Fermilab Tevatron University Rick Field
University of Florida CDF Run 2 Toward an Understanding
of Hadron-Hadron Collisions Fermilab 2006

Toward and Understanding of Hadron-Hadron Collisions:

Toward and Understanding of Hadron-Hadron Collisions From 7 GeV/c p0’s to 600 GeV/c Jets. Some things we have learned about quark and gluon jets at CDF. Jet algorithms and the 'jet' cross section at CDF. Feynman and Field 1st hat!

The Feynman-Field Days:

'Feynman-Field
Jet Model' The Feynman-Field Days FF1: 'Quark Elastic Scattering as a Source of High Transverse Momentum Mesons', R. D. Field and R. P. Feynman, Phys. Rev. D15, 2590-2616 (1977).
FFF1: 'Correlations Among Particles and Jets Produced with Large Transverse Momenta', R. P. Feynman, R. D. Field and G. C. Fox, Nucl. Phys. B128, 1-65 (1977).
FF2: 'A Parameterization of the properties of Quark Jets', R. D. Field and R. P. Feynman, Nucl. Phys. B136, 1-76 (1978).
F1: 'Can Existing High Transverse Momentum Hadron Experiments be Interpreted by Contemporary Quantum Chromodynamics Ideas?', R. D. Field, Phys. Rev. Letters 40, 997-1000 (1978).
FFF2: 'A Quantum Chromodynamic Approach for the Large Transverse Momentum Production of Particles and Jets', R. P. Feynman, R. D. Field and G. C. Fox, Phys. Rev. D18, 3320-3343 (1978). 1973-1983 FW1: 'A QCD Model for e+e- Annihilation', R. D. Field and S. Wolfram, Nucl. Phys. B213, 65-84 (1983). My 1st graduate student!

Hadron-Hadron Collisions:

Hadron-Hadron Collisions What happens when two hadrons collide at high energy? Most of the time the hadrons ooze through each other and fall apart (i.e. no hard scattering). The outgoing particles continue in roughly the same direction as initial proton and antiproton. Occasionally there will be a large transverse momentum meson. Question: Where did it come from? We assumed it came from quark-quark elastic scattering, but we did not know how to calculate it! FF1 1977 (preQCD) Feynman quote from FF1
'The model we shall choose is not a popular one,
so that we will not duplicate too much of the
work of others who are similarly analyzing
various models (e.g. constituent interchange
model, multiperipheral models, etc.). We shall
assume that the high PT particles arise from
direct hard collisions between constituent
quarks in the incoming particles, which
fragment or cascade down into several hadrons.' 'Black-Box Model'

Quark-Quark Black-Box Model:

Quark-Quark Black-Box Model FF1 1977 (preQCD) Quark Distribution Functions
determined from deep-inelastic
lepton-hadron collisions Quark Fragmentation Functions
determined from e+e- annihilations Quark-Quark Cross-Section
Unknown! Deteremined from
hadron-hadron collisions. No gluons! Feynman quote from FF1
'Because of the incomplete knowledge of
our functions some things can be predicted
with more certainty than others. Those
experimental results that are not well
predicted can be 'used up' to determine
these functions in greater detail to permit
better predictions of further experiments.
Our papers will be a bit long because we
wish to discuss this interplay in detail.'

Quark-Quark Black-Box Model:

Quark-Quark Black-Box Model FF1 1977 (preQCD) Predict
particle ratios Predict
increase with increasing
CM energy W Predict
overall event topology
(FFF1 paper 1977) 'Beam-Beam Remnants' 7 GeV/c p0’s!

Telagram from Feynman:

Telagram from Feynman July 1976 SAW CRONIN AM NOW CONVINCED WERE RIGHT TRACK QUICK WRITE
FEYNMAN

Letter from Feynman:

Letter from Feynman July 1976

Letter from Feynman Page 1:

Letter from Feynman Page 1 Spelling?

Letter from Feynman Page 3:

Letter from Feynman Page 3 It is fun! Onward!

