1. Quantum Chromodynamics (QCD)
Andrew Brandt
UT-Arlington/DØ Experiment
Quarknet
June 6, 2001

2. Structure of Matter
Matter
Molecule
Atom
Nucleus
Baryon
Quark
(Hadron) u cm
10-9m
10-10m
10-14m
10-15m
<10-19m
Chemistry
protons, neutrons,
mesons, etc.
p,W,L...
top, bottom,
charm, strange,
up, down
Atomic Physics
Nuclear
Physics
Electron
Mass
(Lepton)
Give scale and relationship to the domain that high energy physicists work in.
Introduce the fundamental bits of matter loosely so that audience can point back to bulk matter.
Domain.
proton ~ 1 GeV/c2
<10-18m
High Energy Physics

3. Forces Forces work by the exchange of Boson’s
Electromagnetic: Photon Exchange
Weak Nuclear Force: Causes Nuclear Decays
neutron
proton
W- boson e-
photon  p+
electron n

4. Forces: Strong Nuclear or Color
Strong Nuclear Force: Quantum Chromodynamics Gluon Exchange, also holds the nucleus together. All quarks carry a color charge Gluons carry two color charges
Different from other Forces: Gluons can interact with other gluons.
Quarks and gluons are free
at small distances (asymptotic freedom), but not at large distances (confinement) 
cannot observe bare color
Always observe quarks in multiplets: Baryons qqq (Proton neutron) and Mesons (quark antiquark pair )
Proton: uud Also contains gluons and quark-antiquark pairs in a sea.
Neutron: udd
Pion: ud

5. Proton Antiproton Collisions
A word about units: HEP uses “natural units”
900 GeV Protons
900 GeV
Antiprotons
The mass of a proton is then given by
Collide protons and antiprotons each with 900 GeV of kinetic energy.

6. Life at Fermilab

7. Particle Colliders as Microscopes
QM: large momenta
= small distances
How we see
different-sized
objects:

8. Rutherford Scattering
The actual result was very different. “It was almost as incredible as if you fired a 15 inch shell at a piece of tissue paper and it came back at you”
Implied the existence of the nucleus.
We perform a similar experiment at Fermilab to look for fundamental structure

9. Proton Structure Proton contains three valance quarks: uud
Also contains sea of virtual quark anti-quark pairs.
All held together by gluons
Quarks and gluons are called partons.
Proton with momentum P. Individual parton carries momentum xP d u s uv uv u s u d dv u

10. Parton-Parton Scattering
Described by QCD.
Scattered
Parton
Anti-Proton
900 GeV
Proton
900 GeV
Scattered
Parton

11. Perturbative QCD and Jet Production
s ~ a2s (LO) ^
Observable jet of
particles in detector q
Parton
distribution
(PDF)
q (x1)
jet g
q (x2) q
jet
Fragmentation
into hadrons p
Hard scatter (pQCD)
s ~ a3s (NLO) ^
Includes radiative corrections
and gluon emission - much
of current QCD is a study of
this additional radiation p

12. Jets Jets are formed by the scattered partons.
QCD requires that colourless objects are produced (hadrons) e.g..: , K, , etc.
At DØ a jet is defined to be the energy deposited in a cone of radius:

13. Measured Event Variables
In a Two Jet event the following is measured:
Jet 1: ET1, h1, 1  
ET = Energy x
sin 
Jet 2: ET2, h2, 2
h = 0

14. The DØ Detector x y z  

15. Charged Particle Tracks
Detection EM
hadronic B Ä
Interaction
Point
Scintillating Fiber
Silicon Tracking
Calorimeter (dense)
Wire Chambers
Absorber Material
electron
photon
jet
muon
neutrino -- or any non-interacting particle missing transverse momentum
Charged Particle Tracks
Energy
Muon Tracks
We know x,y starting momenta is zero, but
along the z axis it is not, so many of our measurements are in the xy plane, or transverse
The Run 2 detector. Schematically how it works.
SVX and the like.

