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- 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

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

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

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.

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

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

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

A five-jet event

6 - jet events

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

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

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

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

?

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

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

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)

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

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

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

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

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

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

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

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

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

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

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)

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)

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

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

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

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

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!

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)

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)

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

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)

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

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

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

?

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

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

Effect of Scale on NLO 2?2 Inclusive Jet Cross

Section Predictions

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

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!!

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

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

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

Limits on Quark Substructure

D0 Run IB results

Limits on Quark Substructure

Inclusive Jet Cross Section Run Ib

- CDF Results
- 0.1lt?lt0.7

Data and Predictions span 7 orders of magnitude!

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!

? 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 ?

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

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

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

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!

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

Inclusive Cross sections at different CM

ET

XT2ET/vs

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

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,

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

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

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

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)

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.

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

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.

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!

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

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

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)

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

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!

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

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

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

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).

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).

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!

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.

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

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).

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).

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).

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)

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

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).

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

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).

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)

PYTHIA Multiple Parton Interactions

Vary impact parameter Tune to data

Note Multiple parton interactions depend on the

PDFs!

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.

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).

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

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

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

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.

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

Inclusive Jet Cross Section with KT Algo.

D0 KT papers hep-ex/0108054 (PRD) and

hep-ex/0109041 (PRL)

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

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?

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!

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!

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)

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

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

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)

Quark Gluon separation

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

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

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!