nikos varelas university of illinois at chicago - smu physics...qcd in epinteractions s ≈300−320...
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Nikos Varelas CTEQ Summer School 2005 1
Nikos Varelas
University of Illinois at Chicago
CTEQ Summer School
Puebla, Mexico
May 19 - 27, 2005
Nikos Varelas CTEQ Summer School 2005 2
Introduction – ee, ep, pp processes– What is a jet – Jet algorithmsJet Characteristics– Jet energy profile– Differences between Quark and Gluon jets– Color coherence effectsJet Production at Tevatron– Challenges with jets– Inclusive jet cross sectionsOutlook
Nikos Varelas CTEQ Summer School 2005 3
QCD in a Nutshell
Similar to QED BUT DifferentPointlike particles called quarksSix different “flavors” (u, d, c, s, t, b)Quarks carry “color” - analogous to electric chargeThere are three types of color (red, blue, green)Mediating boson is called gluon - analogous to photonColor charge is conserved in quark-quark-gluon vertexGluons carry two color “charges” and can interact to each other – very important difference from QED -from Abelian to non-Abelian theoryAt large distances: parton interactions become large (confinement)At small distances: parton interactions become small (asymptotic freedom)
u
d
u
Proton
gluons
quarks
Partons = quarks & gluons
Coupling constant → αs (analogous to α in QED)Free particles (hadrons) are colorless
QCD : Theory of StrongInteractions
Nikos Varelas CTEQ Summer School 2005 4
The “Running” αsSU(3) gauge coupling constant (αS) varies with Q2, decreasing as Q2
increases:
Measurements of the strong coupling are made in many processes at different Q2, clearly establishing the running of αS.
Asymptotic freedom (αS 0 as Q2 ) Infrared slavery (αS as Q2 0)
→→ ∞→
→∞
Compilation of many experiments
Increase of αS as Q2 −> 0 means that color force becomes extremely strong when a quark or gluon tries to separate from the region of interaction (large distance ~ small Q2).
A quark cannot emerge freely, but is “clothed” with color-compensating quark-antiquark pairs.
Leading-Log Approximation
222
ln)233(12)(
Λ−=
QnQ
fs
πα
No free quarks or gluons only jets
Nikos Varelas CTEQ Summer School 2005 5
QCD in e+e− Annihilations
Perturbative phaseαs<1 (Parton Level)
Non-perturbative phaseαs≥1 (Hadron Level)
LEP: 88 GeV < Ecm < 209 GeV
e+e− −> (Z0/γ)* −> hadrons
Z0/γe−
e+
q
q
HADRONIZATION
Hadrons
Z0/γe−
e+
q
q
Z0/γe−
e+
q
q
Z0/γe−
e+
q
qO(αs
0) O(αs1) O(αs
2)
Fixed Order QCD
SLC: Ecm = 91 GeV
Nikos Varelas CTEQ Summer School 2005 6
Why do we Study Jets in e+e− ?
QCD StudiesMeasurements of αsFragmentation functionsColor/spin dynamicsQuark-gluon jet propertiesEvent shape variables (sphericity, thrust, …)
Searches for the HiggsSearches for new physics
Nikos Varelas CTEQ Summer School 2005 7
e+e− Event Displays
e+e− −> µ+µ− e+e− −> qq e+e− −> qqg
Much cleaner events than hadron-hadron collisions
Nikos Varelas CTEQ Summer School 2005 8
QCD in ep Interactions
HERAat GeV 320300 −≈s
squared massparton -electron )(ˆ
squared massproton -electron 2)(
nsferenergy tra fractional
fraction momentumparton 2
transfermomentum-4 )(e outgoingfor momentum-4 ),(e incomingfor momentum-4 ),(
2
22
2
222
sxkxPsxyQkPkPs
EEE
kPqPy
qPQx
kkqQEkEk
-
-
≈+=
=⋅≈+=
′−=
⋅⋅
=
⋅=
′−−=−=
′=′
=
kk
qe Z0/γ/W±
e,ν
k
k'
xPP
jet
proton remnantP
27.5 GeV
820-920 GeV
Nikos Varelas CTEQ Summer School 2005 9
Why do we Study Jets in ep ?