Feynman Talk at Coral Gables (December 1976):

Feynman Talk at Coral Gables (December 1976) 'Feynman-Field
Jet Model' 1st transparency Last transparency

QCD Approach: Quarks & Gluons:

QCD Approach: Quarks andamp; Gluons FFF2 1978 Parton Distribution Functions
Q2 dependence predicted from QCD Quark andamp; Gluon Fragmentation Functions
Q2 dependence predicted from QCD Quark andamp; Gluon Cross-Sections
Calculated from QCD Feynman quote from FFF2
'We investigate whether the present
experimental behavior of mesons with
large transverse momentum in hadron-hadron
collisions is consistent with the theory of
quantum-chromodynamics (QCD) with
asymptotic freedom, at least as the theory
is now partially understood.'

High PT Jets:

High PT Jets 30 GeV/c! Predict
large 'jet' cross-section Feynman, Field, andamp; Fox (1978) CDF (2006) 600 GeV/c Jets! Feynman quote from FFF
'At the time of this writing, there is
still no sharp quantitative test of QCD.
An important test will come in connection
with the phenomena of high PT discussed here.'

A Parameterization of the Properties of Jets:

A Parameterization of the Properties of Jets Assumed that jets could be analyzed on a 'recursive' principle. Field-Feynman 1978 Original quark with flavor 'a' and momentum P0 Let f(h)dh be the probability that the rank 1 meson leaves fractional momentum h to the remaining cascade, leaving quark 'b' with momentum P1 = h1P0. Primary Mesons Assume that the mesons originating from quark 'b' are distributed in presisely the same way as the mesons which came from quark a (i.e. same function f(h)), leaving quark 'c' with momentum P2 = h2P1 = h2h1P0. Add in flavor dependence by letting bu = probabliity of producing u-ubar pair, bd = probability of producing d-dbar pair, etc. Let F(z)dz be the probability of finding a meson (independent of rank) with fractional mementum z of the original quark 'a' within the jet. Rank 2 continue Calculate F(z) from f(h) and bi! Rank 1 Secondary Mesons
(after decay)

Feynman-Field Jet Model:

Feynman-Field Jet Model R. P. Feynman
ISMD, Kaysersberg, France, June 12, 1977 Feynman quote from FF2
'The predictions of the model are reasonable
enough physically that we expect it may
be close enough to reality to be useful in
designing future experiments and to serve
as a reasonable approximation to compare
to data. We do not think of the model
as a sound physical theory, ....'

QCD Monte-Carlo Models: High Transverse Momentum Jets Start with the perturbative 2-to-2 (or sometimes 2-to-3) parton-parton scattering and add initial and final-state gluon radiation (in the leading log approximation or modified leading log approximation). 'Underlying Event' The 'underlying event' consists of the 'beam-beam remnants' and from particles arising from soft or semi-soft multiple parton interactions (MPI). Of course the outgoing colored partons fragment into hadron 'jet' and inevitably 'underlying event' observables receive contributions from initial and final-state radiation. The 'underlying event' is an unavoidable background to most collider observables and having good understand of it leads to more precise collider measurements!

Monte-Carlo Simulationof Quark and Gluon Jets:

Monte-Carlo Simulation of Quark and Gluon Jets ISAJET: Evolve the parton-shower from Q2 (virtual photon invariant mass) to Qmin ~ 5 GeV. Use a complicated fragmentation model to evolve from Qmin to outgoing hadrons. Q2 5 GeV 1 GeV 200 MeV HERWIG: Evolve the parton-shower from Q2 (virtual photon invariant mass) to Qmin ~ 1 GeV. Form color singlet clusters which 'decay' into hadrons according to 2-particle phase space. MLLA: Evolve the parton-shower from Q2 (virtual photon invariant mass) to Qmin ~ 230 MeV. Assume that the charged particles behave the same as the partons with Nchg/Nparton = 0.56! MLLA Curve! = ln(Ejet/pparticle)

Distribution of Particles in Jets:

Distribution of Particles in Jets Ratio of charged hadron multiplicities in gluon and quark jets agrees with NNLLA
Gluon-Quark Ratio = 1.6 0.2
Momentum distribution of charged hadrons in jets well described by MLLA!
Dijet mass range 80-600 GeV
Cutoff Qeff = 230 40 MeV
Ncharged-hadrons/Npartons = 0.56 0.10
CDF Run 1 Analysis Ratio = Ng-jet / Nq-jet Q = Ejet qcone Both PYTHIA and HERWIG predict a Gluon-Quark Ratio that is smaller than the data!

