The Constituent Quark Models

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The Constituent Quark Models
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Outline

• The Quark Model
• Original Quark Model
• Additions to the Original Quark Model
• Color
• Harmonic Potential Model
• Isgur-Karl Model
• M.I.T. Bag Model
• Assumptions
• Predictions

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Constituent Quark Model(Non-relativistic)

• Quasiparticles, have same quantum number like
  fundamental quarks of QCD electric charge,
  baryon number, color, flavor and spin.
• Bare quark dressed by clouds of quark-antiquark
  pairs and gluons.
• Mass is more than 300MeV, compared to bare quark
  about 10MeV.
• Allow treatment similar to nuclear shell model
• Simpler only three players ( for baryons ) while
  nuclei can have many nucleons.
• Harder more freedom,
• three colors, while nucleons are colorless
• three flavors, while nucleons only have neutrons
  and protons.

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Original Quark Model
1964 The model was proposed independently by
Gell-Mann and Zweig Three fundamental building
blocks 1960s (p,n,l) Þ 1970s (u,d,s) mesons
are bound states of a of quark and
anti-quark Can make up "wave functions" by
combining quarks
baryons are bound state of 3 quarks proton
(uud), neutron (udd), L (uds) anti-baryons
are bound states of 3 anti-quarks
? (uds)
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Quarks

• These quark objects are
• point like
• spin 1/2 fermions
• parity 1 (-1 for anti-quarks)
• two quarks are in isospin doublet (u and d), s
  is an
• iso-singlet (0)
• Obey Q I3 1/2(SB) I3 Y/2
• Group Structure is SU(3)
• For every quark there is an anti-quark
• The anti-quark has opposite charge, baryon
  number and strangeness
• Quarks feel all interactions (have mass,
  electric charge, etc)

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Early 1960s Quarks

• Successes of 1960s Quark Model
• Classify all known (in the early 1960s)
  particles in terms of 3 building blocks
• predict new particles (e.g. W-)
• explain why certain particles dont exist (e.g.
  baryons with spin 1)
• explain mass splitting between meson and baryons
• explain/predict magnetic moments of mesons and
  baryons
• explain/predict scattering cross sections (e.g.
  spp/spp 2/3)
• Failures of the 1960's model
• No evidence for free quarks (fixed up by QCD)
• Pauli principle violated (D (uuu) wave
  function is totally symmetric) (fixed up by
  color)
• What holds quarks together in a proton ?
  (gluons! )
• How many different types of quarks exist
  ? (6?)

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Additions to the Original Quark Model Charm

• Another quark was needed to account for some
  discrepancies between predictions of the model
  and experimental results
• Charm would be conserved in strong and
  electromagnetic interactions, but not in weak
  interactions
• In 1974, a new meson, the J/? was discovered that
  was shown to be a charm quark and charm antiquark
  pair

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More Additions Top and Bottom

• Discovery led to the need for a more elaborate
  quark model
• This need led to the proposal of two new quarks
• t top (or truth)
• b bottom (or beauty)
• Added quantum numbers of topness and bottomness
• Verification
• b quark was found in a ? meson in 1977
• t quark was found in 1995 at Fermilab

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Quantum Chromodynamics (QCD)

• QCD gave a new theory of how quarks interact with
  each other by means of color charge
• The strong force between quarks is often called
  the color force
• The strong force between quarks is carried by
  gluons
• Gluons are massless particles
• There are 8 gluons, all with color charge
• When a quark emits or absorbs a gluon, its color
  changes

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Quantum Chromodynamics (QCD)

• Asymptotic freedom
• Quarks move quasi-free inside the nucleon
• Perturbation theoretical tools can be applied in
  this regime
• Quark confinement
• No single free quark has been observed in
  experiments
• Color force increases with increasing distance
• Chiral symmetry

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Quark confinement

• Spatial confinement
• Quarks cannot leave a certain region in space
• String confinement
• The attractive( color singlet) quark-antiquark
• Color confinement

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• What Models do we have?

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Harmonic Potential Model (for N and N states,
mumdm)
?
2
1
?
R
3
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Solution of Harmonic Potential Model
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Spin-Spin Contact Interaction
The three parameters ms,d , as?(0)2, ?0 are
obtained by fitting to experimental data
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Spectrum of low lying N and N states
ms,d 360MeV , ?0 500MeV
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Non-relativistic quark model with the salt of
QCD eg. Isgur-Karl Model

• Start with a non-relativistic quark model with
  SU(3)xSU(2) spin-flavor symmetry.
• SU(3) flavor breaking via quark mass difference.
• (mu,d is not equal to ms).
• Long range confining force independent of flavor
  and spin.
• Only one gluon exchange accounts for short range
  spin and flavor dependent interaction.
• (similar to electrodynamics of two slow moving
  fermions)

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Isgur-Karl Model

• No spin-orbit interaction, comparing to shell
  model
• Spin-spin contact interaction acts when L is zero
  
• Tensor interaction acts when L is Nonzero

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Nstar Spectrum
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M.I.T. Bag Model

• Developed in 1974 at Massachusetts Institute of
  Technology
• It models spatial confinement only

• Quarks are forced by a fixed external pressure
  to move only inside a given spatial region
• Quarks occupy single particle orbitals
• The shape of the bag is spherical, if all the
  quarks are in ground state

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M.I.T Bag Model

• Inside the bag, quarks are allowed to move
  quasi-free.
• An appropriate boundary condition at the bag
  surface guarantees that no quark can leave the
  bag
• This implies that there are no quarks outside the
  bag

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M.I.T. Bag Model

• The boundary condition generates discrete energy
  eigenvalues.

R - radius of the Bag x12.04
Nq of quarks inside the bag
B bag constant that reflects the bag pressure
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M.I.T. Bag Model

• Minimizing E(R), one gets the equilibrium radius
  of the system

Fixing the only parameter of the model B, by
fitting the mass of the nucleon to 938MeV we have
first order predictions
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One gluon exchange

• Model so far excluded all interactions between
  the quarks
• There should be some effective interaction that
  is not contained in B( how do we know that?)

as the strong coupling constant Mq depends on
the quantum no. of the coupled quarks
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Predictions
The masses of N, ?, O, ? were used to fit the
parameters.
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Conclusions

• The quark model
• classifies all known particles in terms of 6
  building blocks
• Explains mass splitting between meson and baryons
• Explain/predict magnetic moments of mesons and
  baryons
• Explain/predict scattering cross sections
• The MIT Bag Model
• predicts fairly accurate masses of the particles
• Explains color confinement
• Helps predict heavy quark spectrum
• Simple models can give us a very good picture!

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