Quantum Chromodynamics (QCD)

1
Quantum Chromodynamics (QCD)

• Andrew Brandt
• UT-Arlington/DØ Experiment

Quarknet June 6, 2001
2
Structure of Matter
Matter
Molecule
Atom
Nucleus
Quark
Baryon
(Hadron)
u
10-14m
cm
10-10m
10-15m
10-9m
lt10-19m
protons, neutrons, mesons, etc. p,W,L...
top, bottom, charm, strange, up, down
Chemistry
Atomic Physics
Nuclear Physics
Electron
Mass
(Lepton)
proton 1 GeV/c2
lt10-18m
High Energy Physics
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Forces

• Forces work by the exchange of Bosons
• Electromagnetic Photon Exchange

• Weak Nuclear ForceCauses Nuclear Decays

neutron
proton
W- boson
e-
p
photon ?
electron
n
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Forces Strong Nuclear or Color

• Strong Nuclear ForceQuantum ChromodynamicsGluon
  Exchange, also holds the nucleus together.All
  quarks carry a color chargeGluons carry two
  color charges
• Different from other ForcesGluons 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 uudAlso contains gluons and
quark-antiquark pairs in a sea. Neutron
udd Pion ud
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Proton Antiproton Collisions

• A word about unitsHEP uses natural units

900 GeV Antiprotons
900 GeV Protons

• The mass of a proton is then given by

• Collide protons and antiprotons each with 900 GeV
  of kinetic energy.

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Life at Fermilab
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Particle Colliders as Microscopes
QM large momenta small distances
How we see different-sized objects
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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

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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
uv
s
uv
s
u
d
dv
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Parton-Parton Scattering

• Described by QCD.

Scattered Parton
Anti-Proton 900 GeV
Proton 900 GeV
Scattered Parton
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Perturbative QCD and Jet Production
Observable jet of particles in detector
q
jet
q (x1)
Parton distribution (PDF)
g
q (x2)
q
jet
Fragmentation into hadrons
p
Hard scatter (pQCD)
Includes radiative corrections and gluon emission
- much of current QCD is a study of this
additional radiation
p
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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

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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
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The DØ Detector
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Detection
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Inclusive Jet Cross Section as a Test of the
Standard Model (pQCD)
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Jet Production and Reconstruction
Highest ET dijet event at DØ

• Fixed cone-size jets
• Add up towers
• Iterative algorithm
• Jet quantities

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Typical DØ Dijet Event
ET,1 475 GeV, h1 -0.69, x10.66 ET,2 472
GeV, h2 0.69, x20.66
MJJ 1.18 TeV Q2 ET,1ET,22.2x105 GeV2
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High Energy Art
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The DØ Central Inclusive Jet Cross Section

• 0.0 ? ??? ? 0.5
• JETRAD

Phys. Rev. Lett. 82, 2451 (1999)
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Data Selection and Corrections
Unfold effects of finite jet energy resolutions
from very steeply falling inclusive jet cross
sections
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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
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Uncertainties in Cross Section Calculations
hlt0.5 Inclusive Jet CS ?s1800GeV

• 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/9801285, EPJ C5,
• 687, 1998)
• - Renormalization Scale (10)
• - PDFs (20 with ET dependence)
• - Clustering Alg. (5 with ET dependence)

PDF's dominate uncertainties ? Jets offer
valuable constraints! But sensitivity is reduced
in ratios, angular distributions...
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CTEQ5
Jets in PDFs
101
x-Q region spanned by experimental data in modern
fits Tevatron jets in blue
Q (GeV)
101
100
100 101 102 103
104
1/ x
Tevatron jet data serves as stronger constraint
in medium x region for CTEQ. MRST uses does not
use these data.
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Inclusive Jets- CDF
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Inclusive Jet Cross Section at 1.8TeV
Preliminary
PRL82, 2451 (1999)
D0 and CDF data in good agreement. NLO QCD
describes the data well.
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Rapidity Dependence of the Inclusive Jet Cross
Section
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Compositeness

• Continuing Search for fundamental building
  blockAtom ? 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

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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?

• The presence of three quark and lepton
  generations suggests that they could be composite
  particles
• Composed of preons

M
cos?
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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
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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)Rsep1.3R(Snowmass Rsep2.0R)

1.3R
2R
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Dijet Cross Section
Phys. Rev. Lett. 82, 2457 (1999)
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Cross Section Ratio

• Calculate Ratio of Cross Sections.
• Two different angular regions

Submitted to PRL hep-ex/9807014
Model with LL coupling
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Quark-Quark Compositeness Limits
Limit on size of preons is
fempto-meters
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Conclusions

• No evidence for Compositeness found at the
  Tevatron
• Standard Model (QCD) in excellent agreement with
  the data
• Quark-Quark Compositeness
• ? gt 2 to 3 TeV depending on models

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Numerous other QCD studies to probe scattering
dynamics
Jets in High E Limit
Photons
Color Flow
Diffraction
etc...
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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)0.1190.004

New measurement of aS by a single experiment
from a single observable over a wide range of Q2.
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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