Brenna Flaugher CTEQ Summer School 2002 1 Production and Evolution of High Energy Jets Outline (both lectures) A look at the data Theoretical framework

Brenna Flaugher CTEQ Summer School 2002

1

Production and Evolution of High Energy Jets

Outline (both lectures)A look at the data

Theoretical frameworkInclusive Jet Cross sections

Multijet EventsDouble Parton Scattering

Underlying EventClustering algorithmsStructure inside jets

Overall Theme: Interplay of Theory and Measurements

Day 1

Day 2


2

Simple view of a proton - antiproton collision

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

pp

jet

jet

detector

z

yx

Pseudo-rapidity:= - ln tan Simple translation (additive) under longitudinal boosts


3

• Fermilab Tevatron collides protons and antiprotons at

√s = 1.96 GeV (was 1.8 TeV in Run 1)

• These collisions produce the highest energy jets (ET~500 GeV)

• Probes proton structure to smallest distance scales

= hc/Mc2 = 197MeVfm/500 GeV = 4x10-17cm

Jets at Fermilab Hadron Collider

Jet ET =Sum of towers = 415 GeV

Electromagnetic

p

p

Hadronic


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

Tracks in magnetic field

Azimuthalangle

Can measure momentum of charged particles in tracking chambers. Neutral particles e.g (π0) are measured only by the calorimeters


7

More complicated events: three-jet event

ET = 328 GeV

η = 0.21φ = 2.5o

ET = 173 GeV

η = -0.57φ = 192.4o

ET = 123 GeV

η = 0.23φ = 170.4o


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A five-jet event


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6 - jet events


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From Partons to Jets

Leading Order TheoryUses 2→2 matrix elements

Leading Log Approximation (LLA):sum leading contributions to all orders (from ~collinear radiation of quarks and gluons around original parton)

Only two jets in final state Only one parton/jet

Parton Shower


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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 √s ? – 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

antiprotonproton

scattered parton

Rapidity (y):

Pseudorapidity (): high energy limit (m«pT, β → 1)

y

z

x

costanh y where = p/E

Rapidity and Pseudo-rapidity are simply additive under longitudinal boosts


15

Parton momentum fractions

x1 = (eη1 + eη2) ET/√s

x2 = (e-η1 + e-η2) ET/√s

x1 and x2 can not exceed unity

η = -ln tan θ/2

xT = 2ET/s and xT2 <x1x2<1

As xT → 1, x1 and x2 are tightly constrained

CM 1

2

1

2

Lab

boost = ½ (1 + 2)

* = ½ (1 - 2)

Lab = * + boost

θ*


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Kinematic Variables• Energy E: E2 = m2 + p2

= ET cosh η

• Transverse Energy ET:

ET= m2 + px2 + py

2 = Esinθ = E2- pz

2• Momentum p:

p2 = px2 + py

2 + pz2

• Longitudinal momentum

pz = E tanh η

= ET sinh η

• Transverse Momentum pT

pT = px2 + py

2 = psinθ

•Invariant Mass for di-jet event:

M122 = (p1 + p2)2

=m12 +m2

2 + 2(E1E2-p1·p2)

•For m1, m2 0

M122 → 2ET1ET2(coshΔη – cosΔφ)


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Phase Space Boundaries for 2 2 Scattering

2

1

s = 2 TeV andJet ET = 100, 200 and 400 GeV

• phase space shrinksas ET increases•for1 ~ -2 , boost → 0•for1 ~ 2 , M12

2~ 4ET2


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Leading Order Two-Jet Cross Section

where,• fi(x,F) (i = g, q, q) is the PDF• |Mij| is lowest order matrix element for ij2 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

Many processes contribute:

At leading order ET1 =ET2 =ET

Usually assume F= R = ~ ET/2


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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

xT = 2ET/s

Fra

ctio

n o

f tot

al

Solid: s = 2 TeV

Dashed: s = 14 TeV

Lowest ET jets from Tevatron are ~20 GeVor xT ~ 0.02gluon initial states dominate

Highest ET jets are ~500 GeV or xT~ 0.5qq dominates, but qg still ~20% of total


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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:


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Parton Luminosity

boost

x 1F

(x1,µ

)x2F

(x2,µ

)

•For ET =100 GeV and √s = 2TeV largest luminosity is when x1 and x2 are equally small boost ~ * =0

• As |boost| or |*| increases luminosity decreases rapidly

• 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 *


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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 doesn’t!)

