Seminar Subatomic Physics

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Seminar Subatomic Physics

• Chapter 3 New developments in hadronic particle
  production
• Nucleon resonances
• Baryon models
• Partial-wave analysis
• Coupled channels
• Bethe-Salpeter equation
• K-matrix approximation

TAPSCrystalBarrel at ELSA
CLAS at Jlab
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pion nucleonscattering
Isospin coupling, invariant mass (4-mom. sum) and
phase-shift analysis yield energy (mass), I, L,
J resonance assignment L2I,2J (mass) and width
(lifetime)

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nucleon g.s. and excitationspartly explained in
the quark model
radially excited spatial states
(1710)
Roper res.
(1440)
chromomagnetic (hyperfine) interaction
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nucleon resonances in quark potential
model qualitative understanding
confining potential
well poorly known
mass (MeV)
gluonic excitations
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pion nucleon scattering
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?- p ? X reaction channels influence of channel
opening unitary reaction model needs to include
all important channels
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cross section (mb)
real part of S11 partial wave ampl. influence of
neglecting channels
?N width ?2? N
w/o ?N final state
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partial-wave analysis
quantum scattering in 3 dimensions (halfplane ?0)
scattering amplitude
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baryon resonances
elastic unitary circle
inelastic
cross section reaches unitary limit
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actual D13 resonance analysis
w/o D13(1900) state
requires high quality cross sections, polarization
observables
coupled-channel K-matrix approach
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calculations at tree-level

• neglect hadronic final-state interaction
• ? violation of unitarity
• requires coupled-channels method
• including rescattering
• e.g. ?N ? K?
• using hadronic form-factors
• violates gauge invariance
• repaired by contact term

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ladder approximationsolution to scattering
problem iterate interaction potential V
Bethe-Salpeter equation 4-dim. integral
equation, ? (all allowed intermediate 2-particle
states)
Bethe-Salpeter propagator
K-matrix approximation modify Re(Gbs) without
violating unitarity
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Summary

• motivation
• low-energy QCD in confinement regime
• not accessible by perturbation theory
• QCD lattice theory numerical solutions
• effective quark models
• program to study
• hadronic and electromagnetic excitation of
  nucleon
• analysed by dynamical model description
  satisfying
• unitarity, analyticity, Lorentz- and
  gauge-invariance
• ? masses, decay widths of resonance states

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Literature
1. Scattering Theory Sakurai, Modern Quantum
Mechanics, Addison-Wesley 1994 p.379-399   2.
Compton scattering on the proton and light nuclei
in the Delta resonance region (K Matrix
approach) O. Scholten, Acta Physica Polonica 33
(2002) 847-871   3. Vector meson production with
photons and nucleon resonance analysis in a
coupled channel approach G. Penner, U. Mosel,
nucl-th/0207069 4. Pseudoscalar and vector meson
production in NN collisions K. Nakayama,
nucl-th/0108032
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Seminar contributions