Direct photoproduction
QCD StudiesMeasurements of αsFragmentation functionsParton Distribution FunctionsColor/spin dynamicsQuark-gluon jet propertiesEvent shapesInclusive- and Multi-jet productionRapidity Gaps/Diffraction
Searches for new physics
Resolved photoproduction
Nikos Varelas CTEQ Summer School 2005 10
Proton-(Anti)proton CollisionsProton beams can be accelerated to very high energies (good)But the energy is shared among many constituents – quarks and gluons (bad)
Transversemomentum Tp≡
To select the interesting collisions: look for outgoing particles produced with high momentum perpendicular to the beamline(“transverse momentum”) → hard collisions• Hard collisions take place at small impact parameter and are more
accurately collisions between partons inside the two protons• Analog of Rutherford’s experiment• Forms the basis of the on-line event selection (“triggering”)
Nikos Varelas CTEQ Summer School 2005 11
pp Interactions
(uud)
JetD
xa xbp pf σ
Jet
a b
c
d
f
DetectorpT = psinθ“Soft” collisions = small pT“Hard” collisions = large pT
θ
= =
(uud)
Tevatronat TeV 2=s
D
D(z,µF) is theFragmentationfunction
Proton Remnant
Parton Distribution Functionsfa/A(xa,µF): Probability function to find a parton of type a inside hadron A with momentum fraction xa
xa: fraction of hadron’s momentum carried by parton a
µF: related to the “hardness” of the interaction“Factorization Scale”
( )cdab →σ̂Partonic level cross section
Nikos Varelas CTEQ Summer School 2005 12
EM E
ICD/MG E
FH E
CH E
“scattering angle”azimuth
pp Interactions cont’dφ
UnderlyingEvent
u
u
d
gq
q d
Hard Scatter
u
u
Complications from the e+e− due to:– Parton Distribution
Functions (PDFs)– “Colored” initial and final
states– Remnant jets - Underlying
event (UE)
Nikos Varelas CTEQ Summer School 2005 13
EM E
ICD/MG E
FH E
CH E
“scattering angle”azimuth
pp Interactions cont’dφ
UnderlyingEvent
u
u
d
gq
q d
Hard Scatter
u
u
Complications from the e+e− due to:– Parton Distribution
Functions (PDFs)– “Colored” initial and final
states– Remnant jets - Underlying
event (UE)
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DØ Event
ET1 ~ 620 GeVET2 ~ 560 GVMJJ ~ 1.2 TeV
Nikos Varelas CTEQ Summer School 2005 14
EM E
ICD/MG E
FH E
CH E
“scattering angle”azimuth
pp Interactions cont’dφ
UnderlyingEvent
u
u
d
gq
q d
Hard Scatter
u
u
Complications from the e+e− due to:– Parton Distribution
Functions (PDFs)– “Colored” initial and final
states– Remnant jets - Underlying
event (UE)
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DØ Event
ET1 ~ 620 GeVET2 ~ 560 GVMJJ ~ 1.2 TeV
Nikos Varelas CTEQ Summer School 2005 15
Au+Au collision at RHIC Now this is a complicated event!
Nikos Varelas CTEQ Summer School 2005 16
Why do we Study Jets in Hadron Colliders?QCD Studies
Measurements of αsFragmentation functionsParton Distribution FunctionsColor/spin dynamicsQuark-gluon jet propertiesEvent shapesInclusive- and Multi-jet productionRapidity Gaps/DiffractionProduction of Vector Bosons + jets
Study of heavy particles (e.g. top production)Searches for HiggsSearches for new physics
Quark sub-structure + …And much more …
Nikos Varelas CTEQ Summer School 2005 17
Explanation of the blob’s
(uud)
JetD
xa xbp pf σ
Jet
a b
c
d
f
Detector
θ
= =
(uud)
D
(uud)
JetDD
xa xbp pf σσ
Jet
a b
c
d
f
Detector
θ
= =
(uud)
DD
pf =
(uud)
Parton Distribution Functions
xf(x,Qo) = Ao xA1 (1-x)A2 P(x)
