Why Regge Trajectories?

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Why Regge Trajectories?

• Alfred Tang
• University of Wisconsin-Milwaukee

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Content

• Regge Trajectories
• Bound State Equations
• QCD string model
• Feynman-Field Perturbative QCD Model
• Iso-hadron Model

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Defining Regge Trajectories
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Chew-Frautschi Plots

• Bootstrap hypothesis
• Chew-Frautschi conjecture
• Linearity assumed to fit data
• Linearity justified by Regge pole theory

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Zone Test
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Non-linear Regge Trajectories
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Schrödinger Equation in p-space

• Simplest example with a linear potential s-state
  SE
• Norbury, et al. used basis function method

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Nystrom-plus-correction Method

• Represent ?(p) as a vector.
• The kernel contains the Q(y) and kinetic terms.
• Solve SE as a matrix equation.
• Extrapolate the eigenvalues.

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Regge Trajectorieswith a linear potential
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Regge Trajectorieswith a Cornell potential
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QCD String
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Lund String Fragmentation Model
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Isgur Flux-tube Model
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Toroidal Hadron
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Feynman-Field Model
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Global Properties
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Pieces of Puzzle

• Regge trajectories are slightly non-linear.
• Bound state equations using Nystrom-plus-correctio
  n method produces RT of increasing slopes.
• Variable Np is needed for different reactions in
  the Feynman-Field model.

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n-Möbius Strip
3
2
1
1
3
2
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Triniton (3-Möbius Strip)
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Iso-hadron Model

• Iso-hadrons have the same quantum numbers and
  symmetries but different masses.
• Partons in lighter iso-hadrons carry greater
  fraction of the hadrons energy and are
  kinematically favorable to fragment into heavier
  hadrons.
• The concentrations of iso-hadrons vary with J.
• Non-linear Regge trajectories are caused by the J
  dependence of iso-hadron concentrations.