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The Structure of the Nucleon
• Introduction• Meson cloud effects: two-
component model• Strange form factors• Results• Summary and conclusions
Roelof BijkerICN-UNAM
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Internal Structure of the Proton
• Anomalous magnetic moment of the proton (Stern, 1930’s)
• Spatial structure of the proton (Hofstadter, 1950’s)
• Scaling: quark structure of the proton (Friedman, Kendall, Taylor, 1960’s)
• 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 FactorsStructure of particles described by form factors
Form factors hide our ignorance of how the composite particle is constructed.
ER,PRE’, k’
E , k
Electron
q q2 = -Q2
G(Q2)
M
Target
Time
or Z
Elastic ScatteringQ2 = 2Mn
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Nucleon Electromagnetic CurrentDirac 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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Photon couples to nucleon via vector meson (,,)Adjust high Q2 behaviour to pQCD scalingInclude the finite width of meson
Vector Meson Dominance
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 nucleon’s 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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Strange Dirac and Pauli form factors
Physical states
Ideally mixed states
Mixing angle (Jain, 1988)
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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
2004
1973
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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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Preliminary results from the CLAS collaboration (JLab)
Nucleon05: Vineyard
Neutron magnetic form factor
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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
SAMPLE – PLB 583, 79 (2004)HAPPEX – arXiv:nucl-ex/0506010
Nucleon05: Riska, Maas, Kox, Pate, …
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HAPPEX – PRC 69, 065501 (2004) arXiv:nucl-ex/0506011PVA4 – 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: Q2<0
Experimentally, the time-like form factors can be probed through (Frascati)
or the inverse reaction (CERN, FNAL)
Theoretically, the space- and time-like form factors are related by analytic continuation
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Comparison between the 1973 and 2004 VMD calculations
IJL (1973)
IW (2004)
BI (2004)
Proton space OK OK
Neutron space X OK
Proton time OK +/-
Neutron time OK X
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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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Vector meson dominance Lomon, Iachello, Hammer
Relativistic chiral soliton model Goeke, Holzwarth
Lattice QCD Schierholz
Relativistic constituent quark model Miller, Simula, Giannini, Plessas, Metsch
Other theoretical calculations
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Vector Meson Dominance
charge magnetization
proton
neutron
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Relativistic Constituent Quark Models
charge magnetization
proton
neutron