  subprocess

And the lowest order cross section can be written
as
22
Parton Luminosity

• In the single effective subprocess approximation
  the parton-parton luminosity (x1F(x1,µ)x2F(x2,µ)
  ) can be written as a function of ??boost and
  ??

• For ET 100 GeV and vs 2TeV
• largest luminosity is when x1 and
• x2 are equally small ?boost ?? 0
• As ?boost or ?? increases
• luminosity decreases rapidly

x1F(x1,µ)x2F(x2,µ)
??boost
23
Digression on the scales ?F and ?R

• ?F and ?R are artifacts of working at fixed order
  in perturbation theory.
• The predictions should not depend on the choice
  of scales (Data doesnt!)
• The renormalization scale ?R shows up in the
  strong coupling constant because it is introduced
  when the bare fields are redefined in terms of
  the physical fields
• The factorization scale ?F is introduced when
  absorbing the divergence from collinear radiation
  into the PDFs
• Can choose any value for ?F and ?R
• Typical choice ?F ?R ET/2 of the jets
• Dependence of predictions on scale indicates
  potential size of higher order contributions
• Dependence on scale should get smaller as higher
  order terms are included
• Usually study predictions with range ? ET/4 to
  2ET

24
Digression on the scales ?F and ?R cont.
as2 for different ?R compared to ?R ET
for different ?F compared to ?F ET at ?1 ?2
0
Ratio
Dependence of LO on choice of scales flat at
10 level for ?ET/2 but normalization uncertain
at 50 level
25
Inclusive Jet Cross Section Measurements

• Fundamental and simple test of QCD predictions
• Include all jets in the event within a given ?
  range
• Can search for signs of composite quarks

26
Inclusive Jet Cross Section and Compositeness

• Compositeness Scale ?c
• ?c ?? pointlike quarks
• ?c ?finite ? substructure
• at mass scale of ?c

• Hypothesis Quarks are bound states of preons
  which interact via new strong interaction

The composite interactions are represented by a
contact term

• Compositeness
• enhances the jet
• cross section
• has different ang.
• dist. from QCD

27
Measurements of Inclusive Jet Cross Section

• In the 80s, only Leading Order 2?2 predictions
  were available
• High energy Jet data was just becoming available
• AFS vs 63 GeV initial hints of 2-jet
  structures
• UA1 and UA2 vs 546 and 630 GeV , (ET
  20-150 GeV)
• CDF 1987 vs 1800 (ET 30-250 GeV)
• Obviously in the data there were events with more
  than 2 jets!
• Try to make data and theory look more alike
• Parton shower Monte Carlo program ISAJET FF
  fragmentation, LLA
• Tune parameters of parton shower and
  hadronization to give agreement with data
  minimizes dependence of corrections on details of
  the model.
• Defined clustering algorithms which could make
  data look like 2?2 process
• Summed energy in a large cones R 1 1.2 (cone
  algorithm)
• Summed neighboring towers (nearest-neighbor
  algorithm)

28
Uncertainties

• LO Theory
• PDFs derived from global fits to data (See talk
  by Walter Giele)
• Choice of scale for evaluation of as and PDFs
• higher order corrections
• Total uncertainty ranged from a factor of 2 to a
  factor of 10 depending on ET
• Experimental Measurement uncertainties
• energy scale (could be a whole talk by itself)
• luminosity
• corrections to go from measured jets to partons
  (e.g. energy that escaped the cone or jet
  cluster)
• underlying event (extra energy that leaked into
  cluster)

29
Inclusive Jet Cross Sections from the 80s
UA1 Unc. 70 50 jet corr. 40 jet calib
10 aging 15 lum ?c gt400 GeV
UA2 Unc. 32 25 Frag. model 15 jet id
11 calib 5 lum ?c gt825 GeV
Theory uncertainties mainly on normalization
compositeness limits set based on shape at high ET
CDF 1987 data Exp. Unc. 70 _at_ 30 GeV 34 _at_ 250
GeV ?c gt700 GeV
While data and theory agreed qualitativly, large
uncertainties existed in both theoretical
predictions and in experimental measurements
30
NLO 2?2 Theory predictions

• Late 80s NLO parton level predictions became
  available
• Aversa et al PLB 210,225 (1988), S.Ellis, Kuntz,
  Soper, PRL 62,2188(1989) ( EKS)

1 loop, 2 parton final state same kinematics as
LO 1 parton jet
tree level, 3 parton final state or 21 parton
final state
Now have possibility of combining partons to
form a jet. Predictions sensitive to size of jet
and way in which partons are combined
31
NLO 2?2 Theory predictions