• 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


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Digression on the scales F and R cont.

αs2 for different R

compared to R = ET

Rat

io

for different F compared

to F = ET at η1 = η2 =0

Dependence of LO on choice of scales flat at ~ 10% level for =ET/2but 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 η range• Can search for signs of composite quarks


26

Inclusive Jet Cross Section and Compositeness• Hypothesis: Quarks are

bound states of preons which interact via new strong interaction

The composite interactions are represented by a contact term:

• Compositeness Scale: c

c = pointlike quarks

c = finite → substructure

at mass scale of c

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


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Measurements of Inclusive Jet Cross Section

• In the 80’s, only Leading Order 2→2 predictions were available• High energy Jet data was just becoming available • AFS √s = 63 GeV – initial hints of 2-jet structures

• UA1 and UA2: √s = 546 and 630 GeV , (ET ~20-150 GeV)

• CDF 1987 √s = 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)


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Uncertainties• LO Theory:

– PDFs – derived from global fits to data (See talk by Walter Giele)

– Choice of scale for evaluation of αs 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)


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Inclusive Jet Cross Sections from the 80’s

UA1 Unc. ~ 70%± 50% jet corr.± 40% jet calib± 10% aging± 15% lumΛc >400 GeV

UA2 Unc. ~32%± 25% Frag. model± 15% jet id± 11% calib± 5% lumΛc >825 GeV

While data and theory agreed qualitativly, large uncertainties existed in both theoretical predictions and in experimental measurements

Theory uncertainties mainly on normalization – compositeness limitsset based on shape at high ET

CDF 1987 dataExp. Unc. 70% @ 30 GeV34% @ 250 GeVΛc >700 GeV


30

NLO 2→2 Theory predictionsLate 80’s NLO parton level predictions became availableAversa et al PLB 210,225 (1988), S.Ellis, Kuntz, Soper, PRL 62,2188(1989) ( EKS)

1 loop, 2 parton final statesame kinematics as LO1 parton = jet

tree level, 3 parton final stateor 2+1 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 towersis reached. Finally:

Snowmass studies (1992) found that for a cone size of 0.7 out-of-cone energy ~ underlying event


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Inclusive cross section compared to NLO

• CDF collected data in 1989:– 4pb-1 √s = 1800 GeV– 8nb-1 √s = 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 Λc>1.4 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 ET = 100 GeV • Best agreement with

very small scale ET/4

• Introduce ad-hoc parameter Rsep which scales radius for parton merging:

ΔRparton = Rsep Reffectively reduces parton cone size

• Snowmass: Rsep = 2

Rsep = 1.3

µ = ET/2 solidµ= ET short dashµ=ET/4 long dash

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

Theory: PRL 69, 3615 (1992)


35

Jet Shape Measurement

µ = ET/2 solidµ= ET short dashµ=ET/4 long dash

Rsep = 1.3

Measure energy

inside subcones around jet axis

F(r) = ET(r)/ET(R)

ET/4 give worst agreementRsep = 1.3 gives best agreement with data

Data:PRL 70, 713 (1993)Thy: PRL 69, 3615 (1992)

Jet ET = 100 GeV


36

Snowmass didn’t 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 ΔR>2Rcone

ET = 123 GeV

η = 0.23

φ = 170.4o

ET = 173 GeV

η = -0.57

φ = 192.4o

ΔR = 0.88


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

(divided by R)

Rsep of 1.3 makes sense! Explains better match betweendata and theory


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:

where ET1 > ET2>ET3 etc.

