The Structure of the Nucleon

• Introduction• Meson cloud effects: two-

component model• Strange form factors• Results• Summary and conclusions

Roelof BijkerICN-UNAM

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

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

Nucleon Electromagnetic CurrentDirac and Pauli form factors

Sachs form factors

The Structure of the Nucleon

• Introduction• Meson cloud effects: two-

component model• Strange form factors• Results• Summary and conclusions

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)

Electromagnetic Currents

• Isoscalar em current

• Isovector em current

• Strange em current

Dirac and Pauli Form Factors

Intrinsic form factor

Iachello, Jackson, Lande, PLB 43, 191 (1973)Iachello, Wan, PRC 69, 055204 (2004)

Bijker, Iachello, PRC 69, 068201 (2004)

• Electromagnetic form factors

• Static properties

The Structure of the Nucleon

• Introduction• Meson cloud effects: two-

component model• Strange form factors• Results• Summary and conclusions

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

Weak Currents

• Neutral weak vector current

• Weak axial current

Strange form factors• Nucleon em form factors

• Proton weak form factor

• Charge symmetry

• Strange form factor

• Static properties

Strange Dirac and Pauli form factors

Physical states

Ideally mixed states

Mixing angle (Jain, 1988)

• 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)

Isoscalar Couplings

Four parameters

One constraint

Strange Couplings

One constraint: no net strangeness contribution to the electric charge

Reduction of the number of parameters!

Summary

• Two-component model for the electromagnetic and weak vector currents

• Intrinsic structure • Isoscalar mesons• Isovector mesons

The Structure of the Nucleon

• Introduction• Meson cloud effects: two-

component model• Strange form factors• Results• Summary and conclusions

Electromagnetic Form Factors

2004

1973

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),

Preliminary results from the CLAS collaboration (JLab)

Nucleon05: Vineyard

Neutron magnetic form factor

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)

pQCD (Belitsky)

Strange Form Factors

SAMPLE – PLB 583, 79 (2004)HAPPEX – arXiv:nucl-ex/0506010

Nucleon05: Riska, Maas, Kox, Pate, …

HAPPEX – PRC 69, 065501 (2004) arXiv:nucl-ex/0506011PVA4 – PRL 93, 022002 (2004) PRL 95, 152001 (2005)

G0 – PRL 95, 092001 (2005)

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

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

The Structure of the Nucleon

• Introduction• Meson cloud effects: two-

component model• Strange form factors• Results• Summary and conclusions

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.

Outlook

• Extend two-component model to baryon resonances

• Strange form factors• Axial form factors

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:

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

Vector Meson Dominance

charge magnetization

proton

neutron

Relativistic Constituent Quark Models

charge magnetization

proton

neutron