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Journal Review

Journal Review. Interpreting the Neutron’s Electric Form Factor: Rest Frame Charge Distribution or Foldy Term? Nathan Isgur, PRL 83 272(1999) Chris Crawford June 16, 2004. Outline. Introduction: how does one interpret G E relativistically? F(q 2 ) $ r (x) Sachs FF’s, Breit frame

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Journal Review

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  1. Journal Review Interpreting the Neutron’s 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 FF’s, 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?

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