small x behavior
large x behavior
in between
Parton Distribution Functions of the proton are measured at a some “hard scale” and evolved via pertrurbativeQCD to the “scale” of the interactionPDFs are determined doing Global Fits of data from DIS (Deep Inelastic Scattering), DY (Drell-Yan), Direct Photons, and production of jets
Nikos Varelas CTEQ Summer School 2005 18
Explanation of the blob’s cont’d Particle Fragmentation Functions
Particle Fragmentation Functions DA/a (zA,µF) measure the probability of finding a particle of type A with momentum fraction zA of parent parton aFragmentation functions are determined doing Global Fits of data from DIS and e+e−
The “evolution” of the Fragmentation functions can be calculated by pQCD
(uud)
JetD
xa xbp pf σ
Jet
a b
c
d
f
Detector
θ
= =
(uud)
D
(uud)
JetDD
xa xbp pf σσ
Jet
a b
c
d
f
Detector
θ
= =
(uud)
DD
Nikos Varelas CTEQ Summer School 2005 19
Explanation of the blob’s cont’d Hard Scattering Cross Section
(uud)
JetD
xa xbp pf σ
Jet
a b
c
d
f
Detector
θ
= =
(uud)
D
(uud)
JetDD
xa xbp pf σσ
Jet
a b
c
d
f
Detector
θ
= =
(uud)
DD( ) ( ) ( ) ⎟⎟
⎠
⎞⎜⎜⎝
⎛= ∑∫ 2
2
2
222
,
1
0
2 ,,,,ˆ,,RF
RsbaijFbjji
FaibaXQQppxfxfdxdxµµ
µασµµσ
What’s the deal with the various scales?µF is the factorization scale that enters in the evolution of the PDF’sand the Fragmentation functions (could be two different scales). It is an arbitrary parameter that can be thought as the scale which separates the long- and short-distance physicsµR is the renormalization scale that shows up in the strong coupling constantQ is the hard scale which characterizes the parton-parton interactionTypical choice: µF = µR = Q ~ pT/4 – 2pT of the jets
σX = (PDF’s for p and p) ⊗ (partoniclevel cross section)
Separate the long-distance pieces (PDF’s) from the short-distance cross section →Factorization
Nikos Varelas CTEQ Summer School 2005 20
Detector
(uud)
JetD
xa xbp pf σ
Jet
a b
c
d
f
Detector
θ
= =
(uud)
D
(uud)
JetDD
xa xbp pf σσ
Jet
a b
c
d
f
Detector
θ
= =
(uud)
DD
Detector
Explanation of the blob’s cont’d
Typical Detector
CDF
Fermilab Accelerators
DØ
Nikos Varelas CTEQ Summer School 2005 21
Tevatron RunsRun I
1992-1996ECM = 1.8 TeV~120 pb-1
(0.63 TeV ~600 nb-1)
Run IIa2002-2005ECM = 1.96 TeV~ 1.5 fb-1
Run IIb2006-2009ECM = 1.96 TeV~4-8 fb-1
Main Injector& Recycler
Tevatron
Chicago↓
⎯p source
Booster
⎯p
p
p ⎯p1.96 TeV
CDFDØ
Nikos Varelas CTEQ Summer School 2005 22
Kinematics in Hadronic Collisions
Rapidity (y) and Pseudo-rapidity (η)θ
Particle
ppz
xy
θβθβ
cos1cos1ln
21ln
21
−+
=−+
≡z
z
pEpEy
Epy == βθβ wheretanhcos
2tanln
cos1cos1ln
21
then)(or 1limit In the
0θ
θθη
β
−=−+
=≡
<<→
=m
T
y
pm
LAB System ≠ parton-partonCM system
⇒
LAB
θ1
θ2
CM
θ∗
Nikos Varelas CTEQ Summer School 2005 23
Kinematics in Hadronic Collisions cont’d
yEpyEEyEp
Tz
T
z
sinh cosh tanh
===Transverse Energy/Momentum
22222222zTyxT pEmpmppE −=+=++≡
Invariant Mass θsinppT ≡
)cos(cosh2)(2
))((
210,
212122
21
21212
12
21φη ∆−∆⎯⎯⎯ →⎯
⋅−++=
++≡
→
µµµµ
TTmm EEEEmm
ppppM
pp
2
1x1P x2P
Partonic Momentum Fractions)0(2 2,12,1 ==≡ ηxsEx TT
( )( ) sEeex
sEeex
T
T
21
21
2
1
ηη
ηη
−− +=
+=
1
1,0
212
21
<<
<<
xxx
xx
Tsxxs ba=→ ˆ(energy) CMParton 2
Nikos Varelas CTEQ Summer School 2005 24
What are Jets ?
Nikos Varelas CTEQ Summer School 2005 25
What are Jets ?
Whatever objects my jetalgorithm finds!
Nikos Varelas CTEQ Summer School 2005 26
What are Jets ?