Charged Multiplicity in Quark and Gluon Jets:

Charged Multiplicity in Quark and Gluon Jets CDF Run 1 data on the average charged particle multiplicities in gluon and quark jets versus Q = Ejet × qcone compared with NLLA, PYTHIA, and HERWIG. HERWIG and PYTHIA correctly predict the charged multiplicity for gluon jets. Both HERWIG and PYTHIA over-estimate the charged multiplicity in quark jets by ~30%! CDF Run 1 Analysis

Distribution of Particles in Quark and Gluon Jets:

Distribution of Particles in Quark and Gluon Jets Momentum distribution of charged particles in gluon jets. HERWIG 5.6 predictions are in a good agreement with CDF data. PYTHIA 6.115 produces slightly more particles in the region around the peak of distribution. x = 0.37 0.14 0.05 0.02 0.007 Momentum distribution of charged particles in quark jets. Both HERWIG and PYTHIA produce more particles in the central region of distribution. Both PYTHIA and HERWIG predict more charged particles than the data for quark jets! CDF Run 1 Analysis

Evolution of Charged Jets“Underlying Event”:

Evolution of Charged Jets 'Underlying Event' Look at charged particle correlations in the azimuthal angle Df relative to the leading charged particle jet.
Define |Df| andlt; 60o as 'Toward', 60o andlt; |Df| andlt; 120o as 'Transverse', and |Df| andgt; 120o as 'Away'.
All three regions have the same size in h-f space, DhxDf = 2x120o = 4p/3. Charged Particle Df Correlations PT andgt; 0.5 GeV/c |h| andlt; 1 Look at the charged particle density in the 'transverse' region! 'Transverse' region very sensitive to the 'underlying event'! CDF Run 1 Analysis

“Transverse” Charged Particle Density:

'Transverse' Charged Particle Density Shows the data on the average 'transverse' charge particle density (|h|andlt;1, pTandgt;0.5 GeV) as a function of the transverse momentum of the leading charged particle jet from Run 1. Compares the Run 2 data (Min-Bias, JET20, JET50, JET70, JET100) with Run 1. The errors on the (uncorrected) Run 2 data include both statistical and correlated systematic uncertainties. 'Transverse' region as defined by the leading 'charged particle jet' Excellent agreement between Run 1 and 2! PYTHIA Tune A was tuned to fit the 'underlying event' in Run I! Shows the prediction of PYTHIA Tune A at 1.96 TeV after detector simulation (i.e. after CDFSIM).

Charged Multiplicity in Charged Particle Jets:

Charged Multiplicity in Charged Particle Jets Plot shows the average number of charged particles (pT andgt; 0.5 GeV, |h| andlt; 1) within the leading charged particle jet (R = 0.7) as a function of the PT of the leading charged jet. The solid (open) points are Min-Bias (JET20) data. The errors on the (uncorrected) data include both statistical and correlated systematic uncertainties. The QCD 'hard scattering' theory curves (Herwig 5.9, Isajet 7.32, Pythia 6.115) are corrected for the track finding efficiency. PYTHIA predict more charged particles than the data for charged jets! Includes charged particles from the 'underlying event'! CDF Run 1 Analysis

Charged Multiplicity in Charged Particle Jets:

Charged Multiplicity in Charged Particle Jets CDF Run 1 data on the multiplicity distribution of charged particles (pT andgt; 0.5 GeV and |h| andlt; 1) within chgjet#1 (leading charged jet) for PT(chgjet#1) andgt; 5 and 30 GeV compared with the QCD 'hard scattering' Monte-Carlo predictions of HERWIG 5.9, ISAJET 7.32, and PYTHIA 6.115. Plot shows the percentage of events in which the leading charged jet (R = 0.7) contains Nchg charged particles. CDF Run 1 Analysis Includes charged particles from the 'underlying event'!