• Dependence on the choice of scale reduced from
  factor of 2 to 30, more precise comparison to
  data possible
• Ushered in a new era of Jet identification
• Could use the same algorithm to cluster partons
  into jets as is used to cluster towers of energy
  in the detector
• Should minimize difference between data and
  theory predictions due to technical differences
• Led to SNOWMASS accord
• cone algorithm to be used by CDF, D0 and Theory
• detailed rules for combining towers (partons)
  into jets
• No out-of-cone energy correction! (part of NLO
  prediction)
• still have to estimate and subtract UE energy
• Other algorithms also exist will be described
  later

32
SNOWMASS Algorithm

• Choose a seed tower from a list of high ET towers
  (partons)
• Define a cone of radius R around the seed tower

Towers (partons) within the cone are associated
with the jet. Calculate new cluster centroid
loop over towers again until stable set of
towers is reached. Finally
Snowmass studies (1992) found that for a cone
size of 0.7 out-of-cone energy underlying event
33
Inclusive cross section compared to NLO

• CDF collected data in 1989
• 4pb-1 vs 1800 GeV
• 8nb-1 vs 546 GeV
• Compared to NLO predictions still uncertain due
  to scale and PDFs, but better than LO
• Statistical uncertainty dominated
• above about 200 GeV ET
• Set new limit on ?cgt1.4 TeV
• CDF also measured jet cross section for different
  cone sizes and looked at Jet shapes for 100 GeV
  Jets
• Interplay between data and theory!

34
Jet cross section dep. on cone size

• Jet cross section for
• cone sizes 0.4, 0.7, 1.0.
• PRL 68 1104 (1992))

µ ET/2 solid µ ET short dash µET/4 long dash

• Jet ET 100 GeV
• Best agreement with very small scale ET/4
• Introduce ad-hoc parameter Rsep which scales
  radius for parton merging
• ?Rparton Rsep R
• effectively reduces parton cone size
• Snowmass Rsep 2

Rsep 1.3
Theory PRL 69, 3615 (1992)
35
Jet Shape Measurement
DataPRL 70, 713 (1993) Thy PRL 69, 3615 (1992)
Jet ET 100 GeV

• Measure energy
• inside subcones around jet axis

Rsep 1.3
µ ET/2 solid µ ET short dash µET/4 long dash
ET/4 give worst agreement Rsep 1.3 gives best
agreement with data
F(r) ET(r)/ET(R)
36
Snowmass didnt specify how to separate close
jets (not an issue with partons)

• CDF merged close jets if 75 of smaller jet
  energy overlapped
• otherwise separated based on distance from
  centroids
• At parton level jets are
• separated if ?Rgt2Rcone

ET 123 GeV ? 0.23 f 170.4o
?R 0.88
ET 173 GeV ? -0.57 f 192.4o
37
Separation between jets in CDF data

• In data look at separation between leading 3 jets
• Plot the minimum separation between the two
  closest clusters
• 50 separated at 1.3 R
• 100 separated at 1.6R

Rsep of 1.3 makes sense! Explains better match
between data and theory
(divided by R)
38
Effect of Rsep on NLO 2?2 Inclusive Jet Cross
Section Predictions

• Cross section for Rsep 2 is larger than for Rsep
  1.3 by flat 5

• Lessons
• Inc. cross section is not very sensitive to Rsep,
  but more detailed comparisons pointed out
  difference between analysis of data and theory
• Details of clustering algorithms are important
  for precise comparisons between data an theory

39
More implications of NLO Phase space

• The Parton momentum fractions at NLO are

ET 50 GeV vs 1.8 TeV
where ET1 gt ET2gtET3 etc.

• Since ET2 can now be lt ET1,
• ?2 can increase compared to LO
• Adding more partons (e.g.NNLO)
• further increases allowed range
• Still have sharp cutoff on ?1
• ?2 can be bigger than ?1

?2
?1
40
Compare LO and NLO predictions
K factor NLO/LO 10 for ?lt1.5, away from
PS boundaries Large corrections for large
?2 ?stay away from there, theory not
reliable at LO or NLO
?
41
Scale dependence
LO

• where L log(µR/ET) and bi are the beta functions

NLO
NNLO
NNLO coefficient C is unknown. Curves show
guesses C0 (solid) CB2/A (dashed) Dependence
on choice of scale is reduced as higher orders
are included
Usual range
d?/dET at ET 100 GeV
µR /ET
42
Another digression on the scale

• Addition of NLO terms reduced dependence of
  prediction on scale when choice ranged from ET/4
  to 2ET
• But, since ET1 and ET2 are no longer required to
  be equal we now have to think about which ET
  should be used for the scale
• µ ? ET of each jet in the event
• Many scales per event
• Cross section is proportional to as(ET)n, can
  extract as from inc. xsec.
• µ ? ET1 Maximum Jet ET in the event
• one scale per event
• can implement in event generator (JETRAD does
  this)
• Can write the theory both ways Two programs used
  by CDF and D0
• EKS analytic NLO program uses µ ? ET
• JETRAD event generator uses µ ? ETMAX

