# Presentation: 491334

## Fermilab Tevatron University

**Rick Field**
**University of Florida**

**CDF Run 2**

**Toward an Understanding**
**of Hadron-Hadron Collisions**

***Fermilab 2006***

- Fermilab Tevatron University                                                 December 14, 2006

## Toward and Understanding of Hadron-Hadron Collisions

**From 7 GeV/c ********0****’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**

**1****st**** hat!**

- Fermilab Tevatron University                                                 December 14, 2006

## The Feynman-Field Days

**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 1****st**** graduate student!**

- Fermilab Tevatron University                                                 December 14, 2006

## 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 P****T**** particles arise from **
**direct hard collisions between constituent **
**quarks in the incoming particles, which **
**fragment or cascade down into several hadrons.”**

**“****Black-Box Model”**

- Fermilab Tevatron University                                                 December 14, 2006

## 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.”**

- Fermilab Tevatron University                                                 December 14, 2006

## 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 ********0****’s!**

- Fermilab Tevatron University                                                 December 14, 2006

## Telagram from Feynman

**July 1976**

**SAW CRONIN AM NOW CONVINCED WERE RIGHT TRACK QUICK WRITE**
**FEYNMAN**

- Fermilab Tevatron University                                                 December 14, 2006

## Letter from Feynman

**July 1976**

- Fermilab Tevatron University                                                 December 14, 2006

## Letter from Feynman Page 1

- Spelling?

- Fermilab Tevatron University                                                 December 14, 2006

## Letter from Feynman Page 3

**It is fun!**

**Onward!**

- Fermilab Tevatron University                                                 December 14, 2006

## Feynman Talk at Coral Gables (December 1976)

**“****Feynman-Field **
**Jet Model”**

**1****st**** transparency**

**Last transparency**

- Fermilab Tevatron University                                                 December 14, 2006

## QCD Approach: Quarks & Gluons

**FFF2 1978**

_**Parton Distribution Functions**_
**Q****2**** dependence predicted from QCD**

_**Quark & Gluon Fragmentation Functions**_
**Q****2**** dependence predicted from QCD**

_**Quark & 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.”**

- Fermilab Tevatron University                                                 December 14, 2006

## High PT Jets

**High P****T**** Jets**

**30 GeV/c!**

_**Predict**_
**large “jet” cross-section**

**Feynman, Field, & 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 P****T**** discussed here.”**

- Fermilab Tevatron University                                                 December 14, 2006

## 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 P****0**

**Let f(********)d******** be the probability that the rank 1 meson *****leaves***** fractional momentum ******** to the remaining cascade, leaving quark “b” with momentum P****1**** = ********1****P****0****.**

**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(********)), leaving quark “c” with momentum P****2**** = ********2****P****1 ****= ********2********1****P****0****.**

**Add in flavor dependence by letting ********u**** = probabliity of producing u-ubar pair, ********d**** = 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(********) and ********i****!**

**Rank 1**

**Secondary Mesons**
**(after decay)**

- Fermilab Tevatron University                                                 December 14, 2006

## 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, ....”**

- Fermilab Tevatron University                                                 December 14, 2006

## Monte-Carlo Simulationof Hadron-Hadron Collisions

_**FF1-FFF1 (1977)**_** “Black-Box” Model**

_**F1-FFF2 (1978)**_** QCD Approach**

_**FF2 (1978)**_** **
**Monte-Carlo simulation of “jets”**

_**FFFW “FieldJet” (1980)**_** **
**QCD “leading-log order” simulation **
**of hadron-hadron collisions**

_**ISAJET**_
**(“FF” Fragmentation)**

_**HERWIG**_
**(“FW” Fragmentation)**

_**PYTHIA**_

**today**

**“****FF” or “FW” Fragmentation**

**the past**

**tomorrow**

_**SHERPA**_

_**PYTHIA 6.3**_

- Fermilab Tevatron University                                                 December 14, 2006

## 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!**

- Fermilab Tevatron University                                                 December 14, 2006

## Monte-Carlo Simulationof Quark and Gluon Jets

**ISAJET:**** Evolve the parton-shower from Q****2**** (*****virtual photon invariant mass*****) to Q****min**** ~ 5 GeV. Use a complicated fragmentation model to evolve from Q****min**** to outgoing hadrons.**

**Q****2**

**5 GeV**

**1 GeV**

**200 MeV**

**HERWIG:**** Evolve the parton-shower from Q****2**** (*****virtual photon invariant mass*****) to Q****min**** ~ 1 GeV. Form color singlet clusters which “decay” into hadrons according to 2-particle phase space.**