Colored partons from the hard scatter evolve via soft quark and gluon radiation and hadronization process to form a “spray” of roughly collinear colorless hadrons −> JETSThe hadrons in a jet have small transverse momenta relative to their parent parton’s direction and the sum of their longitudinal momentaroughly gives the parent parton momentum
Keep in mind that there are particles in a jet originating from other partonsin the event
Jets manifest themselves as localized clusters of energy
Jet
outgoing parton
Fragmentation process
Hard scatter
colorless states - hadrons -
R = +( ) ( )∆η ∆φ2 2coneR
Nikos Varelas CTEQ Summer School 2005 27
What are Jets ?
Colored partons from the hard scatter evolve via soft quark and gluon radiation and hadronization process to form a “spray” of roughly collinear colorless hadrons −> JETSThe hadrons in a jet have small transverse momenta relative to their parent parton’s direction and the sum of their longitudinal momentaroughly gives the parent parton momentum
Keep in mind that there are particles in a jet originating from other partonsin the event
Jets manifest themselves as localized clusters of energy
Jet
outgoing parton
Fragmentation process
Hard scatter
colorless states - hadrons -
R = +( ) ( )∆η ∆φ2 2coneR
Jets
are th
e expe
riment
al sig
nature
s of q
uarks
and gl
uons
Nikos Varelas CTEQ Summer School 2005 28
pp Interactions – Creation of Jets
p=
(uud)
(uud)
p=
{π,K,p,n,…}
Jet
BeamRemnants
BeamRemnants
Initial State Radiation(ISR)
Hadronization
Final State Radiation(FSR)
Detector
Nikos Varelas CTEQ Summer School 2005 29
First Evidence for JetsFirst experimental evidence of quark-initiated jets in e+e- annihilations, SLAC-SPEAR at Ecm ~ 7 GeVG. Hanson et al. (MARK-I Collab), PRL 35, 1609 (1975)
Gluon-initiated jets were discovered in e+e- annihilations DESY-PETRA at Ecm > 15 GeVMARK-J Collab., PRL 43, 830 (1979); TASSO Collab., Phys. Lett. B86, 243 (1979); PLUTO Collab., Phys. Lett. B86, 418 (1979);JADE Collab., Phys. Lett. B91, 142 (1980)
e+e− → q q g
Nikos Varelas CTEQ Summer School 2005 30
Jet AlgorithmsThe goal is to apply the “same” jet clustering algorithm to data and theoretical calculations without ambiguities
Nikos Varelas CTEQ Summer School 2005 31
Jet AlgorithmsThe goal is to apply the “same” jet clustering algorithm to data and theoretical calculations without ambiguities
Jets at the “Parton Level” (i.e., before hadronization)
Fixed order QCD or (Next-to-) leading logarithmic summations to all orders
2 → 2 processLeading Order QCD
2-jet final state1 parton/jet
outgoing parton
Parton showering
Hard scatter
multi-jet final state
Nikos Varelas CTEQ Summer School 2005 32
Jet AlgorithmsThe idea is to come up with a jet algorithm which minimizes the non-perturbativehadronization effects
Hard scatter
Fragmentation process
Jet
hadrons
outgoing parton
Parton showering+ Hadronization
Nikos Varelas CTEQ Summer School 2005 33
Jet Algorithms
Jets at the “Detector Level”Calorimeter - clusters of energy “towers”Tracking - clusters of tracksCombination of detectors
Calorimeter
Calorimeter jet energy resolution:
%5%80⊕≈
TT EEσ
Nikos Varelas CTEQ Summer School 2005 34
Jet Algorithms - Requirements
Experimental:– Detector independence - Can everybody implement this?– Minimization of resolution smearing/angle bias– Stability with Luminosity– Computational efficiency– Maximal reconstruction efficiency
Theoretical:– Infrared safety
• insensitive to “soft” radiation– Collinear safety
– Low sensitivity to hadronization– Invariance under boosts– Same jets at parton/particle/detector levels– Straight forward implementation
The full report of the Run II Jet algorithm specification is available at hep-ex/0005012
Nikos Varelas CTEQ Summer School 2005 35
Jet Finders(Generic Recombination)
Define a resolution parameter ycut
For every pair of particles (i,j) compute the “separation”yij as defined for the algorithm
If min(yij) < ycut then combine the particles (i,j) into k– E scheme: pk=pi+pj massive jets– E0 scheme: massless jets
Iterate until all particle pairs satisfy yij>ycut
No problems with jet overlapLess sensitive to hadronization effects
2
2
vis
ijij E
My =
ji
jikk
jik
E
EEE
pppp
p+
+=
+=
i j
Nikos Varelas CTEQ Summer School 2005 36
The JADE Algorithm )cos1(22
ijjiij EEM θ−=
cutvis
ijij y
EM
y <= )min()min( 2
2
Recombination: pk = pi+pj
Problems with this algorithm– It doesn’t allow resummation when ycut is small– Tendency to reconstruct “spurious” jets