43
Effect of Scale on NLO 2?2 Inclusive Jet Cross
Section Predictions
44
CDF Run 1A Inclusive Cross Section (1996)

• Excess observed above 200GeV
• In 1996 all PDFs gave roughly same shape
• Motivated discussions of new physics as well and
  PDF uncertainties

45
PDF uncertainties 2000
Ratio of inclusive jet cross section for
different PDFs compared to CTEQ4M

• Turns out PDFs are very flexible, even at high ET
  
• 30 changes in shape are OK
• Pretty much squelched discussions of new physics
• Ended 15 year history of using Inc. cross
  section for compositeness search.
• Need more constraints on PDFs!!

46
Alternate Variables Mass and Angle

• can write cross section in terms of dijet mass
  M12 and the center of mass scattering angle ?

M122 4ET2cosh2? cos ? tanh ? t - (1-cos
? )s/2

• Typically measure
• dijet mass spectrum d?/dMJJ
• by integrating over a fixed angular range
• angular distibution d?/dcos?
• for intervals of dijet mass

47
Angular Distribution Not sensitive to PDFS

• Dominant subprocesses have similar shape for
  angular distribution d?/dcos? with different
  weights

• Can use to test for compositeness with smaller
  theoretical uncertainties
• Measure angular distribution directly
• Measure dijet mass in different angular regions
  and
• take ratios to cancel PDF uncertainties

48
Angular Distribution and quark substructure
QCD is dominated by 1/(1-cos ?)2 Contact
terms by 1/(1cos ?)2 Difference in forward
? region is hard to measure

• Change to a better angular variable

d?/d?
Much more sensitive to contact term
large difference from QCD in central region
49
Limits on Quark Substructure
D0 Run IB results
50
Limits on Quark Substructure
51
Inclusive Jet Cross Section Run Ib

• CDF Results
• 0.1lt?lt0.7

Data and Predictions span 7 orders of magnitude!
52
Inclusive cross section in detail (linear scale)
CDF Run 1B data

• Good agreement with data over most of ET range
  for CTEQ4HJ predictions
• But note CTEQ4HJ was fit to CDF Run 1a data!
• Still need more constraints!
• See Talk by Walter Giele next week!

53
? dependence of inclusive cross section

• D0 result
• Solid CTEQ4HJ
• Open CTEQ4M
• NLO QCD predictions (JETRAD) provide good
  description of data.
• Agreement gets a little worse as go to higher ?

54
CDF and D0 Comparison

• CDF and D0 see fantastic agreement in 0.1lt?lt0.7
  range
• Note, this is corrected for the different
  luminosity cross sections used at the time of the
  measurements

55
Inclusive cross section and as
d?/dET ?s(µR )2A ?s(µR )3(B
2b0LA) ?s(µR )4(C 3b0LB
(3b02L2 2b1L)A)

• Use inclusive jet cross section data and NLO
  theory to extract as (only possible if use µR
  ?ETjet)
• Clearly observe running of as over a wide range
  of Jet ET
• ? ?s(Mz) 0.1178 .0001(stat.) .0081 -.0095
  (exp. sys), Thy unc. 5 PDFs, 5 scale

56
END Day 1

• Basic theoretical and experimental ingredients
  for high ET Jet studies at hadron colliders
• A little history of high ET jet measurements
• Interplay of data and theory
• Sample of the highest ET results from CDF and D0
• Tomorrow More detailed look at Jets and Jet
  events
• A few more high ET jet measurements
• Multi- jet events
• Double parton scattering
• Underlying event
• KT clustering algorithm
• Structure within jets

57
Production and Evolution of High ET Jets Day 2

• Yesterday we looked at events and discussed
  comparing data to LO and NLO predictions for 2? 2
  scattering (even though we saw events with many
  jets!)

• NLO 2?2 scattering
• 2 or 3 partons are produced from the collision
  of one parton in each of the incoming hadrons
• Initial partons have a fraction of proton
  longitudinal momentum and small pT 0
• Each outgoing parton forms a jet or 2 partons
• combine into one jet

• Data and Theory are in pretty good agreement
  over large ET range (20-500 GeV) where cross
  section falls by 7 orders of magnitude!