• Since ET2 can now be < ET1, |η2| can increase compared to LO

• Adding more partons (e.g.NNLO)further increases allowed range

• Still have sharp cutoff on η1

• η2 can be bigger than η1

η1

η2

ET= 50 GeV√s = 1.8 TeV


40

Compare LO and NLO predictions

η

K factor = NLO/LO

~10% for |η|<1.5, away from PS boundaries

Large corrections for large | η2|

→stay away from there, theory not reliable at LO or NLO


41

Scale dependence

where L = log(µR/ET) and bi

are the beta functionsd/

dET

at E

T =

10

0 G

eV

µR /ET

NNLO coefficient C is unknown.Curves show guessesC=0 (solid)C=±B2/A (dashed)

Dependence on choiceof scale is reducedas higher orders are included

LO

NLO

NNLO

Usual range


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 αs(ET)n, can extract αs 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


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Effect of Scale on NLO 2→2 Inclusive Jet Cross Section Predictions


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• Excess observed above 200GeV

• In 1996 all PDFs gave roughly same shape

• Motivated discussions of new physics as well and PDF uncertainties

CDF Run 1A Inclusive Cross Section (1996)


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PDF uncertainties 2000

• 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!!

Ratio of inclusive jet cross section for different PDFs compared to CTEQ4M


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Alternate Variables: Mass and Angle• can write cross section in terms of dijet mass M12 and the

center of mass scattering angle θ* :

M122 = 4ET

2cosh2η*cos θ* = tanh η*t = - (1-cos θ* )s/2

Typically measure • dijet mass spectrum: d/dMJJ

by integrating over a fixed angular range• angular distibution : d/dcosθ* for intervals of dijet mass


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Angular Distribution – Not sensitive to PDFS

• Dominant subprocesses have similar shape for angular distribution d/dcosθ* 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

Change to a better angular variable:

d/d

χ

QCD is dominated by ~ 1/(1-cos θ*)2

Contact terms by ~ ~ 1/(1+cos θ*)2

Difference in forward η region is hard to measure

Much more sensitive to contact term

large difference from QCDin central region


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Limits on Quark SubstructureD0 Run IB results


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Limits on Quark Substructure


51

Inclusive Jet Cross Section Run Ib

CDF Results

0.1<|η|<0.7

Data and Predictions span 7 orders of magnitude!


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Inclusive cross section in detail (linear scale)

• 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!

CDF Run 1B data


53

η 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 η


54

CDF and D0 Comparison

CDF and D0 see fantastic agreement in 0.1<|η|<0.7 range

Note, this is corrected for the different luminosity cross sections used at the time of the measurements


55

Inclusive cross section and αs

• Use inclusive jet cross section data and NLO theory to extract αs

(only possible if use µR ∝ETjet)

• Clearly observe running of αs over a wide range of Jet ET

s(Mz) = 0.1178 ± .0001(stat.) +.0081 -.0095 (exp. sys), Thy unc. 5% PDFs, 5% scale

d/dET = s(µR )2A

+ s(µR )3(B + 2b0LA) + s(µR )4(C + 3b0LB + (3b0

2L2+ 2b1L)A)


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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!)

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

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 partonscombine into one jet


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


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Inclusive Cross sections at different CM

XT=2ET/√s

ET


60

Scaled Cross Section• Can rewrite inclusive jet cross section in terms of dimensionless

quantity xT

• Scaling means predictions are independent of √s

• 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

xT = 2ET/s

Rat

io

Shape of CDF and D0 Data and Theory agree above xT ~ 0.15,


62

Ratio of cross sections √s = 630/√s=1800

• 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

Proton AntiProton

PT(hard)

Outgoing Parton

Outgoing Parton

Underlying Event Underlying Event

Initial-State Radiation

Final-State Radiation


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

– θ3 = scattering angle of 3rd jet– Ψ3= 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, N=6 uses approximation, ΔR partons > 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