Radial Charged Distribution in Charged Particle Jets:

Radial Charged Distribution in Charged Particle Jets Charged multiplicity flow in the radial distance R in h-f space from chgjet#1 (leading charged jet) for charged particles with pT andgt; 0.5 GeV and |h| andlt; 1 when PT(chgjet#1) andgt; 5 and 30 GeV. The points are andlt;Nchgandgt; in a 0.02 bin of R. Charged PTsum flow in the radial distance R in h-f space from chgjet#1 (leading charged jet) for charged particles with pT andgt; 0.5 GeV and |h| andlt; 1 when PT(chgjet#1) andgt; 5 and 30 GeV. The points are the scalar andlt;PTsumandgt; in a 0.02 bin of R.

Run 1 Fragmentation Function:

Run 1 Fragmentation Function CDF Run 1 data on the momentum distribution of charged particles (pT andgt; 0.5 GeV and |h| andlt; 1) within chgjet#1 (leading charged jet). The points are the charged number density, F(z) = dNchg/dz, where z = pchg/P(chgjet#1) is the ratio of the charged particle momentum to the charged momentum of chgjet#1. The integral of F(z) is the average number of particles within chgjet#1. Includes charged particles from the 'underlying event'! CDF Run 1 Analysis

Run 1 Fragmentation Function:

Run 1 Fragmentation Function CDF Run 1 data from on the momentum distribution of charged particles (pT andgt; 0.5 GeV and |h| andlt; 1) within chgjet#1 (leading charged jet) for PT(chgjet#1) andgt; 5 GeV compared with the QCD 'hard scattering' Monte-Carlo predictions of HERWIG, ISAJET, and PYTHIA. The points are the charged number density, F(z) = dNchg/dz, where z = pchg/P(chgjet#1) is the ratio of the charged particle momentum to the charged momentum of chgjet#1. CDF Run 1 Analysis

Run 1 Fragmentation Function:

Run 1 Fragmentation Function Data from Fig. 3.8 on the momentum distribution of charged particles (pT andgt; 0.5 GeV and |h| andlt; 1) within chgjet#1 (leading charged jet) for PT(chgjet#1) andgt; 30 GeV compared with the QCD 'hard scattering' Monte-Carlo predictions of HERWIG, ISAJET, and PYTHIA. The points are the charged number density, F(z) =dNchg/dz, where z = pchg/P(chgjet#1) is the ratio of the charged particle momentum to the charged momentum of chgjet#1. CDF Run 1 Analysis

The “Transverse” Regionsas defined by the Leading Jet:

The 'Transverse' Regions as defined by the Leading Jet Look at charged particle correlations in the azimuthal angle Df relative to the leading calorimeter jet (JetClu R = 0.7, |h| andlt; 2).
Define |Df| andlt; 60o as 'Toward', 60o andlt; -Df andlt; 120o and 60o andlt; Df andlt; 120o as 'Transverse 1' and 'Transverse 2', and |Df| andgt; 120o as 'Away'. Each of the two 'transverse' regions have area DhDf = 2x60o = 4p/6. The overall 'transverse' region is the sum of the two transverse regions (DhDf = 2x120o = 4p/3). Charged Particle Df Correlations pT andgt; 0.5 GeV/c |h| andlt; 1 'Transverse' region is very sensitive to the 'underlying event'! Look at the charged particle density in the 'transverse' region! CDF Run 2 Analysis

Charged Particle Density Df Dependence:

Charged Particle Density Df Dependence Look at the 'transverse' region as defined by the leading jet (JetClu R = 0.7, |h| andlt; 2) or by the leading two jets (JetClu R = 0.7, |h| andlt; 2). 'Back-to-Back' events are selected to have at least two jets with Jet#1 and Jet#2 nearly 'back-to-back' (Df12 andgt; 150o) with almost equal transverse energies (ET(jet#2)/ET(jet#1) andgt; 0.8) and with ET(jet#3) andlt; 15 GeV. Shows the Df dependence of the charged particle density, dNchg/dhdf, for charged particles in the range pT andgt; 0.5 GeV/c and |h| andlt; 1 relative to jet#1 (rotated to 270o) for 30 andlt; ET(jet#1) andlt; 70 GeV for 'Leading Jet' and 'Back-to-Back' events. Refer to this as a 'Leading Jet' event Refer to this as a
'Back-to-Back' event Subset

“Transverse” Charge Density PYTHIA Tune A vs HERWIG :

'Transverse' Charge Density PYTHIA Tune A vs HERWIG Shows the average charged particle density, dNchg/dhdf, in the 'transverse' region (pT andgt; 0.5 GeV/c, |h| andlt; 1) versus ET(jet#1) for 'Leading Jet' and 'Back-to-Back' events. 'Leading Jet' 'Back-to-Back' Now look in detail at 'back-to-back' events in the region 30 andlt; ET(jet#1) andlt; 70 GeV! Compares the (uncorrected) data with PYTHIA Tune A and HERWIG after CDFSIM.

Charged Particle DensityPYTHIA Tune A vs HERWIG :

Charged Particle Density PYTHIA Tune A vs HERWIG HERWIG (without multiple parton interactions) produces too few charged particles in the 'transverse' region for 30 andlt; ET(jet#1) andlt; 70 GeV!

“Transverse” PTsum Density PYTHIA Tune A vs HERWIG :

'Transverse' PTsum Density PYTHIA Tune A vs HERWIG Shows the average charged PTsum density, dPTsum/dhdf, in the 'transverse' region (pT andgt; 0.5 GeV/c, |h| andlt; 1) versus ET(jet#1) for 'Leading Jet' and 'Back-to-Back' events.
Compares the (uncorrected) data with PYTHIA Tune A and HERWIG after CDFSIM. 'Leading Jet' 'Back-to-Back' Now look in detail at 'back-to-back' events in the region 30 andlt; ET(jet#1) andlt; 70 GeV!

Charged PTsum DensityPYTHIA Tune A vs HERWIG :

Charged PTsum Density PYTHIA Tune A vs HERWIG HERWIG (without multiple parton interactions) does not produces enough PTsum in the 'transverse' region for 30 andlt; ET(jet#1) andlt; 70 GeV!

Jet Algorithms:

Jet Algorithms Clustering algorithms are used to combine calorimeter towers or charged particles into 'jets' in order to study the event topology and to compare with the QCD Monte-Carlo Models. We do not detect partons! The outgoing partons fragment into hadrons before they travel a distance of about the size of the proton. At long distances the partons manifest themselves as 'jets'. The 'underlying event' can also form 'jets'. Most 'jets' are a mixture of particles arising from the 'hard' outgoing partons and the 'underlying event'. Every 'jet' algorithms correspond to a different observable and different algorithms give different results. Since we measure hadrons every observable is infrared and collinear safe. There are no divergences at the hadron level! Studying the difference between the algorithms teaches us about the event structure.

Jet Corrections & Extrapolations:

Jet Corrections andamp; Extrapolations Calorimeter Level Jets → Hadron Level Jets:
We measure 'jets' at the 'hadron level' in the calorimeter.
We certainly want to correct the 'jets' for the detector resolution and efficiency.
Also, we must correct the 'jets' for 'pile-up'.
Must correct what we measure back to the true 'hadron level' (i.e. particle level) observable! Particle Level Jets (with the 'underlying event' removed):
Do we want to make further model dependent corrections?
Do we want to try and subtract the 'underlying event' from the observed 'particle level' jets.
This cannot really be done, but if you trust the Monte-Carlo modeling of the 'underlying event' you can do it by using the Monte-Carlo models (use PYTHIA Tune A).
This is no longer an observable, it is a model dependent extrapolation! Hadron Level Jets → Parton Level Jets:
Do we want to use the data to try and extrapolate back to the parton level? What parton level, PYTHIA (Leading Log) or fixed order NLO?
This also cannot really be done, but again if you trust the Monte-Carlo models you can try and do it by using the Monte-Carlo models (use PYTHIA Tune A) including ISR and FSR.
Cannot extrapolate the data to fixed order NLO! I do not believe we should extrapolate
the data to the parton level! We should
publish what we measure (i.e. hadron level
with the 'underlying event')!
To compare with theory we should
'extrapolate' the parton level to the
hadron level (i.e. add hadronization and
the 'underlying event' to the parton level)!
PYTHIA, HERWIG, MC@NLO Hadron ← Parton Useless without a model of hadronization! Next-to-leading order parton level calculation
0, 1, 2, or 3 partons!