58
Production and Evolution of High ET Jets Day 2

• Today will describe a more complex (realistic?)
  model for the data
• Cover some of the details that were glossed over
  on Day 1
• Inclusive cross sections at different CM energies
• Multi jet measurements
• Double parton scattering
• Underlying Event
• Clustering algorithms
• Structure within jets

59
Inclusive Cross sections at different CM
ET
XT2ET/vs
60
Scaled Cross Section

• Can rewrite inclusive jet cross section in terms
  of dimensionless quantity xT
• Scaling means predictions are independent of vs

• QCD does not scale due to dependence of
  strong coupling
• constant and parton momentum distributions
  on the factorization
• and renormalization scales ?R and ?F
• In ratio of cross sections many
  uncertainties, both theoretical and
• experimental will cancel

61
Ratio of scaled cross sections?s 630 GeV / ?s
1800 GeV
Ratio
xT 2ET/?s
Shape of CDF and D0 Data and Theory agree above
xT 0.15,
62
Ratio of cross sections vs 630/vs1800

• Uncertainty from PDFs cancels in ratio!
• Normalization of NLO predictions do not match
  data
• Open issue no good explanation

63
Reality (closer) of proton- antiproton collision

• Initial state radiation (ISR) incoming parton
  emits a gluon extra jets, PT? 0
• Final state radiation (FSR) outgoing parton
  emits a gluon - extra jets
• Remnants of proton and antiproton interact
  producing low ET particles (Underlying Event)
• Can have collisions between more than one
  proton-antiproton pair ?Multiple interactions,
  can see multiple verticies in the detector
• Can have collisions between more than one parton
  within each incoming proton or
• antiproton ? double parton interactions

64
Event Generators

• Monte Carlo programs such as HERWIG, ISAJET, and
  PYTHIA are used today to reproduce all aspects of
  the events
• All based on LO matrix elements Leading Log
  Approximation.
• Include the effects of Initial and Final State
  radiation
• Different parton shower models are used by the
  different programs
• primary goal is to generate the shower of partons
  near the scattered parton direction.
• also includes some wide angle radiation which
  could produce additional jets.
• Hadronization model to covert colored partons to
  colorless hadrons
• Parton shower and hadronization parameters can be
  (are) adjusted to give good agreement with data.
• Underlying event
• assumed to be similar to Minimum Bias events in
  number of particles produced and their PT
  spectrum
• empirical and parameters can be tuned to give
  agreement with the data
• Output of these programs is a list of particles
  (mostly hadrons) which can be fed into a detector
  simulation

65
Fragmentation models

• Independent Fragmentation (Feynman-Field) Used
  in ISAJET and others
• each parton fragments independently
• scattered partons shower independently
• resulting partons are converted into hadrons
  independently
• can trace every particle back to original
  scattered parton
• can tune every aspect to give agreement with
  data.
• String Fragmentation Used in PTHYIA and others
• separate partons are connected by color strings
  with uniform energy/unit length
• Cluster Fragmentation Used by HERWIG and others
• Pairs of color color connected neighboring
  partons are combined into color signlets.
• Cluster and String models have more physics and
  less tunable parameters (see talk by Mrenna)

66
Correcting the data

• Generators are essential for correcting the
  measured data
• energy radiated outside the cluster or cone
• underlying event energy that sneaks into the
  cluster or cone
• feed detector simulations to study detector
  response
• Try minimize dependence of corrections on MC
  model by tuning parameters to data and by using
  data where ever possible.
• to minimize parton shower/hadronization
  differences we usually correct back to particle
  level
• cluster algorithm is run on generated particles
  (hadrons)
• derive corrections from difference between energy
  measured in the detector and the particle
  cluster
• Then we compare corrected data to LO or NLO
  parton level predictions
• ? Corrections depend on what you are
  comparing to!!
• for comparisons to LO an out-of-cone correction
  is needed
• for NLO no need for out-of-cone, NLO predictions
  can throw energy out of the cones.
• Can also compare raw data to fully simulated
  predictions
• disadvantage is that for any new prediction you
  need to resurrect and run the full simulation
  (generator detector simulation)
• These MC models also used in other measurements
  (e.g. top mass, Higgs search, etc) to derive
  corrections and uncertainties.

67
Multijet events High ET radiation

• CDF and D0 have studied event topologies up to 8
  Jets
• Many kinematic variables examples
• ?3 scattering angle of 3rd jet
• ?3 angle between 3-jet plane and plane
  containing lead jet and the beam
• Compare to QCD Generator Detector simulation
• HERWIG - 2?2 matrix elements parton shower
• NJETs leading order 2 ? N matrix elements, N
  2,...5, N6 uses approximation, ?R partons gt 0.9
• Phase space match mNj and mj/mNj to HERWIG

6-Jet events
68
Multijet events (3 jets)

• Angular distributions for 3-jet events (CDF)
• Phase space is uniform ? most different from
  data at edges!
• NJETs and HERWIG both pretty close to Data

?3 scattering angle of 3rd jet
angle between 3-jet plane and plane containing
lead jet and the beam.
69
Angular Distributions for 6-Jet events

• Successively combine lowest mass jet pairs to
  form 3-jet-like event
• plot the same angular variables
• Phase space is uniform ? divergences at edges
  are even
• more pronounced than in 3-jet case
• NJETs and HERWIG both pretty close to Data
• NJETS is closer to data at edges
• Amazing that HERWIG can reproduce 6-jet events at
  all!