i.e. consider the following configuration where two soft gluons are emitted close to the quark and antiquarkThe gluon-gluon invariant mass can be smaller than that of any gluon-quark and therefore the event will be characterized as a 3-jet one instead of a 2-jet event
(Evis is the sum of all particle energies)
x 3-Jet event √ 2-Jet event
ijθij
Nikos Varelas CTEQ Summer School 2005 37
The Durham or “kT” Algorithm )cos1)(,min(2 222
ijjiij EEM θ−=
cutvis
ijij y
EM
y <= 2
2
)min(
),min(2
),min(2)2
1(1),min(2
:get we smallFor
222
222
222TjTi
ijji
ijjiij
ij
kkEEEEM ≈⎟⎟⎠
⎞⎜⎜⎝
⎛≈⎟
⎟⎠
⎞⎜⎜⎝
⎛+−−≈
θθ
θ
L
Recombination: pk = pi+pj
It allows the resummation of leading and next-to-leading logarithmic terms to all orders for the regions of low ycut
kT
√ 2-Jet event
Nikos Varelas CTEQ Summer School 2005 38
The “kT” Jet Algorithm for Hadron Colliders
The kT jet algorithm successively merges pairs of partons, particles, calorimeter towers, or tracks in order of increasing relative transverse momentum (kT)It contains a parameter D (~0.5-1) that controls the termination of the merging and characterizes the approximate size of the resulting jetskT jets are infrared and collinear safeThere are no overlapped jetsEvery parton, particle, or detector tower is unambiguously assigned to a single jetNo biases from seed towersLess sensitive to hadronization effects
Nikos Varelas CTEQ Summer School 2005 39
The “kT” Algorithm cont’d Input: List of Energy preclusters )2.0( ≈∆ preclusterR
2
22
,2
, ),min(DR
ppd ijjTiTij
∆=
2,iTii pd =
dij?
Move i to list of jets
Anyleft?
No
No
MinYes
Yes
Combine i+j
( ) ( )222jijiij yyR φφ −+−=∆
p p
Cone jetkT jet
jiij
jiij
EEE
ppp
+=
+=rrr
D ∼ 0.5-1
Output: List of jets )( DR ≥∆
p p
Nikos Varelas CTEQ Summer School 2005 40
The Cone Jet Algorithm for Hadron CollidersA more intuitive representation of a jet that is given by recombination jet findersIt requires “seeds” with a minimum energy of ≤ 1 GeV (to save computing time)– Preclusters are formed by combining seed towers with their
neighbors within a cone of radius R is η−φ space– For each precluster the ET-weighted centroid is found and a new
cone of radius R is drawn around it– Iterate until stable solution is found
Jet cones may overlap so need to split/merge overlapping jets
Jet Seeds
Calorimeter ET
Merge if shared ET > 50-75% of min(ET1,ET2)
DØ - CDF
Nikos Varelas CTEQ Summer School 2005 41
The DØ/CDF Jet Cone Algorithm for Run I In Run I: DØ and CDF used Snowmass (1990) clustering and defined angles via momentum vectors
DØ and CDF’s Angles:CDF’s ET:
DØ’s ET: ∑⊂
=Ji
iT
JT EE
Nikos Varelas CTEQ Summer School 2005 42
The Cone Algorithm at 3-Parton Final States Apply Snowmass jet algorithm– Each parton must be within Rcone of centroid
The two partons must be within RsepxRcone of one another, where Rsep varies from 1 - 2 (Rsep=1.3 for DØ/CDF)– introduce ad-hoc parameter Rsep to control parton recombination in
the theoretical jet algorithm and simulate the role of seeds andmerging in the experimental algorithm
– it doesn’t generalize to higher orders Rcone
Rsep
Num
ber o
f jet
s
Rsep=1.3
DØ Cone Radius = 0.7
Delta_R
Run I
If jets from separate events are overlaid thenthey can be distinguished at 1.3xRcone=0.9 for 0.7 cone jets:
Nikos Varelas CTEQ Summer School 2005 43
The Next Generation of Cone Algorithm Issues with the Snowmass Cone Algorithm
Sensitivity to infrared and collinear radiationNot proper 4-vector kinematics used in particle clustering and in calculating the final jet parameters
The Solution: Develop a “seedless” jet algorithm with proper kinematics
Infrared and Collinear safeVery computationally intensive
What was done: Develop the Midpoint jet algorithmApproximates the seedless algorithmInfrared safe Proper 4-vector kinematics used in all steps massive jets
Nikos Varelas CTEQ Summer School 2005 44
The Midpoint Jet Cone Algorithm for Run II
Proto-jets are formed by combining seed particles with their neighbors within a cone of radius Rcone using the E-scheme
Particles = calorimeter towers, MC hadrons or partonsMidpoint seeds are added between proto-jets
Only midpoints between proto-jets satisfying the following conditions are considered: ∆R > Rcone and ∆R < 2×Rcone
Proto-jets found around seeds and midpoints can share particles
Merging/splitting procedure has to be appliedMerge jets, if more than a fraction f (50% for DØ, 75% for CDF) of min(pT1,pT2) of overlapping jets is contained in the overlap regionOtherwise split jets; assign the particles in the overlap region to the nearest jet
Keep only final jets with pT > threshold
Nikos Varelas CTEQ Summer School 2005 45
Not a Perfect World After All!
