Journal Review

1
Journal Review

• Interpreting the Neutrons Electric Form Factor
  Rest Frame Charge Distribution or Foldy Term?
• Nathan Isgur, PRL 83 272(1999)
• Chris Crawford
• June 16, 2004

2
Outline

• Introduction how does one interpret GE
  relativistically?
• F(q2) r(x)
• Sachs FFs, Breit frame
• relativistic problem
• Foldy contribution to r2n
• Zitterbewegung
• Toy model nSD to validate method
• Valence quark model nddu calculation
• Conclusion
• r2n dynamical, not relativistic

3
Form Factor Formalism

• Fourier transform of charge distribution
• Coulomb interaction
• What happens when r2 ! 2 ?

4
Sachs Form Factors

• Klein-Gordon decomposition
• Breit frame Q2 ! q2 (no time integral)

5
Relativistic Problem

• Breit Frame depends on Q2
• undefined s d3q
• Relativistic CQM models difficult
• rest-frame models difficult to boost
• light-cone models trouble constructing JP
• Charge-distribution interpretation
• only valid in limit as Q2 ! 0

6
Neutron Charge Radius

• meson interactions
• n ! p- p
• quark interactions
• mp/mn -3/2 mp mN/md 3
• spin-spin SU(6) breaking N-D splitting
• also charge segregation d! out, u! inside
• r2n -0.113 fm2 (negative)

7
Foldy Term

• L. Foldy, Phys. Rev. 83, 688 (1951)
• relativistic correction to F1
• r2Foldy -0.126 fm2

8
Zitterbewegung Motion

• Dirac free particles velocity eigenvalues 1
• oscillations on scale of lc
• positive/negative energy interference

9
Toy Model

• antiscalar S Dirac D,
• Foldy term
• relativistic calculation
• pseudo-charge-conjugation invariance
• Wigner rotations vkT/mD

10
Valence Quark Model

• ddu ! scalars via 3 zitterbewegung terms
• pseudo-charge-conjugation invariance, Wigner
  rotations arguments still valid
• Foldy term must have cancelled
• How valid was validation toy model?
• other relativistic corrections not considered?

11
Conclusion

• there are no relativistic corrections to lowest
  order in Q2/m2 (FF-transform picture valid?)
• any net r2En must arise in this order from new
  dynamics which can produce an intrinsic internal
  charge distribution
• in N.R. limit, r2Foldy r2Endduin QCD limit,
  both determined by LQCD
• non-valence components in neutron wave function?