70
Double Parton Scattering

• Two partons in each incoming hadron have a hard
  collision

m2 (1) if A and B are (in) distinguishable ?eff
process independent contains information
on spatial distribution of partons inside the
proton Uniform large ?eff Lumpy small ?eff
Uniform hard sphere ?eff 11 mb
71
Double Parton Scattering History

• Search in 4-jet samples for pairs of uncorrelated
  dijet events (m1)
• AFS ?eff 5mb Z.Phys. C34, 163 (1987)
• UA2 ?eff gt 8.3 mb PLB268, 145(1991)
• CDF ?eff 12.1 10.2 -5.4 mb PRD68, 4857
  (1993)
• hard sphere prediction protons are spherical
  and have uniform parton density ?eff 11mb
• CDF measurement with Run 1a photon 3 jet data
  (16 pb-1)
• PRD 56, 3811 (1997), PRL 79, 584 (1997)
• Isolated sample of events with 53 with double
  parton scattering events
• Used low ET jets to maximize cross sections
• Extracted result without relying on MC
  predictions

72
Double Parton Scattering Photon 3 jets
SP

• Look for events with a photon jet event plus an
  uncorrelated dijet event
• sensitive variable is angle between
• photon-jet and jet-jet pair
• Photon ET gt 16 GeV
• Jet ETgt5 GeV
• ET2 , ET3 lt 7 GeV
• ?R between photon and jets gt 0.8
• 16853 events with one vertex
• 5983 events with two pp interactions
  (2 vertex)
• generated uncorrelated DP models from data
• used 2-vertex data sample
• photon 1 jet 2-jet event (MIXDP)

73
Double Parton Scattering

• Find pairing that minimizes PT imbalance

SP
Data
Measure angle between the pairs ?S Single
parton (SP) scattering peaks at p Double parton
(DP) scattering is flat (uncorrelated to
photon) Fit Data to mixture of SP and DP
DP
Data is 52.6 2.5 0.9 DP! No evidence for
correlations between the two scatters ?eff 14.5
1.7 1.7 2.3 mb
74
Look for correlations in x

• Enrich sample
• ?S gt 1.2 ? 90 DP
• Compare data to
• model (no correlations)
• Data and model agree ?
• No observable correlations!

75
Reality (closer) of proton- antiproton collision

• Talked about
• production of extra jets (Initial and Final
  state radiation)
• Double parton interactions shown that they
  definately exist and rate is consistant with hard
  uniform sphere
• Multiple proton-antiproton collisions are
  identified in trackign chambers by two or more
  verticies.
• Now the Underlying Event or remnants of proton
  and antiproton collision

76
Underlying Event data

• Typically jet data is corrected for underlying
  event based on estimates from the data
• Jet Data
• Measure energy in cones located at ?? 90o from
  leading jet.
• plot energy of Min. and Max. energy separately.
• Observe (and expected) energy
• in higher ET cone is affected by radiation
  from other jets jets are rarely exactly 180 o
  apart
• Pretty good agreement with HERWIG for min. Cone
• Data is higher from Max cone.

Min. Cone
77
Underlying Event Minimum Bias data

• Minimum Bias Data
• triggered on hits in forward and backward
  scintillators
• events usually have one vertex and low ET
  particles
• no obviously discernable jet structure
• Min. Bias Data is result of soft collision
  between proton and antiproton
• Should be similar to interactions of remnants
  from a hard collision
• Note no sharp cut offs Jets dont suddenly
  appear at some threshold.
• We cant see very low ET jets because particles
  spread out.
• CDF measured energy in cones placed randomly in
  minimum bias data
• ? found same energy as in minimum cone
  analysis of Jet data
• (2.2 GeV)
• Note must be careful to correct for additional
  interactions MB data had an average of 1.05
  int., Jet data had an average of 2.1
• Take a large uncertainty (30 ) on Underlying
  event energy corrections because it is not well
  defined theoretically

78
Underlying Event Models
Min-Bias?

• The underlying event in a hard scattering process
  has a hard component (particles that arise from
  initial final-state radiation and from the
  outgoing hard scattered partons) and a soft
  component (beam-beam remnants).
• However the soft component is color connected
  to the hard component so this separation is (at
  best) an approximation.

