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Introduction The hypercentral Constituent Quark Model

Electromagnetic form factors in the relativized Hypercentral CQM M. De Sanctis, M.M.Giannini, E. Santopinto, A. Vassallo. Introduction The hypercentral Constituent Quark Model The elastic nucleon form factors (relativistic effects) Conclusion. N 05 Frascati, 13 october 2005.

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Introduction The hypercentral Constituent Quark Model

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  1. Electromagnetic form factors in the relativized Hypercentral CQMM. De Sanctis, M.M.Giannini, E. Santopinto, A. Vassallo Introduction The hypercentral Constituent Quark Model The elastic nucleon form factors (relativistic effects) Conclusion N05 Frascati, 13 october 2005

  2. New Jlab data on nucleon f.f. Give rise to problems: • compatibility with old (Rosenbluth plot) data • why the ratio GE/GM decreases? • is there any zero in the f.f. ?

  3. VMD models (fits) FF = Fintr * VMD propagators Mesons Fintr JIL dipole monopole G K  QCD-interpolation

  4. Skyrme ModelHolzwarth 1996,2002 ff given by soliton + VMD dip at Q2 3 GeV2 Boosting of the soliton dip at Q2 10 GeV2 Skyrmion (nucleon) mass 1648 MeV

  5. The Hypercentral Constituent Quark ModelM. Ferraris et al., Phys. Lett. B364, 231 (1995)

  6. SPACE WAVE FUNCTION Jacobi coordinates r - r = 1 2   1 2 √ 2 r + r 2r - 1 2 3 =  √  6 3 Hyperspherical coordinates ( (x   (size) x = 2 + 2   (shape)  arc tg 

  7. Quark-antiquark lattice potential G.S. Bali Phys. Rep. 343, 1 (2001)

  8. G.S. Bali Phys. Rep. 343, 1 (2001) 3-quark lattice potential

  9. Electromagnetic properties • Photocouplings M. Aiello et al., PL B387, 215 (1996) • Helicity amplitudes (transition f.f.) M. Aiello et al., J. of Phys. G24, 753 (1998) • Elastic form factors of the nucleon M. De Sanctis et al., EPJ A1, 187 (1998) • Structure functions to be published Fixed parameterspredictions

  10. Dynamical model (Mainz group)

  11. please note • the calculated proton radius is about 0.5 fm (value previously obtained by fitting the helicity amplitudes) • not good for elastic form factors • there is lack of strength at low Q2 (outer region) in the e.m. transitions • emerging picture: quark core (0.5 fm) plus (meson or sea-quark) cloud

  12. ELASTIC FORM FACTORS1. - Relativistic corrections to the elastic form factors2. - Results with the semirelativistic CQM3. - Quark form factors

  13. 1.- Relativistic corrections to form factors • Breit frame • Lorentz boosts applied to the initial and final state • Expansion of current matrix elements up to first order in quark momentum • Results Arel (Q2) = F An.rel(Q2eff) F = kin factor Q2eff = Q2 (MN/EN)2 De Sanctis et al. EPJ 1998

  14. calculated

  15. 2.- Results with the semirelativistic CQMM. De Sanctis, M. G., E. Santopinto, A. Vassallo, nucl-th/0506033 • Relativistic kinetic energy • Boosts to initial and final states • Expansion of current to any order • Conserved current

  16. V(x) = - /x + x  and t not much different from the NR case

  17. Calculated values!

  18. Q2 F2p/F1p Q F2p/F1p

  19. 3.- Quark form factorsM. De Sanctis, M. G., E. Santopinto, A. Vassallo, nucl-th/0506033 • Quark form factors are added in the current ff = Fintr * quark form factors semirelativistichCQM input (calculated) • Monopole + dipole form for qff • Fit of: • GEp/GMp ratio (polarization data) • GMp; GEn ;GMn

  20. Q2 F2p/F1p Q F2p/F1p

  21. Conclusion • The hCQM provides a consistent framework for the description of all the 4 nucleon electromagnetic form factors • Relativity is crucial in explaining the decrease of the ratio GE/GM • Quark form factors are necessary in order to get a good reproduction of the Q2 behaviour (meson cloud is missing)

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