Significant amounts of energy is not clustered in Midpoint algorithm
To reduce this effect CDF is using two values for the cone radius: one during search for stable cones (Rcone/2) and the second (Rcone) during the calculation of the final jet properties Search Cone Algorithm… this leads to other “features”
Overall this effect is quite small
Nikos Varelas CTEQ Summer School 2005 46
Not a Perfect World After All!
Significant amounts of energy is not clustered in Midpoint algorithm
To reduce this effect CDF is using two values for the cone radius: one during search for stable cones (Rcone/2) and the second (Rcone) during the calculation of the final jet properties Search Cone Algorithm… this leads to other “features”
This effect is currently under study
between the two experiments
Overall this effect is quite small
Nikos Varelas CTEQ Summer School 2005 47
Looking Inside the Jets
( )rΨ
The investigation of jet profiles gives insights into the transition between the parton produced in the hard process and the observed spray of hadronsJet profiles are sensitive to the quark/gluon jet mixture
Could separate quark and gluon jets in a statistical wayEnergy Flow (Jet Shape):
Measure the average transverse energy flow in sub-cones as a function of radial distance from the jet axis Use calorimeter towers or charged tracks
22 )()( φη ∆+∆=r
Nikos Varelas CTEQ Summer School 2005 48
Jet energy profiles at Tevatron Run II
Gluon enriched jets (low-x/low-pT jets at Tevatron) are “broader” (i.e. less collimated, higher multiplicity of soft energy particles) than Quark-enriched jets (high-x/high-pT jets)
Nikos Varelas CTEQ Summer School 2005 49
Jet energy profiles at Tevatron
Gluon enriched jets (low-x/low-pT jets at Tevatron) are “broader” (i.e. less collimated, higher multiplicity of soft energy particles) than Quark-enriched jets (high-x/high-pT jets)
Run II
gg
g
~ CF = 4/3
~ CA= 3
q qg 2
2
Quark & Gluon jets radiate proportional to their color factor:
><><
≡><
><≡
tymultiplicijet quark tymultiplicijet gluon
q
g
nn
r
At Leading Order (Ejet →∞):
With higher order corrections at Ejet (LEP) ~ 40 GeV:
25.249~ ==
F
A
CCr
5.1~r
Nikos Varelas CTEQ Summer School 2005 50
Property of gauge theories. Similar effect in QED, the “Chudakoveffect” observed in cosmic ray physics in 1955
In QCD color coherence effects are due to the interference of soft gluon radiation emitted along color connected partonsTwo types of Coherence:– Intrajet Coherence
• Angular Ordering of the sequential parton branches in a partoniccascade
– Interjet Coherence• String or Drag effect in multijet hadronic events
Coherence
eeθγθ e
γe−
e+
γθθ eee >
Nikos Varelas CTEQ Summer School 2005 51
Shower Development“Traditional Approach”
Shower develops according to pQCD into spray of partons until a scale of Q0 ~ 1 GeV.