• For ISAJET (no color flow) the soft and hard
  components are completely independent and the
  model for the beam-beam remnant component is the
  same as for min-bias but with a larger ltPTgt.
• HERWIG breaks the color connection with a soft
  q-qbar pair and then models the beam-beam remnant
  component the same as HERWIG min-bias (cluster
  decay).

79
Underlying Event Multiple Parton Interactions

• PYTHIA models the soft component of the
  underlying event with color string fragmentation,
  but in addition includes a contribution arising
  from multiple parton interactions (MPI) in which
  one interaction is hard and the other is
  semi-hard.

• The probability that a hard scattering events
  also contains a semi-hard multiple parton
  interaction can be varied but adjusting the
  cut-off for the MPI.
• One can also adjust whether the probability of a
  MPI depends on the PT of the hard scattering,
  PT(hard) (constant cross section or varying with
  impact parameter).
• One can adjust the color connections and flavor
  of the MPI (singlet or nearest neighbor, q-qbar
  or glue-glue).
• Also, one can adjust how the probability of a MPI
  depends on PT(hard) (single or double Gaussian
  matter distribution).

80
Charged particle distributions in data
Underlying Event plateau

• Define Df lt 60o as Toward, 60o lt Df lt 120o
  as Transverse,
• and Df gt 120o as Away.
• All three regions have the same size in h-f
  space, DhxDf 2x120o 4p/3
• Plot the average number of charged particles (PT
  gt 0.5 GeV, h lt 1, including jet1) vs Jet1 PT
• The solid (open) points are the Min-Bias (JET20)
  data. Smooth connection!

81
Transverse PT distributions

• Plot the PT distribution of the Transverse
  ltNchggt, dNchg/dPT.
• for different jet PT
• The integral of dNchg/dPT is the Transverse
  ltNchggt.
• The triangle and circle (square) points are the
  Min-Bias (JET20) data.

82
Transverse ltNchggt vs PTJet1
Isajet 7.32
Pythia 6.115
Herwig 5.9

• Compare data to the the QCD hard scattering
  predictions of HERWIG 5.9, ISAJET 7.32, and
  PYTHIA 6.115 (default parameters with PT(hard)gt3
  GeV/c).
• Tracking eff. has been included in MC predictions

83
ISAJET Transverse Nchg versus PT(jet1)
ISAJET total
Outgoing jets Initial and Final State Radiation
Beam-Beam Remnants

• ISAJET 7.32 (default parameters with PT(hard)gt3
  GeV/c) .
• ISAJET has two categories that contribute to
  transverse region
• charged particles that arise from the break-up of
  the beam and target (beam-beam remnants)
• charged particles that arise from the outgoing
  jet plus initial and final-state radiation (hard
  scattering component).

84
HERWIG Transverse Nchg versus PT1
HERWIG
Beam-Beam Remnants
Outgoing Jets plus Initial Final-State Radiatio
n

• HERWIG 5.9 (default parameters with PT(hard)gt3
  GeV/c).
• HERWIG has two categories
• charged particles that arise from the break-up of
  the beam and target (beam-beam remnants)
• charged particles that arise from the outgoing
  jet plus initial and final-state radiation (hard
  scattering component).

85
PYTHIA Transverse Nchg versus PT1
PYTHIA
Outgoing Jets plus Initial Final-State Radiatio
n
Beam-Beam Remnants plus Multiple Parton
Interactions

• PYTHIA 6.115 (default parameters with PT(hard)gt3
  GeV/c).
• PYTHIA particles are divided into two categories
• charged particles that arise from the break-up of
  the beam target (beam-beam remnants including
  multiple parton interactions)
• charged particles that arise from the outgoing
  jet plus initial and final-state radiation (hard
  scattering component).

86
Compare Hard Scattering Components
ISAJET
PYTHIA
HERWIG

• HERWIG and PYTHIA modify the leading-log picture
  to include color coherence effects
• leads to angle ordering within the parton
  shower
• Angle ordering produces less high PT radiation
  within a parton shower. (See talk by S. Mrenna)

87
ISAJET TransversePT Distribution
PT(charged jet1) gt 30 GeV/c Transverse ltNchggt
3.7
PT(charged jet1) gt 5 GeV/c Transverse ltNchggt
2.0

• Look at PT distribution for jets with ETgt 5 and
  30 GeV

88
ISAJET Transverse PT Distribution
PT1gt5GeV
PT1gt30GeV
exp(-2pT)

• Dashed curve is the beam-beam remnant component
  and the solid curve is the total (beam-beam
  remnants plus hard component).