Good and Bad Algorithms:

Good and Bad Algorithms In order to correct what we see in the calorimeter back to the hadron level we must use an algorithm that can be defined at both the calorimeter and particle level. If you insist on extrapolating the data to the parton level then it is better to use an algorithm that is well defined at the parton level (i.e. infrared and collinear safe at the parton level). If you hadronize the parton level and add the 'underlying event' (i.e. PYTHIA, HERWIG, MC@NLO) then you do not care if the algorithm is infrared and collinear safe at the parton level. You can predict any hadron level observable!

Four Jet Algorithms:

Four Jet Algorithms JetClu is bad because the algorithm cannot be defined at the particle level. Bad The MidPoint and Modified MidPoint (i.e. Search Cone) algorithms are not infrared and collinear safe at the parton level. Towers not included in a jet (i.e. 'dark towers')!

KT Algorithm:

KT Algorithm kT Algorithm:
Cluster together calorimeter towers by their kT proximity.
Infrared and collinear safe at all orders of pQCD.
No splitting and merging.
No ad hoc Rsep parameter necessary to compare with parton level.
Every parton, particle, or tower is assigned to a 'jet'.
No biases from seed towers.
Favored algorithm in e+e- annihilations! KT Algorithm Only towers with ET andgt; 0.5 GeV are shown Raw Jet ET = 533 GeV Raw Jet ET = 618 GeV Will the KT algorithm be effective in the collider environment where there is an 'underlying event'? CDF Run 2

KT Inclusive Jet Cross Section:

KT Inclusive Jet Cross Section KT Algorithm (D = 0.7)
Data corrected to the hadron level
L = 385 pb-1
0.1 andlt; |yjet| andlt; 0.7
Compared with NLO QCD (JetRad) corrected to the hadron level. Sensitive to UE + hadronization effects for PT andlt; 300 GeV/c!

Search Cone Inclusive Jet Cross Section:

Search Cone Inclusive Jet Cross Section Modified MidPoint Cone Algorithm (R = 0.7, fmerge = 0.75)
Data corrected to the hadron level and the parton level
L = 1.04 fb-1
0.1 andlt; |yjet| andlt; 0.7
Compared with NLO QCD (JetRad, Rsep = 1.3) Sensitive to UE + hadronization effects for PT andlt; 200 GeV/c!

Hadronization and “Underlying Event” Corrections:

Hadronization and 'Underlying Event' Corrections Compare the hadronization and 'underlying event' corrections for the KT algorithm (D = 0.7) and the MidPoint algorithm (R = 0.7)! The KT algorithm is slightly more sensitive to the 'underlying event'! We see that the KT algorithm (D = 0.7) is slightly more sensitive to the underlying event than the cone algorithm (R = 0.7), but with a good model of the 'underlying event' both cross sections can be measured at the Tevatrun!
Note that DØ does not make any
corrections for hadronization
or the 'underlying event'!?