Thereafter, non-perturbative processes take over and produce the final state hadrons
Coherence effects are included probabilistically (e.g., Angular Ordering, color dipole) and in the hadronization model
DGLAP Splitting Kernel
Nikos Varelas CTEQ Summer School 2005 52
Shower Development“Traditional Approach”
Shower develops according to pQCD into spray of partons until a scale of Q0 ~ 1 GeV.
Thereafter, non-perturbative processes take over and produce the final state hadrons
Coherence effects are included probabilistically (e.g., Angular Ordering, color dipole) and in the hadronization model
DGLAP Splitting Kernel
“Local Parton Hadron Duality (LPHD) Approach”
Parton cascade is evolved further down to a scale of about Q0 ~ 250 MeV.
No hadronization process; Hadron spectra = Parton spectra
Simplicity. Only two essential parameters (ΛQCD and Q0) and an overall normalization factor
Nikos Varelas CTEQ Summer School 2005 53
What is an Event Generator ?A “C” (of “Fortran”) program that generates events, trying to simulate Nature!Events vary from one to the next (random numbers)Expect to reproduce average behavior and fluctuations of real dataEvent Generators include:– Parton Distribution functions– Initial state radiation– Hard interaction– Final state radiation– Beam jet structure– Multiple Parton Interactions– Hadronization and decays
Some programs in the market:JETSET, PYTHIA, LEPTO, ARIADNE, HERWIG, COJETS...
Some parton-level only:VECBOS, NJETS, JETRAD, HERACLES, COMPOS, ALPGEN, PAPAGENO, MADGRAPH, EUROJET...
q
calo
rim
eter
jet
Time
q g
π K
part
onje
tpa
rtic
le je
t
hadrons
γ
CH
FH
EM
p
• •
p
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Hadronization ModelsIndependent fragmentation– it is being used in ISAJET and COJETS– simplest scheme - each parton fragments independently following
the approach of Field and FeynmanString fragmentation– it is being used in JETSET, PYTHIA, LEPTO, ARIADNE
Cluster fragmentation– it is being used in HERWIG
String Fragmentation: Separating partons connected by color string which has uniform energy per unit length, corresponding to a linear quark confining potential
Cluster Fragmentation: Pairs of color connected neighboringpartons combine into color singlets.
Z0/γe−
e+
q
q
Z0/γe−
e+
q
q
Nikos Varelas CTEQ Summer School 2005 55
e+e− interactions:Coherence Observations
First observations of final state color coherence effects in theearly ’80’s (JADE, TPC/2g, TASSO, MARK II Collaborations) (“string” or“drag” effect)
q
q
γ q
q
g
e+e− → q q ge+e− → q q γ
Depletion of particle flow in region between q and qjets for qqg events relative to that of qqγ jets.
Nikos Varelas CTEQ Summer School 2005 56
gqqeeqqee →→ −+−+ vsγ
Particle flow in event planeφ (deg.)
1/N
dn/
dφ
Particle flow in event plane
Particle FlowParticle Flow X
1/N
dn/
dX
10-2
10-1
1
0 50 100 150 200 250 300 350
10-1
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure �� �a� Charged particle �ow in the event plane for two�jet radiative events� and
three�jet multihadronic events� Error bars for the q�qg sample are smaller than the dots�
�b� Charged particle �ow with respect to the reduced angle X�
�
Gluon jet
String effect
gqqγqq
Data agree with analytic LPHD calculations
gluon jet or photon
φ
Leading quark jet
2nd quark jet
Leading quark jet 2nd quark jet
Nikos Varelas CTEQ Summer School 2005 57
Coherence Observations cont’dpp interactions:
Colored constituents in initial and final state (more complicated that e+e−)
Emission from each parton is confined to a cone stretching to its color partner
Nikos Varelas CTEQ Summer School 2005 58
Color Coherence – Wgqq →
Compare pattern of soft particle flow around jet to that around (colorless) W
Color connections
Nikos Varelas CTEQ Summer School 2005 59
p=
(uud)
(uud)
p=
Color Coherence –
W
Event Plane
Transverse Plane
Wgqq →Soft gluon radiation preferentially emittedin the event plane
Initial-Final StateConstructive interference
Nikos Varelas CTEQ Summer School 2005 60
p=
(uud)
(uud)
p=
Color Coherence –
W
Event Plane
Transverse Plane
Wgqq →Soft gluon radiation preferentially emittedin the event plane
Compare pattern of soft particle flow around jet to that around (colorless) W
Initial-Final StateConstructive interference
Color connections
1
1.5
2
(a)
Data
PYTHIA (AO ON, SF)
(b)
Data
PYTHIA (AO OFF, SF)
1
1.5
2
0 π/4 π/2 3π/4
(c)
Data
PYTHIA (AO OFF, IF)
Jet/W
Tow
er M
ultip
licity
Rat
io
0 π/4 π/2 3π/4 π
(d)
Data
MLLA+LPHD
Far BeamNear Beam
Run I
Ratio of partile multipliity around the Jet to that around the W
Nikos Varelas CTEQ Summer School 2005 61
Jet Production @ TevatronMotivation:
– Search for breakdown of the Standard Model at shortest distances• At Tevatron energies:
– Search for new particles decaying into jet final states– Search for quarks substructure– Constrain gluon density at high x– Precision studies of QCD
mp
GeVp
T
T
19104~GeV 500
fmMeV 200~c~distance
500~
−×⋅
⇒h
World’s best
microscope !
