# Presentation: 350405

## Don Lincoln
Fermilab

- Don Lincoln
- Fermilab

- Tevatron Run I QCD Results
- Don Lincoln
- f

## Quantum      Chromo               Dynamics

- Topics Today
- Inclusive Jet Cross-Section (Cone Algorithm)
- Measurement of s
- Inclusive Jet Cross-Section (kT Algorithm)
- Event shape variables
- Jet structure/quark-gluon                             separation

- Study of the force governing the behavior of quarks and gluons

- New

## Cone Definition of Jets

- Cone DefinitionR=0.7 in 
- Merging and splitting of jets required if they share energy
- Rsep required to compare theoretical predictions to data
**    ****(R****sep****is the minimum separation of 2 partons to be considered distinct jets)**

**Centroid found with****4-vector addition**
**E****jet**** = ******** E****i**
**E****T****jet**** = E****jet**** sin ********jet**
**(CDF’s Definition)**

******** ****= -ln[tan(**********/2)]**

**Suggests need for**
**more robust algorithm**

- Observable remnant of
- parton-parton hard scatter

**Notes:**
D uses Ellis and Soper’s definition

## State of the Art 1995(The Controversy)

- State of the Art 1995(The Controversy)

- High pT excess is
- exciting prospect

- PRL 77 438 (1996)

- PRL 82 (1999) 2451

## Controversy Resolved(?)

- PRD 64 032001 (2001)
- Erratum-ibid. D65 039903 (2002)

- PRD 64 032003 (2001)

- More modern pdf’s
- (esp. CTEQ4M and CTEQ4HJ)
- ameliorate the disagreement

- CDF

## CDF 1B Result

| PDF | 2 | Confidence Level |
| --- | --- | --- |
| CTEQ4M | 63.1 | 1% |
| CTEQ4HJ | 46.8 | 10.1% |
| MRST | 49.5 | 7% |

- Plots show statistical error only
-  2 below include systematic error
- 33 degrees of freedom
- Rsep = 1.3 × R (R = 0.7)

- PRD 64 032003 (2001)

## s  from Inclusive Jet

- s  from Inclusive Jet

- PRL 88 042001 (2002)

* ***s2*X*(0) is LO prediction
* ***s3*X*(0)*k*1 is NLO prediction
*X*(0) and *k*1 determined from JETRAD
- MS scheme used (CTEQ4M)
- Jet cone algorithm used with     *R*sep = 1.3
* ***s determined in 33 *E**T* bins

## s  from Inclusive Jet

- s  from Inclusive Jet

- s determined at MZ
-  50 < ET < 250 GeV
-  All ET (CTEQ4HJ)
-  World Average

- PRL 88 042001 (2002)

- Theory errors
- ~ 5% (~2)

## KT Definition of Jets

- KT Definition of Jets

-   KT Definition
- cells/clusters are combined if their relative kT2 is “small” (relative transverse momentum) (D=1.0 or 0.5 is a scaling parameter)

**min**(*d**ii**, d**ij*) = *d**ij *  Merge
**min**(*d**ii**, d**ij*) = *d**ii  * Jet

- Infrared safe
-  Same definition for partons, 	Monte Carlo and data
-  Allows subjet definitions

**Ellis-Soper PRD 48 3160**

## Inclusive Cross Section Using KT Algorithm

- Inclusive Cross Section Using KT Algorithm

- Predictions IR and UV safe
- Merging behavior well-defined for both experiment and theory

- | < 0.5
- D = 1.0

- Phys. Lett. B 525 211 (2002)

## Comparison with Theory

- Normalization differs by 20% or more
- No significant deviations of predictions from data, when correlated systematic errors are included
- When first 4 data points ignored, probabilities are 60-80%

- D**** Preliminary

**PDF****	****	****	********/dof****	****    Prob**
- MRST		1.12	 	31
- MRSTg		1.38		10
- MRSTg		1.17		25
- CTEQ3M		1.56		  4
- CTEQ4M		1.30		15
- CTEQ4HJ	1.13		29

- Phys. Lett. B 525 211 (2002)

## Transverse ‘Thrust’ at D Using KT jets 

- Event shapes used at e+e- and ep to test QCD developments like resummation calculations and non-perturbative corrections
- Non-perturbative corrections: of the order of 1/Q. Related to hadronization effects.
- Resummations: needed  at small values of the shape variable where fixed-order perturbative calculations are expected to fail.