**MLLA:**** Evolve the parton-shower from Q****2**** (*****virtual photon invariant mass*****) to Q****min**** ~ 230 MeV. Assume that the charged particles behave the same as the partons with N****chg****/N****parton**** = 0.56!**

**MLLA Curve!**

***= ln(E******jet******/p******particle******)***

- Fermilab Tevatron University                                                 December 14, 2006

## 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 Q****eff ****= 230 ******** 40 MeV**
**N****charged-hadrons****/N****partons**** = 0.56 ******** 0.10**

**CDF Run 1 Analysis**

*Ratio = N**g-jet** / N**q-jet*

*Q = E**jet **** ****cone*

**Both PYTHIA and HERWIG predict a Gluon-Quark Ratio that is smaller than the data!**

- Fermilab Tevatron University                                                 December 14, 2006

## Charged Multiplicity in Quark and Gluon Jets

**CDF Run 1 data on the average charged particle multiplicities in gluon and quark jets versus Q = E****jet**** ****× ********cone**** 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**

- Fermilab Tevatron University                                                 December 14, 2006

## 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**

- Fermilab Tevatron University                                                 December 14, 2006

## Evolution of Charged Jets“Underlying Event”

**Look at charged particle correlations in the azimuthal angle ********relative to the leading charged particle jet.**
**Define ****|********| < 60****o**** as “Toward”****, ****60****o**** < |********| < 120****o**** as “Transverse”****, and ****|********| > 120****o**** as “Away”****.**
**All three regions have the same size in ********-******** space, ********x******** = 2x120****o ****= 4********/3.**

**Charged Particle ******** Correlations P****T**** > 0.5 GeV/c |********| < 1**

**Look at the charged particle density in the “transverse” region!**

**“****Transverse” region very sensitive to the “underlying event”!**

**CDF Run 1 Analysis**

- Fermilab Tevatron University                                                 December 14, 2006

##  “Transverse” Charged Particle Density

** ****“****Transverse” ****Charged Particle Density**

**Shows the data on the average “transverse” charge particle density (|********|<1, p****T****>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).**

- Fermilab Tevatron University                                                 December 14, 2006

## Charged Multiplicity in Charged Particle Jets

**Plot shows the average number of charged particles (p****T**** > 0.5 GeV, |********| < 1)  within the leading charged particle jet (R = 0.7) as a function of the P****T**** 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**

- Fermilab Tevatron University                                                 December 14, 2006

## Charged Multiplicity in Charged Particle Jets

**CDF Run 1 data on the multiplicity distribution of charged particles (p****T**** > 0.5 GeV and |********| < 1) within chgjet#1 (*****leading charged  jet*****) for P****T****(chgjet#1) > 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 N****chg**** charged particles.  **

**CDF Run 1 Analysis**

**Includes charged particles from the “underlying event”!**

- Fermilab Tevatron University                                                 December 14, 2006

## Radial Charged Distribution in Charged Particle Jets

**Charged multiplicity flow in the radial distance R in ********-******** space from chgjet#1 (*****leading charged jet*****) for charged particles with p****T**** > 0.5 GeV and |********| < 1 when P****T****(chgjet#1) > 5  and 30 GeV.  The points are <Nchg> in a 0.02 bin of R. **

**Charged PTsum flow in the radial distance R in ********-********space from chgjet#1 (*****leading charged jet*****) for charged particles with p****T**** > 0.5 GeV and |********| < 1 when P****T****(chgjet#1) > 5  and 30 GeV.  The points are the *****scalar***** <PTsum> in a 0.02 bin of R. **

- Fermilab Tevatron University                                                 December 14, 2006

## Run 1 Fragmentation Function

**CDF Run 1 data on the momentum distribution of charged particles (p****T**** > 0.5 GeV and |********| < 1) within chgjet#1 (*****leading charged  jet*****).  The points are the charged number density, F(z) = dN****chg****/dz, where z = p****chg****/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**

- Fermilab Tevatron University                                                 December 14, 2006

## Run 1 Fragmentation Function

**CDF Run 1 data from on the momentum distribution of charged particles (p****T**** > 0.5 GeV and |********| < 1) within chgjet#1 (*****leading charged jet*****) for P****T****(chgjet#1) > 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) = dN****chg****/dz, where                    z = p****chg****/P(chgjet#1) is the ratio of the charged particle momentum to the charged momentum of chgjet#1.**