θ3 = scattering angle of 3rd jet angle between 3-jet plane and plane containing lead jetand 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

m=2 (1) if A and B are (in) distinguishable

eff process independent

contains information onspatial 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 (m=1)

– AFS eff ~ 5mb [Z.Phys. C34, 163 (1987)]

– UA2 eff > 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• 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 > 16 GeV• Jet ET>5 GeV• ET2 , ET3 < 7 GeV• ΔR between photon and jets > 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)

SP


73

Double Parton Scattering

Find pairing that minimizes PT imbalance

Measure angle between the pairs: ΔS

Single parton (SP) scattering peaks at π

Double parton (DP) scattering is ~ flat (uncorrelated to photon)

Fit Data to mixture of SP and DP

SP

DP

Data

Data is 52.6 ±2.5 ±0.9% DP!No evidence for correlationsbetween the two scatters

eff = 14.5 ±1.7 + 1.7 – 2.3 mb


74

Look for correlations in x

• Enrich sample:

ΔS > 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

Proton AntiProton

PT(hard)

Outgoing Parton

Outgoing Parton

Underlying Event Underlying Event

Initial-State Radiation

Final-State Radiation


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 Δ =±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 don’t suddenly appear at some threshold.

• We can’t 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.

Proton AntiProton

“Hard” Collision

initial-state radiation

final-state radiation outgoing parton

outgoing parton

color string

color string

+

“Soft” Component “Hard” Component


final-state radiation outgoing jet

Beam-Beam Remnants

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 <PT>.

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”.

color string

color string

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).

+

“Semi-Hard” MPI “Hard” Component


final-state radiation outgoing jet Beam-Beam Remnants

or

“Soft” Component


80

Charged particle distributions in data

• Define || < 60o as “Toward”, 60o < || < 120o as “Transverse”,

• and || > 120o as “Away”.

• All three regions have the same size in - space, x = 2x120o = 4/3

• Plot the average number of charged particles (PT > 0.5 GeV, || < 1, including jet#1) vs Jet1 PT

• The solid (open) points are the Min-Bias (JET20) data. Smooth connection!

Charged Jet #1Direction

“Toward”

“Transverse” “Transverse”

“Away”

Underlying Event“plateau”

Nchg versus PT(charged jet#1)

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35 40 45 50

PT(charged jet#1) (GeV/c)

<N

ch

g>

in

1 G

eV

/c b

in1.8 TeV ||<1.0 PT>0.5 GeV

"Toward"

"Away"

"Transverse"

CDF Preliminarydata uncorrected


81

Transverse PT distributions

• Plot the PT distribution of the “Transverse” <Nchg>, dNchg/dPT.

for different jet PT

• The integral of dNchg/dPT is the “Transverse” <Nchg>.

• The triangle and circle (square) points are the Min-Bias (JET20) data.

Charged Jet #1Direction

“Toward”


“Away”

"Transverse" PT Distribution (charged)

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 2 4 6 8 10 12 14

PT(charged) (GeV/c)

dN

ch

g/d

PT

(1

/Ge

V/c

)

CDF Preliminarydata uncorrected

1.8 TeV ||<1 PT>0.5 GeV/c

PT(chgjet1) > 2 GeV/c




82

Transverse <Nchg> vs PTJet1

• 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)>3 GeV/c).

• Tracking eff. has been included in MC predictions

Pythia 6.115

Herwig 5.9

Isajet 7.32Charged Jet #1

Direction

“Toward”


“Away”

"Transverse" Nchg versus PT(charged jet#1)

0

1

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5

0 5 10 15 20 25 30 35 40 45 50


"Tra

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in

Herwig Isajet Pythia 6.115 CDF Min-Bias CDF JET20

1.8 TeV ||<1.0 PT>0.5 GeV

CDF Preliminarydata uncorrectedtheory corrected


83

ISAJET: “Transverse” Nchg versus PT(jet#1)

• ISAJET 7.32 (default parameters with PT(hard)>3 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).