16. Inclusive Jet Cross Section as a Test of the Standard Model (pQCD)
Single Inclusive Jets:

17. Jet Production and Reconstruction
Time
“parton jet”
“particle jet”
“calorimeter jet”
hadrons  CH FH EM
Highest ET dijet event at DØ
RECO [Slide 1]
Very briefly mention RECO version used.
Mention that these are fixed-cone jets of R=0.7 found by iterative algorithm, Et is the scalar Et sum of the towers.
List corrections we apply (basically) to RECO. No more is needed for AIDA restoration or Ht-revertexing at this point, but following three slides will be about eta bias -- so just briefly prepare listeners for this!
Fixed cone-size jets
Add up towers
Iterative algorithm
Jet quantities:

18. “Typical DØ Dijet Event”
ET,1 = 475 GeV, h1 = -0.69, x1=0.66
ET,2 = 472 GeV, h2 = 0.69, x2=0.66
MJJ = 1.18 TeV
Q2 = ET,1×ET,2=2.2x105 GeV2

19. High Energy Art

20. The DØ Central Inclusive Jet Cross Section
DØ Run 1B
PDF,
substructure, … ?
d2/dET d ET
How well do we know proton
structure (PDF)?
Is NLO ( ) QCD “sufficient”?
Are quarks composite?
0.0    0.5
JETRAD
Phys. Rev. Lett. 82, 2451 (1999)

21. Data Selection and Corrections
Unfold effects of finite jet energy resolutions from very steeply falling inclusive jet cross sections E0 DØ
“observed”
“true”
“smearing”
“unsmearing” or “unfolding” ET
(GeV)
Smearing
Correction
0.86
0.90
0.94
0.98 50
100
150
200
250
300
350
400
450
500

22. Data Selection and Corrections
Cut on central p-pbar vertex position
Eliminate events with large missing ET
Apply jet quality cuts
Jet energy scale correction:
“calorimeter”  “particle” jet
“parton jet”
“particle jet”
“calorimeter jet”
hadrons  CH FH EM
E = (EObs-Offset)*Det.Uniformity
RH * Out of Cone Showering
RECO [Slide 1]
Very briefly mention RECO version used.
Mention that these are fixed-cone jets of R=0.7 found by iterative algorithm, Et is the scalar Et sum of the towers.
List corrections we apply (basically) to RECO. No more is needed for AIDA restoration or Ht-revertexing at this point, but following three slides will be about eta bias -- so just briefly prepare listeners for this!

23. Uncertainties in Cross Section Calculations
|h|<0.5 Inclusive Jet CS s=1800GeV
NLO pQCD predictions (s3):
- Ellis, et al., Phys. Rev. D, 64, (1990) EKS
- Aversa, et al., Phys. Rev. Lett., 65, (1990)
- Giele, et al., Phys. Rev. Lett., 73, (1994) JETRAD
Choices (hep-ph/ , EPJ C5,
687, 1998):
- Renormalization Scale (~10%)
- PDFs (~20% with ET dependence)
- Clustering Alg. (~5% with ET dependence) 2R
1.3R
DØ uses: JETRAD, , Rsep= 1.3.
PDF's dominate uncertainties  Jets offer valuable constraints!
But sensitivity is reduced in ratios, angular distributions...

24. Jets in PDFs CTEQ5 Q (GeV) 1/ x Tevatron jet data serves as stronger
101
x-Q region spanned by
experimental data in modern fits
Tevatron jets in blue
Q (GeV)
101
CTEQ5
100
1/ x
Tevatron jet data serves as stronger
constraint in medium x region
for CTEQ. MRST uses does not
use these data.

25. Inclusive Jets- CDF

26. Inclusive Jet Cross Section at 1.8TeV
Preliminary
PRL82, 2451 (1999)
This plot shows the Data-Theory/Theory plot for CDF and D0 results together. The D0 x-sec has been remeasured to match CDFs pseudorapidity range of 0.1 to 0.7. CDF is now presenting their systematic uncertainties for the final Run I measurement for the first time. They are plotted down here together with the uncertainties from D0. Roughly 10% for D0, 15% for CDF in the lowest Et bins; 22% for D0 and 27% for CDF at 400GeV. Overall nice agreement between the two experiments and with NLOQCD.
D0 and CDF data in good agreement. NLO QCD describes the data well.

