Lectures at Bosen 2003

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Baryon Excitation through Meson Hadro- and
Photoproduction in a Coupled-Channels Framework
Agung B. Waluyo Cornelius Bennhold
Department of Physics The George Washington
University
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Outline

• Introduction
• Chiral Symmetry Inspired Model
• Examples of findings
• P11(1440), D13(1700), and P31 states.
• Missing resonances.
• Reactions ?N ? ?N, ?N ? ??, and ?N ? ??
• Summary and Conclusion

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Quantum Chromodynamics (QCD)--- the fundamental
theory of the strong interaction (in
terms of quarks and gluons)

• At high energy, perturbative (asymptotic freedom)

• At low energy, non-perturbative (confinement)

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Nucleon resonance spectral lines dont quite
look like this
Nucleon resonances are broad and overlapping!
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Chiral Symmetry Inspired Model
is within a coupled-channels framework

• Each resonance can be reached through each
  asymptotic channel
• All channels couple through all other channels
  through intermediate state
• Hadronic T matrices are directly related to
  photon multipoles (El, and Ml)

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The Bethe-Salpeter equation M V ?V G0 T
Solved in the K-matrix approximation.
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Background contributions
Baryon poles ?
N, ?, and ?
?, ?, ?, a0, and K
Meson resonance poles ?
Constructed from chiral lagrangians
Gauge Invariant Contact Term
?
Higher order chiral contact terms (?PT)
Coupling Constant are treated as free parameters!
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Hadronic Contact Terms
Weinberg-Tomozawa
Higher Order Contact Terms
Symmetric
k and k four-momenta of incoming and outgoing
meson P (pp), p and p four-momenta of
incoming and outgoing baryons ?s are free
parameters
Anti Symmetric
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Higher Order Electromagnetic Contact Terms
q and k four-momenta meson and photon, P
(pp), p and p four-momenta of incoming and
outgoing baryons.
? photon polarization vector ?s free
parameters Each term is gauge invariant
by construction.
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Resonance contributions

N, ?
?N ?N K? ??
A1/2, A3/2 helicity amplitudes
branching ratios
N
masses
Free parameters adjusted to data
How do we describe high-spin N states? (3/2? ,
5/2?)
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What data do we fit for W ? 2 GeV?
Observables
?N, ?N ? ?N ?N, ?N ? K? ?N, ?N ? K?
PW/Multipole Solutions
?N ? ?N GW-DAC current solution ?N ? ?N GW-DAC current solution ?N ? 2?N total partial wave (Manley 1981)
We only show the results that do not include the
?N, K?, and K? hadroproduction data. The more
complete global fits are still ongoing.
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Resonance Regions
According to PDG!
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Examples of findings
New Topic
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P11(1440)
?N ? ? N multipole
? N ? ? N partial wave
Mass (GeV) ?total (MeV) ??N () ? 2?N()
Waluyo 1500 630 58 42
Penner 1518(5) 668(41) 57(1) 43(1)
Vrana 1479(80) 490(120) 72(5) -
PDG 1430-1470 250-450 60-70 30-40
Similar!
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D13(1700)
?N ? ? N multipole
? N ? ? N partial wave
Different!
Mass (MeV) ?total(MeV) ??N () ? 2?N () ? ?N () ? ?? () ? ?? ()
Waluyo 1728 181 0.4 41 13 22 22
Penner Not found - - - - - -
Vrana 1736(33) 175(133) 4(2) 96(58) 0(1) - -
PDG 1650-1750 50-150 5-15 85-95 0.0-0.1 lt 3 -
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Where is the ground state of P31(?)
?N ? ? N multipole
? N ? ? N partial wave
1750
1910
Is it at ..
or
?
()
()
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What are coupled-channels models results for the
ground state of P31?
Model Giessen GW
N couplings Rarita-Schwinger Pascalutsa
Off-shell problem Mainly from P33 to P31 No offshell!
Results P31(1750) P31(1910)
When Pascalutsa couplings are applied P31(1910)
Message for the P31 wave, background
contributions are important to obtain the final
result!
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Missing Resonances?
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Compare experimental N and quark model states
Quark models predict many more states than are
seen experimentally!
Capstick and Roberts quark model
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Search in ? N ? ? N partial wave in
1800ltWlt2000 MeV
Therefore we need information from other
channels!
PDG P13(1900)
3rd P11?
3rd S11?
PDG F15(2000)
3rd D13?
No flux available!
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Do we find missing resonancesin the range of
1800ltWlt2000 MeV?
(100 lt ?N lt 600-700 MeV)
N Width (MeV) ?2 improved? Y/N?
3rd S11
3rd P11
3rd D13
?
N
lt 20
lt 30
?
N
409
Y
?
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Threshold Region S11(1535), D13(1520), S11(1650)
Differential cross section for ?p ? ?p
?
?
?
Data M. Dugger et. al. CLAS coll. PRL 89, 2002
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d?/d? for ?p ? ?p at higher energies
N Contribution
D15(1675) Very small
D13(1700) Very small
P11(1710) Large
P13(1720) Large
D13(1900) Small
P13(1900) Large
F15(2000) Very small
Data M. Dugger et. al. CLAS coll. PRL 89, 2002
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? Polarization observable for ?p ?
?p
N Contribution
S11(1535) Dominant
D13(1520) Small
D13(1700) Small
D13(1900) Small
F15(1680) Small
F15(2000) Small
Data J. Ajaka - Graal colloboration PRL 81, 1998.
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d?/d? for ?p ? K? at lower energies
Subthreshold Contributions From lower N
N Contribution
P13(1720)
D13(1700)
Backward rise
Forward rise
Data Mc Nabb et. al., CLAS 2003
No contributions from D15(1675) and F15(1680)
(?K?0)!
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d?/d? for ?p ? K? at higher energies
N Contribution
P13(1900)
D13(1900)
Backward rise
Forward rise
Data Mc Nabb et. al., CLAS 2003
No contribution from F15(2000) (?K?0)!
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?-polarization observable for ?p ? K?
N Contribution
D13(1700)
D13(1900)
at lower W
at higher W
Data Mc Nabb et. al., CLAS 2003
Cos ?
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d?/d? for ?p ? K?0 at lower energies
Subthreshold contributions from lower N
N Contribution
D13(1700) Forward peaking
P13(1720) Backward rise
Data Mc Nabb et. al., CLAS 2003
K provides strength in the entire energy region.
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d?/d? for ?p ? K?0 at higher energies
N Contribution
S31(1900) Very Small
P31(1910) Small
P33(1920) Small
D35(1930) Large
Data Mc Nabb et. al., CLAS 2003
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Summary and Conclusion

• We have investigated 21 N and ? states for W lt
  2.0 GeV through Meson hadro- and photoproduction
  in a coupled-channels framework
• Bethe-Salpeter equation ? K-matrix approximation
• 2? system ? a scalar-isovector ?-meson
• New chiral contact terms
• Consistent Pascalutsa couplings for spin-3/2 and
  5/2 resonances
• We extract N properties and find
• Similarities for the N in the 1st N region
• Differences for the N in the 3rd and higher N
  regions
• 3rd S11, P11, and P13 missing resonances do not
  appear at 1900 MeV, but 3rd D13 appears at 1946
  MeV
• We are able to describe observables well ?N ?
  ?N, ?N ? ?N, ?N ? ?N, ?p ? K?, ?N ? ??0, and ?p
  ? K0 ?
• Improve model
• Fit to ?-photoproduction observables
• 2?N ? ??, ?N,
• Beyond K-matrix