89
HERWIG Transverse PT Distribution
PT(charged jet1) gt 30 GeV/c Transverse ltNchggt
2.2
PT(charged jet1) gt 5 GeV/c Transverse ltNchggt
1.7
90
HERWIG TransversePT Distribution
exp(-2pT)
same

• The dashed curve is the beam-beam remnant
  component and the solid curve is the total
  (beam-beam remnants plus hard component).

91
PYTHIA Transverse PT Distribution
Includes Multiple Parton Interactions
PT(charged jet1) gt 30 GeV/c Transverse ltNchggt
2.9
PT(charged jet1) gt 5 GeV/c Transverse ltNchggt
2.3
Can vary the parameters for Multiple interactions
assumes a varying impact parameter and a
hadronic matter overlap consistent with a
single or double Gaussian matter distribution,
with a smooth turn-off PT0PARP(82)
92
PYTHIA Multiple Parton Interactions
Vary impact parameter Tune to data
Note Multiple parton interactions depend on the
PDFs!
93
Tuned PYTHIA Transverse PT Distribution
Includes Multiple Parton Interactions
PT(charged jet1) gt 30 GeV/c Transverse ltNchggt
2.7
PT(charged jet1) gt 5 GeV/c Transverse ltNchggt
2.3

• Tuned PYTHIA CTEQ4L, MSTP(82)4 (hard core),
  PT0PARP(82)2.4 GeV/c.

94
Tuned PYTHIA Transverse PT Distribution
Includes Multiple Parton Interactions

• PYTHIA 6.115 with PT(hard) gt 0, CTEQ4L,
  MSTP(82)4, PT0PARP(82)2.4 GeV/c.
• The dashed curve is the beam-beam remnant
  component and the solid curve is the total
  (beam-beam remnants plus hard component).

95
The Underlying Event Summary Conclusions

• ISAJET (FF) produces too many (soft) particles
  and the wrong dependence on PT1.
• HERWIG and PYTHIA (modified LLA) do a better job
  describing the underlying event.
• ISAJET and HERWIG do not have enough beam-beam
  remnants with PT gt 0.5 GeV/c.
• PYTHIA (with multiple parton interactions) has
  best description of the underlying event.
• Recently an underlying event that depends on
  multiple parton interactions was included in
  HERWIG.
• Multiple parton interactions gives a natural way
  of explaining the underlying event in a hard
  scattering, and have been observed in photon
  jet data
• Warning to Top-mass type studies
• Multiple parton interactions are very sensitive
  to the parton structure functions. You must
  first decide on a particular PDF and then tune
  the multiple parton interactions to fit the data

96
Fragmentation models and Clustering

• Independent Fragmentation (ISAJET)
• each parton fragments independently
• simple to trace parentage of hadrons
• doesnt describe data very well
• Cluster Fragmentation (HERWIG)
• Pairs of color color connected neighboring
  partons are combined into color singlets.
• Cant trace parentage of hadrons back to original
  partons
• Gives generally good agreement with data
• Clustering
• imposing a cone algorithm conceptually implies
  independent fragmentation
• Cluster fragmentation suggests imposing a cone
  will be artificially cutting color lines
• Successive recombination algorithms (e.g. KT)
  maybe more natural
• Difficulty with KT algorithms is derivation of
  corrections for variable size jets ? Recent D0
  result

97
Jet Algorithms NLO, NNLO considerations

• Jet algorithm should be insensitive to
• infrared and collinear divergences
• hadronization
• logitudinal boosts

Infrared problem adding an infinately soft
parton should not change the number of jets
Collinear problem replacing any parton with a
collinear pair of partons should not change the
number of jets
Note The calorimeter towers the
preclustering (grouping) of towers in a
detector integrate over these effects in the data
Cone Algorithm is Not IR safe at NNLO KT is safe
at all orders
98
KT algorithm at Hadron Colliders

• Successively associate pairs of particles
• dij min(PTi2,PTj2) ?Rij2/D2
• where ?Rij2 (?i ?j)2 (fi fj)2
• and for each particle define di PTi2

Uses one parameter D ? minimum separation
between final jets For D1 and Rijltlt1 dij
relative pT (KT)
Find minimum of di and dij ? dmin If dmin
dij ? merge particles If dmin di ? remove i
from particle list and add to jet list Keep going
until all particles are assigned to a
jet. Result list of jets with separation between
them D

Note all particles in a cone of radius R around
the centroid are not necessarily included in the
KT jet and particles far from the centroid can
be included.
99
KT Algorithm

• soft and collinear particles are merged first
• Final jets separation gt D
• D is the only parameter (cone algo has Cone
  Radius and Rsep)
• KT algo is IR safe to all orders
• At LO KT cone (1parton/jet)
• At NLO D 1 gives same result as R0.7, Rsep1.3
• (Ellis-Soper PRD 48, 3160)
• At higher orders this relationship might not
  hold