27. Rapidity Dependence of the Inclusive Jet Cross Section
ET (GeV)
d2 dET d (fb/GeV)
0.0    0.5
0.5    1.0
1.0    1.5
1.5    2.0
2.0    3.0
DØ Preliminary
Run 1B
Nominal cross sections &
statistical errors only

28. Are Quarks composite particles?
Compositeness
Atom
Nucleus
Nucleon
Quark
Continuing Search for fundamental building block Atom  Nucleus  Nucleons  Quarks
Three quark and lepton generations suggests that quark and leptons are composites.
Question
Are Quarks composite particles?
Search for compositeness in Proton Anti-proton collisions

29. Search for Compositeness
Define the preons interaction scale as 
Existence of substructure at energies below  indicated by presence of four-fermion contact interactions.
Strength of interactions related to
Proton
Quark
Preons?
t’Hooft: interactions at high energy leads to massless composite fermions via unbroken chiral symmetries of the preons and confinement by their strong precolour interactions.
The presence of three quark and lepton generations suggests that they could be composite particles
Composed of “preons” M
cos

30. Predictions
If quarks are made up of smaller particles then expect more events at high mass, and at smaller scattering angles
Prediction for
composite
quarks
Number of Events
Number of Events
Prediction for
fundamental
quarks
cos * M

31. Dijet Production
To search for compositeness we need a good prediction for Standard Model dijet production  NLO QCD.
NLO event generator JETRAD (Giele, Glover, Kosower Nucl. Phys. B403, 633)
Need to choose pdf
Choose Renormalization and Factorization scales (set equal)
Rsep: maximum separation allowed between two partons to form a jet (mimic exp. algorithm) Rsep=1.3R (Snowmass: Rsep=2.0R)
Factorization Scale: Arbitrary parameter that separates the long and short distance physics. A parton with PT < mu will be absorbed into the hadron structure.
Renormalization Scale: scale introduced to remove divergences, as perturbation series reaches infinity dependence drops to zero.
1.3R 2R

32. Dijet Cross Section
Phys. Rev. Lett. 82, 2457 (1999)

33. Cross Section Ratio Submitted to PRL: hep-ex/9807014
Calculate Ratio of Cross Sections.
Two different angular regions
Submitted to PRL: hep-ex/
Model with LL coupling

34. Quark-Quark Compositeness Limits
Limit on size of preons is
fempto-meters

35. Conclusions No evidence for Compositeness found at the Tevatron
Standard Model (QCD) in excellent agreement with the data
Quark-Quark Compositeness
 > 2 to 3 TeV depending on models

36. Numerous other QCD studies to probe scattering dynamics
W/Z PT,W/Z+Jets +
+...
W, Z
q(x)
Jets in
High E Limit 
Photons
Color
Flow
Diffraction
etc...

37. Measurement of aS from Inclusive Jet Production
NLO x-section can be parametrized as
Measured
by CDF
Obtained from JETRAD
Fitting the NLO prediction to the data determines aS(ET)
aS(ET) is evolved to aS(MZ) using 2-loop renormalization group equation
Systematic uncertainties (~8%) from understanding of calorimeter response
Measured value consistent with world average of aS(MZ)=0.119±0.004
CDF measures the value of the strong coupling constant from the inclusive jet cross section over a large range of transverse energies. The NLO x-sec can be parametrized as a function of the strong coupling constant and two parameters, A and B, that depend on the Jet transverse energy. CDF measures the x-section, the parameters A and B can be obtained from JETRAD. For simplicity the renormalization and factorization scale are set to Et/2. Fitting the NLO prediction to the measured x-sec determines alpha_s as a function of transverse energy. The result is shown in this plot in blue compared to the expected running of alpha_s with Et.
The measured alpha_s can then be evolved to the value of alpha_s at the Z mass using a 2 loop renormalization group equation. The result is shown in this plot in red. The measured value for alpha_s at the Z mass obtained when using the CTEQ4M parton distribution is (stat). The systematic uncertainty comes mostly from the understanding of the calorimeter response and is below 10%. This result extended the measurement of alpha_s to a very high Q2 range and clearly shows the running of alpha_s. The result is consistent with the world average for alpha_s at the Z mass of
New measurement of aS by a single experiment & from a single observable over a wide range of Q2.

38. Conclusions Standard Model (QCD) in excellent agreement with the data
No evidence for Compositeness of quarks found at the Tevatron
Studies continue improving theory, detectors,
and using better microscopes