- Traditional variable (thrust) not suitable for hadron-collider environment.  (Lorentz boost invariance)
- Transverse Thrust:

## Dijet Transverse Thrust cross section

- KT algorithm (parameter D = 1)

- Event Selection:

-  Vertex cut (| z | < 50 cm, *e* ~ 90 %)
-  Jet quality cuts (*e* ~ 99.5 % )
- 	( 0.05 < *EMF *< 0.95,  *CHF  *< 0.4 )
- Trigger-specific leading jet pT cuts
-  Cut on  missing ET (ET/pTlj  < 0.7)
-  |1| < 1, |2| < 1, |3| < 3 (if present)
-  Bin in

- Non-Traditional Aspects
- Use only leading two jets
- to calculate T2T
- Bin in HT3
- Compromise on measuring
- hard scale and insensitivity
- to noise.

- Jet production rate  s3 is NLO
- Event  shape observables s3 is LO** **

## Dijet Transverse Thrust cross section

- Only statistical errors included

- Preprint forthcoming

- Deviations at
- High (1-T)  higher order
- Low  (1-T)  resummation

- Systematic error
- work underway

## KT Algorithm and Subjets

- KT Algorithm and Subjets

- For subjets, define “large” KT

- (ycut = 10-3, D = 0.5)

- PRD 65 052008 (2002)

**Notes:**
Theoretically it is infrared safe.  Cone algorithm is not because of soft radiation in NNLO calculations.
The same algorithm can be applied to partons from fixed-order or resummed calculations, and to MC particles and to data.  In the cone algorithm, R_sep is an ad-hoc parameter used to accommodate the difference between jet definitions at the parton and detector levels.
An arbitrary procedure must be used to split and merge jets when using the cone algorithm

## Quark/Gluon Separation

- Quark/gluon separation interesting
- QCD/fragmentation studies
- Useful for enhancing quark-only final states (c.f. tt  all jets)
- Find quark (gluon) enhanced samples.

- Parton Level

- Use 55 < pt < 100 GeV
- x630 ~ 0.09 – 0.16
- x1800 ~ 0.03 – 0.055

## D Subjet Multiplicity Using KT Algorithm

- D**** Subjet Multiplicity Using KT Algorithm

- Assume ***M******g ******, M******Q*** independent of ********* s***

- PRD 65 052008 (2002)

- Uncorrected

- After fragmentation

## D Subjet Multiplicity Using KT Algorithm

- D**** Subjet Multiplicity Using KT Algorithm

- Raw Subjet Multiplicities	Extracted Quark and Gluon Multiplicities

- Higher M  more gluon jets at 1800 GeV

- PRD 65 052008 (2002)

## D Subjet Multiplicity Using KT Algorithm

**HERWIG** prediction          = 1.91 ± 0.16 (stat)

- D**** Subjet Multiplicity Using KT Algorithm

- Largest uncertainty comes fromthe gluon fractions in the PDFs

- PRD 65 052008 (2002)

## Summary #1

- CDF’s new inclusive jet analysis does not show the dramatic high pT excess of earlier analyses and highlights need for better high-*x* gluon pdfs
- CDF has recently published a nice analysis measuring s from 50-250 GeV and evolved it to Mz, where it agrees nicely with the world average
- Analysis does show sensitivity to the high p excess  described above

## Summary #2

- DØ has recently completed an extensive program using the kT jet-finding algorithm
- Inclusive jet cross-section
- Reasonable agreement with NLO calculations
- Prefers CTEQ4HJ and MRST pdfs
- k jets contain more energy than similar cone jets
- Event shape analysis (using transverse thrust)
- Very preliminary results shown here. Preprint available soon.
- Jet structure analysis
- Good agreement with HERWIG
- Approximately twice as much radiation from gluon jets as from quark jets.

## www-d0.fnal.gov/~lucifer/PowerPoint/LaThuile2002.ppt

## D Subjet Multiplicity Using KT Algorithm

- D**** Subjet Multiplicity Using KT Algorithm

- Perturbative and resummed calculations predict that gluon jets have higher subjet multiplicity than quark jets, on average.
- Linear Combination:
***<M>****** = ******f******g****** ******M******g****** + (1-******f******g******) M******Q***

***Mean Jet Multiplicity***

***Quark Jet Fraction***

***Gluon Jet Fraction***

- After fragmentation

- PRD 65 052008 (2002)

- Monte Carlo

## D Subjet Multiplicity Using KT Algorithm

- D**** Subjet Multiplicity Using KT Algorithm

- Assume ***M******g ******, M******Q*** independent of ********* s***

- PRD 65 052008 (2002)

- Uncorrected