Nikos Varelas CTEQ Summer School 2005 62
Challenges with JetsTriggering on Jets– reduce rate from ~106 to ~ tens of Hz
• multiple triggering stages; Level-1,2,3– implement fast/crude jet clustering algorithms for L1/2
Selection of a Jet Algorithm– at detector, particle, parton/NLO++ level
Jet Reconstruction, Selection, and Trigger EfficienciesJet Calibration– underlying event definition (subtract or not?)– out-of-cone showering effects– correction back to particle jet or original parton?
Jet Resolution– difficulties with low-ET region and near reconstruction threshold
Simulation of Jet/Event/Detector Characteristics– precision of detector modeling vs CPU time– ability to overlay zero/minimum-bias events from data – tuning of fragmentation model, selection of PDF, hard scale
parameter Q, …– Interface a ME event generator with a parton-shower simulation
Nikos Varelas CTEQ Summer School 2005 63
High-ET Jet Production
1P1P
2P2P
11Px 11Px
22 Px 22 Px
1jet 1jet
2jet 2jet
( )sασ̂ ( )sασ̂
( )1/ xf Aa ( )1/ xf Aa
( )2/ xf Bb ( )2/ xf Bb
Quark substructure ?PDFs ?
ET
d2σdET dη
Central η region
Significant gluon contribution at high pT
ddP
dx f x dx f xddPT
aa b
a A a b b B bT
σµ µ
σ≈ ∫∑ ∫
,/ /( , ) ( , )
$
ddP
ab cd MT
s
N
N
N
$( )
( )σ α µπ
→ ≈⎛⎝⎜
⎞⎠⎟∑
2
Currently 3-jet production @ NLO
Nikos Varelas CTEQ Summer School 2005 64
Resent results from Tevatron
(GeV)Tp50 100 200 400
dy (
pb/G
eV)
T/d
pσ2 d
-410
-310
-210
-110
1
10
210
310
410
510
|y| < 0.4 (x10)
0.4 < |y| < 0.8
NLO QCD
CTEQ6.1M
T = pFµ = Rµ
= 1.96 TeVs-1
L = 378 pb
DØ Run II preliminary
Run IIMid-point jet algorithm kT jet algorithm
DØ
NLOJET++
Nikos Varelas CTEQ Summer School 2005 65
Resent results from Tevatron cont’dRun II kT jet algorithmMid-point jet algorithm
0.8
0.9
1
1.1
1.2
1.3
0.0 < |y| < 0.4
rela
tive
chan
ge o
f inc
l. je
t cro
ss s
ectio
n
0.8
0.9
1
1.1
1.2
1.3
100 200 300 400 500 600
0.4 < |y| < 0.8
pT (GeV)
non-perturbative corrections
PYTHIA 6.225underlying eventhadronization
Hadronization + Underlying event/multiple-parton scatteringcorrections using Pythia applied to NLO QCD
Nikos Varelas CTEQ Summer School 2005 66
⎟⎟⎠
⎞⎜⎜⎝
⎛
=
→←
TeV 14s
ppThe far future...
distance resolution ~10-20 m
16 orders of magnitude drop
Nikos Varelas CTEQ Summer School 2005 67
Jets celebrate their 30th year since first observed in e+e-
Jets have provided the means to study the SM and explore possibilities beyondThere are still issues to be resolved with the jet algorithms
See the current effort in the TeV4LHC WorkshopMore sophisticated jet algorithms are under development
Tevatron Run II is setting the stage for jet physics at LHC
CMSCMS
http://conferences.fnal.gov/tev4lhc/