UCT Seminar III: The Parton Model

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UCT Seminar IIIThe Parton Model QCD

• Peter Steinberg
• Brookhaven National Laboratory
• Fulbright Scholar Program

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Outline

• What is a proton?
• Quark model
• Probing a proton
• Deep-inelastic scattering
• DIS observations
• Scaling at x.3
• Scaling violations
• QCD in DIS
• DGLAP evolution
• Splitting functions
• PDFs
• Gluon structure function
• Extraction
• Available sets

• Applications
• Cross sections of hard processes
• Heavy flavor
• Drell-yan
• Limits to pQCD approach
• Total cross section
• Nuclear effects
• EMC Effect
• Shadowing
• Parton Saturation
• Fragmentation functions
• Evolution eqns

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Studying Proton Structure

• At low energies, study elastic scattering
• Non-relativistic Quantum Mechanics
• Rutherford static, spinless
• Mott electron has spin
• Form factors
• Relativistic Quantum Mechanics
• Rosenbluth Formula
• Measurements of proton

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Whats a Proton?
n

• We have heard that a proton is a set of three
  quarks bound strongly by gluons
• How do we know this?
• Can we ask more quantitative questions?

p
p
u
d
u
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Elastic Scattering Experiments

• Rutherford discovered the atomic nucleus through
  scattering alpha particles
• Mott also worked out the consequences of
  scattering electrons (spin ½)

a
Z
e
Z
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Pointlike, Finite Mass Target

• What if our target has finite mass, and can
  recoil?

E
E
q
q
M
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Extended Charge Distributions

• What if the object is not point-like but has an
  extended charge distribution

Modifies cross sectionformula in simple way
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Relativistic Version
Fermis GoldenRule
Amplitiude
Electron (easy)
Proton (hard extended!)
Rosenbluth Formula
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Proton Charge Radius
McAllister Hofstader used Rosenbluth
formula(assuming F1F2) and extracted ltr2gt½
.75.25 fm
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Deep Inelastic Scattering

• Need two variables angle and E

k
k
q
p
Energy lost byelectron
W
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Bjorken Scaling

• In 1968, Bjorken postulated that
• Thus, there is no characteristic momentum scale
• ? no characteristic size
• ? constituents are pointlike

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Observation of Scaling
At moderate x,no Q2 dependence
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Feynmans Parton Model

• Feynman postulated that protons were made of
  pointlike constituents partons
• They share momentum of proton
• Natural interpretation in terms of quarks

Probability of parton having betweenx and xdx
of protons momentum
Sum Rules
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Explanation of Scaling

• Feynmans picture makes sense in the
  infinite-momentum frame
• If partons are massless, real particles

Feynman
Bjorken
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Modern DIS language
Callan-Gross Relation(spin ½ partons!)
F2 contains E-M structure of proton!
For moderate x, no Q2 dependence F2(x,Q2) ? F2(x)
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Structure Functions PDFs

• We measure structure functions
• F2 from DIS of electrons on protons
• F3 from DIS of neutrinos
• We infer Parton Distribution Functions
• Crucial feature PDFs are universal!
• Can measure ep and predict np

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Are quarks the whole story?

• Proton is described as a bag containing free
  charged quarks
• But lets put some pieces together

Quarks carry only half the proton momentum!
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Adding QCD

• We have been talking about valence quarks
• Quarks are not completely free in the nucleon
• Bound by gluons we should see them
• There are also sea quarks quantum fluctuations

u
u
s
d
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QCD leads to Evolution

• As you hit the proton harder, you resolve shorter
  lived fluctuations gluons sea
• The quarks you see can come from several sources

Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
(DGLAP)
Gluon splits to q-anti-q,each one with a
fractionof gluon x
Quark radiates gluon,and so loses energy
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DGLAP splitting functions

• Splitting functions P(z) can be calculated
  perturbatively in QCD (simple feynman diagrams)
• Thus, while structure functions cannot be
  calculated (intrinsically npQCD), their
  evolution in x and Q2 can be!
• Experimental tests of this (to higher orders in
  as) are great triumph of QCD

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QCD Structure of the proton

• Higher energies let us push down to lower x
• HERA data
• 30 GeV electron/positron
• 900 GeV proton
• All features expected from QCD are seen
• Scaling at x.2
• Violations of scaling
• _at_ low x
• _at_ high x

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Proton has a Gluon PDF as well!

• From global fits, one can extract even the gluon
  structure of the proton as a function of x and Q2
• If gluons were not self-coupling, one might
  expect g(x) 1/x
• Instead, g(x) rises rapidly at low x
• This is EXTREMELY important for RHIC physics

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Putting it all together

• DIS data sets exist at many different systems
  energies
• Theorists can do calculations and make global
  fits to the data to extract PDFs

• CTEQ
• MRST
• GRV

TheoreticalCollaborations
1/xl
RHIC
CTEQ6
(1-x)a
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Is a nucleon always a nucleon?

• We know that nucleons are bound in nuclei
• Is their structure modified?
• Studied by ratios, divided by number of nucleons
• Different regions of x revealed different effects
• EMC effect
• Shadowing
• Saturation

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Parton Saturation

• Gluon distribution rises rapidly at low-x
• Gluons of x1/(2mR) overlap in transverse plane
  with size 1/Q
• Below saturation scale Qs2 gluon recombination
  occurs
• Saturation scale measures density of partons in
  the transverse plane
• Increases with A and/or ?s

Saturation describes HERA data!
Scale depends on thickness
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Conclusions

• Scattering experiments teach us a lot!
• Simple probe can study complex target
• Nucleons really contain charged quarks
• But they have a lot more as well
• Gluons sea quarks carry ½ momentum
• QCD (via DGLAP equations)
• Evolution of nucleon structure
• Gluons show huge increase at low x
• Nucleons are not the same in nuclei
• DIS results are an important part of the heavy
  ion puzzle
• Especially at high energy (above SPS)