Beam-BeamRemnants

Outgoing jets +Initial and Final State Radiation

ISAJET total "Transverse" Nchg versus PT(charged jet#1)

0

1

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"Tra

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1.8 TeV ||<1.0 PT>0.5 GeV


Beam-Beam Remnants

Isajet Total

Hard Component


84

HERWIG: “Transverse” Nchg versus PT1

• HERWIG 5.9 (default parameters with PT(hard)>3 GeV/c).• HERWIG has two categories:

– charged particles that arise from the break-up of the beam and target (beam-beam remnants)


Beam-BeamRemnants

Outgoing Jetsplus

Initial & Final-StateRadiation

HERWIG"Transverse" Nchg versus PT(charged jet#1)

0

1

2

3

4

0 5 10 15 20 25 30 35 40 45 50

PT (charged jet#1) (GeV/c)

"Tra

ns

ve

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V/c

bin

1.8 TeV ||<1.0 PT>0.5 GeV Beam-Beam Remnants

Hard Component


Herwig Total


85

PYTHIA: “Transverse” Nchg versus PT1

• PYTHIA 6.115 (default parameters with PT(hard)>3 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)


Beam-Beam Remnants

plusMultiple Parton

Interactions

Outgoing Jetsplus

Initial & Final-StateRadiation

PYTHIA"Transverse" Nchg versus PT(charged jet#1)

0

1

2

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4

0 5 10 15 20 25 30 35 40 45 50


"Tra

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1.8 TeV ||<1.0 PT>0.5 GeV


Beam-Beam Remnants

Pythia 6.115 Total

Hard Component


86

Compare Hard Scattering Components

• 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)

HERWIG

PYTHIA

ISAJET"Transverse" Nchg versus PT(charged jet#1)

0

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"Tra

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1.8 TeV ||<1.0 PT>0.5 GeV

theory corrected

Hard Scattering ComponentIsajet

Pythia 6.115

Herwig


87

ISAJET: “Transverse”PT Distribution

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

PT(charged jet#1) > 5 GeV/c“Transverse” <Nchg> = 2.0



1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 2 4 6 8 10 12 14

PT(charged) (GeV/c)d

Nc

hg

/dP

T (

1/G

eV

/c)


1.8 TeV ||<1




Isajet 7.32


0

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1.8 TeV ||<1.0 PT>0.5 GeV


Beam-Beam Remnants

Isajet Total

Hard Component


88

ISAJET: “Transverse” PT Distribution

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


1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 2 4 6 8 10 12 14

PT(charged) GeV/cd

Nc

hg

/dP

T (

1/G

eV

/c)


PT(charged jet#1) > 30 GeV/c

1.8 TeV |eta|<1Isajet Total

Beam-Beam Remnants


1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 1 2 3 4 5 6 7

PT(charged) GeV/c

dN

ch

g/d

PT

(1

/Ge

V/c

)



1.8 TeV ||<1

Isajet Total

Beam-Beam Remnants

exp(-2pT)

same

PT1>5GeV PT1>30GeV


89

HERWIG: “Transverse” PT Distribution




0

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PT (charged jet#1) (GeV/c)

"Tra

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Hard Component


Herwig Total


1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 2 4 6 8 10 12 14


Nc

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T (

1/G

eV

/c)


1.8 TeV ||<1




Herwig 5.9


90

HERWIG: “Transverse”PT Distribution

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


1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 1 2 3 4 5 6 7

PT(charged) GeV/c

dN

ch

g/d

PT

(1

/Ge

V/c

)



1.8 TeV ||<1

Beam-Beam Remnants

Herwig Total


1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 2 4 6 8 10 12 14

PT(charged) GeV/c

dN

ch

g/d

PT

(1

/Ge

V/c

)



1.8 TeV ||<1

Herwig Total

Beam-Beam Remnants

exp(-2pT)

same


91

IncludesMultipleParton

Interactions

PYTHIA: “Transverse” PT Distribution




0

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Beam-Beam Remnants

Pythia 6.115 Total

Hard Component


1.0E-05

1.0E-04

1.0E-03

1.0E-02

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1.0E+01

0 2 4 6 8 10 12 14


Nc

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/dP

T (

1/G

eV

/c)


1.8 TeV ||<1




Pythia 6.115

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 PT0=PARP(82)


92

Note: Multiple parton interactions depend on the PDF’s!