100
Inclusive Jet Cross Section with KT Algo.
D0 KT papers hep-ex/0108054 (PRD) and
hep-ex/0109041 (PRL)
101
KT Algorithm ? Cone in DATA

• Cross sections are different at low PT
• Match leading two jets in ?-f (?Rlt0.2)
• plot PTKT ETcone vs PT

KT jets are more energetic 7 ( 4GeV) at 60
GeV 3 (6 GeV) at 200 GeV
If shift the cone cross section by this measured
difference then the cross sections agree
102
Compare KT and Cone jets with HERWIG

• Generate Jet events with HERWIG down to particles
• Run KT and Cone algos on particles
• match the two leading clusters in ?-f (?Rlt0.2)
  and plot the difference

HERWIG shows KT algo picks up more energy than
cone Level is smaller than in data 2 (1) at
60(200)GeV HERWIG flat 2 GeV Data 4 - 6 GeV
Overall uncertainty is 2 on energy scale so
these agree at 2?
103
KT and Cone Jets look inside HERWIG Jets

• Look at distance to furthest particle from jet
  centroid
• KT jets have more particles far from centroid
• Cone also has particles outside radius due to
  merged jets but at a lower level than KT jets

Number of particles in jet is 30 larger for KT
jets
KT and cone jets are different!
104
Quantify effect of hadronization

• Generate HERWIG jets
• Compare KT and Cone algos at parton level and
  after hadronization particle level for two
  leading jets
• KT jets pick up more energy than in parton level
  by including partons far from the original
  parton.
• cone jets lose energy outside the cone

Add the HERWIG hadronization effect to the NLO
predictions ? Difference between data and theory
at low pT is reduced ? Remaining difference is
large ? More interplay between data and theory is
needed!
105
Quark and Gluon Jets with the KT algorithm

• Quarks and gluons radiate proportional to their
  color factors

• Expect gluon jets to be broader than quark jets
• Gluon jets should have softer fragmentation,
• (more low energy particles)

106
Separation of quark and gluon jets

• LEP extensive studies of quark-gluon separation
  (Bill Garys talk)
• At Fermilab we can compare the samples from
  different CM energies

For the ET range of 50-60 GeV, HERWIG predicts a
gluon jet fraction of 66 vs 1800 GeV
and 47 vs 630 GeV
107
Quark Gluon separation (D0 analysis)

• use the KT algorithm to look for subjet
  structures
• inside the jets
• dij min(pTi2,pTj2) ?Rij2/D2 gt ycutpTjet2
• For ycut 1, Nsubjet 1
• For ycut ? 0 Nsubjet ? 8
• Count the number of subjets and compare to
  predictions
• Chose fixed ycut 0.001
• This corresponds to minimum of 3 of total jet pT
  in a subjet

108
Quark Gluon separation and subjets

• Plot the number of jets of multiplicity M
  normalized by the total number of jets for
  different subjet multiplicities at CM 1800 and
  630 GeV
• The subjet multiplicity M in a sample is a
  combination of the multiplicities of quark ( Mq)
  and gluon (Mg) jets
• M fMg (1-f)Mq
• where f is the fraction of gluon jets and (1-f)
  is the fraction of quark jets

For two samples with different fractions Mq
f1800M630 f630M1800/(f1800-f630) Mg
(1-f630)M1800- (1-f1800)M630 /(f1800-f630)
109
Quark Gluon separation
110
Compare Subjet Multiplicity to Predictions

• HERWIG is in great agreement with data.
• ? ask Steve Mrenna
• to explain how HERWIG can do so well!
• Analytic resummed calculation predicts higher
  multiplicies in gluon jets
• Smaller effect in quark jets

111
QCD in Run II

• Run I
• 20 events with ETgt 400 GeV
• Run II
• 1K events ETgt 400 GeV
• 100 Events ETgt 490 GeV
• Great reach in high x and Q2
• search for new physics
• test QCD predictions in new regions

Jet ET
112
Summary

• Covered a wide variety of topics related to
  production and evolution of high energy jets
• Inclusive jet cross sections
• Multijet production
• Double parton scattering
• Underlying event
• Cone and KT clustering algorithms
• Separation of quark and gluon jets
• Set stage for upcoming talks
• What is in the theory and the event generators
  and how well they agree with data
• More details on generators from Steve Mrenna
• Walter Giele will talk about how to derive new
  PDFs
• Keep in mind some of these issues when you hear
  talks on searches for new physics, the HIGGS,
  precision top mass etc.
• Main message Experimental and Theoretical
  understanding progress together
• Run II has new CM energy (1.96 TeV) and lots of
  new data!