The Structure of the Nucleon

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The Structure of the Nucleon

• Introduction
• Meson cloud effects two-component model
• Strange form factors
• Results
• Summary and conclusions

Roelof Bijker ICN-UNAM
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Internal Structure of the Proton

• Anomalous magnetic moment of the proton (Stern,
  1930s)
• Spatial structure of the proton (Hofstadter,
  1950s)
• Scaling quark structure of the proton
  (Friedman, Kendall, Taylor, 1960s)
• EMC effect, spin crisis (1988)
• Form factor ratio (2000)
• Investigate the structure of the nucleon through
  the electromagnetic and weak form factors in the
  space- and time-like regions

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Form Factors
Structure of particles described by form factors
Elastic Scattering Q2 2Mnw
Form factors hide our ignorance of how the
composite particle is constructed.
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Nucleon Electromagnetic Current
Dirac and Pauli form factors
Sachs form factors
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The Structure of the Nucleon

• Introduction
• Meson cloud effects two-component model
• Strange form factors
• Results
• Summary and conclusions

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Vector Meson Dominance
Photon couples to nucleon via vector meson
(?,?,?) Adjust high Q2 behaviour to pQCD
scaling Include the finite width of ? meson
Two-component model Intrinsic structure
(valence quarks) Meson cloud
(quark-antiquark pairs)
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Electromagnetic Currents

• Isoscalar em current
• Isovector em current
• Strange em current

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Dirac and Pauli Form Factors
Intrinsic form factor
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Iachello, Jackson, Lande, PLB 43, 191
(1973) Iachello, Wan, PRC 69, 055204 (2004)
Bijker, Iachello, PRC 69, 068201 (2004)
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• Electromagnetic form factors
• Static properties

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The Structure of the Nucleon

• Introduction
• Meson cloud effects two-component model
• Strange form factors
• Results
• Summary and conclusions

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Strange Form Factors

• The strangeness distribution is a very sensitive
  probe of the nucleons properties
• The strange (anti)quarks come uniquely from the
  sea there is no contamination from up or down
  valence quarks
• New data from SAMPLE, HAPPEX, PVA4 and G0
  Collaborations
• ? meson mostly strange quarks

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Weak Currents

• Neutral weak vector current
• Weak axial current

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Strange form factors

• Nucleon em form factors
• Proton weak form factor

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• Charge symmetry
• Strange form factor
• Static properties

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Ideally mixed states
Physical states
Mixing angle (Jain, 1988)
Strange Dirac and Pauli form factors
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• Meson-nucleon couplings
• Current-meson couplings
  Quark in the vector mesons couples only to the
  quark vector current of the same flavor with a
  flavor-independent strength

Jaffe PLB 229, 275 (1989)
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Isoscalar Couplings
Four parameters
One constraint
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Strange Couplings
One constraint no net strangeness contribution
to the electric charge
Reduction of the number of parameters!
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Summary

• Two-component model for the electromagnetic and
  weak vector currents
• Intrinsic structure
• Isoscalar mesons
• Isovector mesons

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The Structure of the Nucleon

• Introduction
• Meson cloud effects two-component model
• Strange form factors
• Results
• Summary and conclusions

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Electromagnetic Form Factors
1973
2004
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Electric Form Factors
Andivahis (1994), Christy (2004), Qattan (2004)
Herberg (1999), Passchier (1999), Zhu (2001),
Golak (2001), Schiavilla (2001), Madey (2003),
Bermuth (2003), Warren (2004),
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Neutron magnetic form factor
Preliminary results from the CLAS collaboration
(JLab) Nucleon05 Vineyard
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Scaling Behavior

• Dimensional analysis (Brodsky, Farrar), pQCD
  (Brodsky, Lepage)
• Polarization transfer data
• Quark orbital angular momentum (Miller,Ralston)
• Valid in VMD in an intermediate Q2 region, but
  not in the asymptotic region (Iachello)

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pQCD (Belitsky)
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Strange Form Factors
Nucleon05 Riska, Maas, Kox,
Pate,
SAMPLE PLB 583, 79 (2004) HAPPEX
arXivnucl-ex/0506010
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HAPPEX PRC 69, 065501 (2004)
arXivnucl-ex/0506011 PVA4 PRL 93, 022002
(2004) PRL 95, 152001 (2005)
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G0 PRL 95, 092001 (2005)
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Time-like form factors Q2lt0
Experimentally, the time-like form factors can
be probed through (Frascati)
or the inverse reaction (CERN, FNAL) Theoreticall
y, the space- and time-like form factors are
related by analytic continuation
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Comparison between the 1973 and 2004 VMD
calculations
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The Structure of the Nucleon

• Introduction
• Meson cloud effects two-component model
• Strange form factors
• Results
• Summary and conclusions

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Summary and Conclusions

• The nucleon has a complex structure valence
  quarks and meson cloud
• Space-like form factors well reproduced
• Neutron data in the space- and time-like regions
  seem to be inconsistent (Hammer et al.,
  Tomasi-Gustafsson Rekalo, Brodsky et al., )
• pQCD not reached up to 10 (GeV/c)2
• New experiments to study the nucleon form factors
  for higher values of Q2
• Extension to strange form factors reduces by one
  the number of parameters. Excellent description
  of the SAMPLE, HAPPEX, PVA4 and G0 data.

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Outlook

• Extend two-component model to baryon resonances
• Strange form factors
• Axial form factors

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N-? Transition From Factors

• Two-componet model (Iachello Wan, IJMPA 20,
  1846 (2005))
• Generic structure
• Intrinsic form factors from previous study of
  baryon resonances (Bijker, Iachello, Leviatan, AP
  236, 69 (1994))
• Isovector vector meson ?

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Other theoretical calculations
Vector meson dominance Lomon, Iachello,
Hammer Relativistic chiral soliton model
Goeke, Holzwarth Lattice QCD
Schierholz Relativistic constituent quark model
Miller, Simula, Giannini, Plessas, Metsch
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Vector Meson Dominance
charge
magnetization
proton
neutron
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Relativistic Constituent Quark Models
charge
magnetization
proton
neutron