PYTHIA Multiple Parton Interactions


0

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"Tra

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1.8 TeV ||<1.0 PT>0.5 GeV

CDF Preliminarydata uncorrectedtheory corrected CTEQ3L MSTP(82)=3

PARP(82) = 1.35 GeV/c

CTEQ3L MSTP(82)=3PARP(82) = 1.55 GeV/c

GRV94L MSTP(82)=3PARP(82) = 1.55 GeV/c

CTEQ4L MSTP(82)=3PARP(82) = 1.8 GeV/c

Vary impact parameter: Tune to data


93


Interactions

Tuned PYTHIA: “Transverse” PT Distribution

• Tuned PYTHIA: CTEQ4L, MSTP(82)=4 (hard core), PT0=PARP(82)=2.4 GeV/c.




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Pythia CTEQ4L (4, 2.4 GeV/c)

Hard Component



1.0E-05

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0 2 4 6 8 10 12 14


Nc

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/dP

T (

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/c)





1.8 TeV ||<1



94


Interactions

Tuned PYTHIA: “Transverse” PT Distribution

• PYTHIA 6.115 with PT(hard) > 0, CTEQ4L, MSTP(82)=4, PT0=PARP(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).


1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 2 4 6 8 10 12 14

PT(charged) GeV/c

dN

ch

g/d

PT

(1

/Ge

V/c

)



1.8 TeV ||<1


Beam-Beam Remnants


1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 1 2 3 4 5 6 7

PT(charged) GeV/c

dN

ch

g/d

PT

(1

/Ge

V/c

)



1.8 TeV ||<1

Beam-Beam Remnants



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 > 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– doesn’t describe data very well

• Cluster Fragmentation (HERWIG)– Pairs of color color connected neighboring partons are

combined into color singlets.– Can’t 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 safeat NNLOKT is safe at all orders


98

KT algorithm at Hadron CollidersSuccessively associate pairs of particles:

dij = min(PTi2,PTj

2) ΔRij2/D2

where ΔRij2 = (ηi – ηj)2 + (φi + φj)2

and for each particle define di = PTi2

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 ≥ DNote – 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.

Uses one parameter: D → minimum separation between final jets

For D=1 and Rij<<1dij = relative pT (=KT)


99

KT Algorithm

• soft and collinear particles are merged first

• Final jets separation > 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 R=0.7, Rsep=1.3 (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 η-φ (ΔR<0.2)

• plot PTKT – ET

cone vs PT

KT jets are more energetic7% ( ~4GeV) at 60 GeV3% (~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 η-φ (ΔR<0.2) and plot

the differenceHERWIG shows KT algo picks up more energy than cone

Level is smaller than in data2% (1%) at 60(200)GeV

HERWIG ~ flat 2 GeVData: 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 Gary’s 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% √s = 1800 GeV and~47% √s = 630 GeV


107

Quark – Gluon separation (D0 analysis)

use the KT algorithm to look for subjet structures

inside the jets:

dij = min(pTi2,pTj

2) ΔRij2/D2 > ycutpTjet

2

For ycut = 1, Nsubjet = 1

For ycut → 0 Nsubjet → ∞

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 ET> 400 GeV• Run II

~1K events ET> 400 GeV

~100 Events ET> 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!

Documents

Brenna Flaugher CTEQ Summer School 2002 1 Production and Evolution of High Energy Jets Outline (both lectures) A look at the data Theoretical framework