**CDF Run 1 Analysis**

- Fermilab Tevatron University                                                 December 14, 2006

## Run 1 Fragmentation Function

**Data from Fig. 3.8 on the momentum distribution of charged particles (p****T**** > 0.5 GeV and |********| < 1) within chgjet#1 (*****leading charged jet*****) for P****T****(chgjet#1) > 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 = p****chg****/P(chgjet#1) is the ratio of the charged particle momentum to the charged momentum of chgjet#1. **

**CDF Run 1 Analysis**

- Fermilab Tevatron University                                                 December 14, 2006

## The “Transverse” Regionsas defined by the Leading Jet

**The “Transverse” Regions****as defined by the Leading Jet**

**Look at charged particle correlations in the azimuthal angle ********relative to the leading calorimeter jet (JetClu R = 0.7, |********| < 2).**
**Define ****|********| < 60****o**** as “Toward”****, ****60****o**** < -******** < 120****o ****and 60****o**** < ******** < 120****o**** as “Transverse 1” and “Transverse 2”****, and ****|********| > 120****o**** as “Away”****.  Each of the two “transverse” regions have area ******** = 2x60****o ****= 4********/6.  ****The overall “transverse” region is the sum of the two transverse regions (******** = 2x120****o ****= 4********/3).**

**Charged Particle ******** Correlations p****T**** > 0.5 GeV/c |********| < 1**

**“****Transverse” region is very sensitive to the “underlying event”!**

**Look at the charged particle density in the “transverse” region!**

**CDF Run 2 Analysis**

- Fermilab Tevatron University                                                 December 14, 2006

## Charged Particle Density  Dependence

**Charged Particle Density ******** Dependence**

**Look at the ****“transverse” region**** as defined by the leading jet (JetClu R = 0.7, |********| < 2) or by the leading two jets (JetClu R = 0.7, |********| < 2). ****“Back-to-Back”**** events are selected to have at least two jets with Jet#1 and Jet#2 nearly “back-to-back” (********12**** > 150****o****) with almost equal transverse energies (E****T****(jet#2)/E****T****(jet#1) > 0.8) and with E****T****(jet#3) < 15 GeV. **

**Shows the ******** dependence of the charged particle density****, dN****chg****/d********d********, for charged particles in the range p****T**** > 0.5 GeV/c and |********| < 1 relative to jet#1 (rotated to 270****o****)  for 30 < E****T****(jet#1) < 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**

- Fermilab Tevatron University                                                 December 14, 2006

## “Transverse” Charge Density PYTHIA Tune A vs HERWIG 

**“****Transverse” Charge Density**** PYTHIA Tune A vs HERWIG **

**Shows the ****average charged particle density****, dN****chg****/d********d********, in the ****“transverse” region**** (p****T**** > 0.5 GeV/c, |********| < 1) versus E****T****(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 < E****T****(jet#1) < 70 GeV!**

**Compares the (*****uncorrected*****) data with ****PYTHIA Tune A**** and ****HERWIG**** after CDFSIM.**

- Fermilab Tevatron University                                                 December 14, 2006

## Charged Particle DensityPYTHIA 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 < E****T****(jet#1) < 70 GeV!**

- Fermilab Tevatron University                                                 December 14, 2006

## “Transverse” PTsum Density PYTHIA Tune A vs HERWIG 

**“****Transverse” PTsum Density**** PYTHIA Tune A vs HERWIG **

**Shows the ****average charged PTsum density****, dPT****sum****/d********d********, in the ****“transverse” region**** (p****T**** > 0.5 GeV/c, |********| < 1) versus E****T****(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 < E****T****(jet#1) < 70 GeV!**

- Fermilab Tevatron University                                                 December 14, 2006

## Charged PTsum DensityPYTHIA 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 < E****T****(jet#1) < 70 GeV!**

- Fermilab Tevatron University                                                 December 14, 2006

## 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.   **

- Fermilab Tevatron University                                                 December 14, 2006

## Jet Corrections & Extrapolations

**Jet Corrections & 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!**

- Fermilab Tevatron University                                                 December 14, 2006

## 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!**

- Fermilab Tevatron University                                                 December 14, 2006

## 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”)!**

- Fermilab Tevatron University                                                 December 14, 2006