Summary and Conclusions:

Summary and Conclusions Neither HERWIG or PYTHIA describe perfectly the distribution charged particles in quark and gluon jets at the Tevatron! To learn about the fragmentation function at large z we should compare the inclusive 'jet' cross-section to the inclusive charged particle cross section! We have events with 600 GeV 'jets' so we must have events with 300 GeV/c charged particles! Was this measured in Run 1? A lot of work has been done in comparing to analytic MLLA calculations (Korytov and students), but more work needs to be done in improving the fragmentation models in HERWIG and PYTHIA! I wish I could show you the following:
CDF measured fragmentation functions at different Q2 compared with PYTHIA and HERWIG.
The kT distribution of charged particles within 'jets' compared with PYTHIA and HERWIG.
The ratio of the inclusive charged particle cross-section to the inclusive 'jet' cross-section compared with PYTHIA and HERWIG. Sergo’s latest 'blessing' from the CDF-QCD group!

Inclusive & Exclusive 3-Jet Study:

Inclusive andamp; Exclusive 3-Jet Study CDF Run 2 CDF analysis using 1fb-1. At least 1 Jet ('trigger' jet)
(PT andgt; PTtrig, |h| andlt; 1.0) Exactly 3 jets (Exclusive)
(PT andgt; PTmin, |h| andlt; 2.5) More than 2 jets (Inclusive)
(PT andgt; PTmin, |h| andlt; 2.5) Order Jets by PT
Jet1 highest PT, etc. Jet1 Jet2 Jet3 Jet4 MidPoint R = 0.4
and
JetClu R = 0.4 Charged Particle Jets
RDF Algorithm
R = 0.4

MIT Search Scheme 12:

MIT Search Scheme 12 Exclusive 3 Jet Final State Challenge Exactly 3 jets
(PT andgt; 20 GeV/c, |h| andlt; 2.5) At least 1 Jet ('trigger' jet)
(PT andgt; 40 GeV/c, |h| andlt; 1.0) CDF Data
(MIT JetClu R=0.4) PYTHIA Tune A Normalized to 1 Order Jets by PT
Jet1 highest PT, etc. R(j2,j3)

Exc3J R(j2,j3) Normalized:

Exc3J R(j2,j3) Normalized Let Ntrig40 equal the number of events with at least one jet with PT andgt; 40 GeV/c and |h| andlt; 1.0 (this is the 'offline' trigger). Let N3Jexc20 equal the number of events with exactly three jets with PT andgt; 20 GeV/c and |h| andlt; 2.5 which also have at least one jet with PT andgt; 40 GeV/c and |h| andlt; 1.0. Let N3JexcFr = N3Jexc20/Ntrig40. The is the fraction of the 'offline' trigger events that are exclusive 3-jet events. The CDF data (MIT JetClu R=0.4) on dN/dR(j2,j3) at 1.96 TeV compared with PYTHIA Tune AW (PARP(67)=4), Tune DW (PARP(67)=2.5), Tune BW (PARP(67)=1). PARP(67) affects the initial-state radiation which contributes primarily to the region R(j2,j3) andgt; 1.0. Normalized to N3JexcFr The data have more 3 jet events with small R(j2,j3)!? CDF Data
(MIT JetClu R=0.4) data corrected using 'jet corrections'!

Exc3J R(j2,j3) Normalized:

Exc3J R(j2,j3) Normalized Let Ntrig40 equal the number of events with at least one jet with PT andgt; 40 GeV/c and |h| andlt; 1.0 (this is the 'offline' trigger). Let N3Jexc20 equal the number of events with exactly three jets with PT andgt; 20 GeV/c and |h| andlt; 2.5 which also have at least one jet with PT andgt; 40 GeV/c and |h| andlt; 1.0. Let N3JexcFr = N3Jexc20/Ntrig40. The is the fraction of the 'offline' trigger events that are exclusive 3-jet events. The CDF data (MIT JetClu R=0.4) on dN/dR(j2,j3) at 1.96 TeV compared with PYTHIA Tune DW (PARP(67)=2.5) and HERWIG (without MPI). Final-State radiation contributes to the region R(j2,j3) andlt; 1.0. Normalized to N3JexcFr If you ignore the normalization and normalize all the distributions to one then the data prefer Tune BW, but I believe this is misleading.
UF-MIT (and Steve Mrenna) are working
to understand
the CDF inclusive and exclusive
3-jet data!

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