## 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!**

**K****T**** Algorithm**

**Only towers with E****T**** > 0.5 GeV are shown**

- Raw Jet ET = 533 GeV

- Raw Jet ET = 618 GeV

**Will the K****T**** algorithm be effective in the collider environment where there is an “underlying event”? **

**CDF Run 2**

- Fermilab Tevatron University                                                 December 14, 2006

## KT Inclusive Jet Cross Section

**K****T**** Algorithm (D = 0.7)**
**Data corrected to the hadron level**
**L***** *****= 385 pb****-1**
**0.1 < |y****jet****| < 0.7**
**Compared with NLO QCD (JetRad) corrected to the hadron level.**

**Sensitive to UE + hadronization effects for P****T**** < 300 GeV/c!**

- Fermilab Tevatron University                                                 December 14, 2006

## Search Cone Inclusive Jet Cross Section

**Search Cone ****Inclusive Jet Cross Section**

**Modified MidPoint Cone Algorithm (R = 0.7, f****merge**** = 0.75)**
**Data corrected to the hadron level and the parton level**
**L***** *****= 1.04 fb****-1**
**0.1 < |y****jet****| < 0.7**
**Compared with NLO QCD (JetRad, R****sep**** = 1.3)**

**Sensitive to UE + hadronization effects for P****T**** < 200 GeV/c!**

- Fermilab Tevatron University                                                 December 14, 2006

## Hadronization and “Underlying Event” Corrections

**Compare the hadronization and “underlying event” corrections for the K****T**** algorithm (D = 0.7) and the MidPoint algorithm (R = 0.7)!**

**The K****T**** algorithm is slightly more sensitive to the “underlying event”!**

**We see that the K****T**** 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 D****Ø**** does not make any **
**corrections for hadronization**
**or the “underlying event”!?**

- Fermilab Tevatron University                                                 December 14, 2006

## 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 Q****2**** compared with PYTHIA and HERWIG.**
**The k****T**** 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!**

- Fermilab Tevatron University                                                 December 14, 2006

## Inclusive & Exclusive 3-Jet Study

**CDF Run 2**

**CDF analysis using 1fb****-1****.**

_**At least 1 Jet (“trigger” jet)**_
**(P****T**** > PT****trig****, |********| < 1.0)**

_**Exactly 3 jets (**__***Exclusive***__**)**_
**(P****T**** > PT****min****, |********| < 2.5)**

_**More than 2 jets (**__***Inclusive***__**)**_
**(P****T**** > PT****min****, |********| < 2.5)**

_**Order Jets by P**__**T**_
**Jet1 highest P****T****, etc.**

- Jet1

- Jet2

- Jet3

- Jet4

**MidPoint R = 0.4 **
**and **
**JetClu R = 0.4**

_**Charged Particle Jets**_
**RDF Algorithm**
**R = 0.4**

- Fermilab Tevatron University                                                 December 14, 2006

## MIT Search Scheme 12

**MIT Search Scheme 12**

**Exclusive 3 Jet Final State Challenge**

_**Exactly 3 jets**_
**(P****T**** > 20 GeV/c, |********| < 2.5)**

_**At least 1 Jet (“trigger” jet)**_
**(P****T**** > 40 GeV/c, |********| < 1.0)**

**CDF Data **
**(MIT JetClu R=0.4)**

**PYTHIA Tune A**

**Normalized to 1**

_**Order Jets by P**__**T**_
**Jet1 highest P****T****, etc.**

**R(j2,j3)**

- Fermilab Tevatron University                                                 December 14, 2006

## Exc3J R(j2,j3) Normalized

**Let ****Ntrig40**** equal the number of events with at least one jet with P****T**** > 40 GeV/c and |********| < 1.0 (this is the “offline” trigger).**

**Let ****N3Jexc20**** equal the number of events with exactly three jets with P****T**** > 20 GeV/c and |********| < 2.5 which also have at least one jet with P****T**** > 40 GeV/c and |********| < 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) > 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”!**

- Fermilab Tevatron University                                                 December 14, 2006

## Exc3J R(j2,j3) Normalized

**Exc3J R(j2,j3) Normalized**

**Let ****Ntrig40**** equal the number of events with at least one jet with P****T**** > 40 GeV/c and |********| < 1.0 (this is the “offline” trigger).**

**Let ****N3Jexc20**** equal the number of events with exactly three jets with P****T**** > 20 GeV/c and |********| < 2.5 which also have at least one jet with P****T**** > 40 GeV/c and |********| < 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) < 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!**

- Fermilab Tevatron University                                                 December 14, 2006