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Isospin Mixing in 4He Ground State: Nucleon Strange Form Factor

Explore isospin mixing in the 4He ground state and its influence on the nucleon strange form factor in collaboration with researchers from esteemed institutes. Delve into parity-violating scattering phenomena, electron-nucleus interactions, and experimental data interpretation. Discover the impact of NN interactions and realistic potentials on the research outcomes, examining various theoretical frameworks and proposed models to understand complex nuclear physics phenomena.

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Isospin Mixing in 4He Ground State: Nucleon Strange Form Factor

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  1. Dedicated to Adelchi Isospin mixing in the 4He ground state and the nucleon strange form factor XI Convegno di Cortona M.Viviani INFN - Pisa (Italy) In collaboration with A. Kievsky, L.E. Marcucci, S. Rosati, L. Girlanda R. Schiavilla (Jlab)

  2. 2 g g Z0 Parity violating scattering e-4He • Electron-nucleus scattering • The parity violating left-right asymmetry ALR Cortona Ottobre 2006

  3. g Z0 Strange quark contribution • EM & neutral-weak currents Cortona Ottobre 2006

  4. Nucleon Strange Form Factors • Dirac-Pauli • Sachs Cortona Ottobre 2006

  5. The experiments • Experiments on nucleon: • Jefferson Lab (USA): HAPPEX & G0 • MIT-Bates (USA): SAMPLE • Mainz: A4 • Sensitive to an admixture of GE(s) and GM(s) • HAPPEX 2005; G0 2005; SAMPLE 2004; A4 2004 • Experiments on 4He: • HAPPEX-He @ Jlab • In the case of a target (J,T)=(0+,0), at low Q2: Cortona Ottobre 2006 Musolf et al, 1994

  6. World Data at Q2 ~ 0.1 GeV2 • HAPPEX-He @ Jlab (2006-preliminary, K.Aniol QNP06) • ALR = +6.43  0.23 (stat)  0.22 (syst) ppm Extrapolated from G0 Q2=[0.12,0.16] GeV2 2005 world data Cortona Ottobre 2006

  7. 4He LR asymmetry (1) • Currents • Three contributions • Left-right asymmetry Cortona Ottobre 2006

  8. 4He LR asymmetry (2) • Charge density operators Cortona Ottobre 2006

  9. 4He LR asymmetry (3) • At low Q2: MEC and spin-orbit contribution in J=0 are small and then • One needs to know: Cortona Ottobre 2006

  10. NN interaction • Realistic (phenomenological) potentials • Argonne V18 [Wiringa et al, 1995] • CD Bonn [Machleidt, 2001] • Nijmegen [Stoks et al, 1994] • Doleshall [Doleshall et al, 2000] • Effective field theory based on chiral symmetry • [Weinberg 1991, van Kolck 1994] • N3LO potential[review: Epelbaum, 2005] • “Julich” [Epelbaum et al, 2005] • “N3LO” [Emtem & Machleidt, 2003 ] • “Effective” potentials • Vlow-k[Bogner, Kuo & Schwenk, 2003, Coraggio et al, 2005] • JISP [Shirokov et al, 2005] • UCOM [Roth et al, 2004] Cortona Ottobre 2006

  11. AV18 N3LO NN potentials in p-space CD BONN  very long tail VN3LO(k,k’)0 for k,k’>5 fm-1 Vlow-k(k,k’)=0 for k,k’>2.1 fm-1 Cortona Ottobre 2006 Vlow-k

  12. CSB NN interaction [Gardestig & Phillips, 2005] • Isospin symmetry breaking • np singlet scattering length –23.74±0.02 fm • pp singlet scattering length –17.3±0.4 fm (Coulomb corrected) • nn singlet scattering length –18.5±0.4 fm • They come ultimately from u-d different charge & mass • In the “modern” Hamiltonians: • Coulomb • Nuclear effects (mass difference between +, - and 0,…) • Other e.m. interactions (magnetic moments,…) • n-p mass difference • Important for • Strange FF of 4He • Reaction d+d 4He+ 0 [Miller et al, nucl-ex/0602021] CSB from PT: [Epelbaum & Meissner, 2005] Cortona Ottobre 2006

  13. 4NF from PT: [Epelbaum, 2006, Rozpedzik et al., 2006] 3N force • “Old models” • Brazil & Tucson Melbourne [Friar et al, 1999] • Urbana [Pudliner et al, 1997] • New proposed models • Illinois (3 exchanges)[Pieper et al, 2001] • Chiral symmetry • [Friar et al, 1999] • [Epelbaum et al, 2002] • N3LO: work in progress • CSB:  and  exchange (effects unknown) • [Kaiser, 2006] Cortona Ottobre 2006

  14. m k i j HH method (1) Fabre de la Ripelle, 1983 • Hyperspherical coordinates • HH functions Cortona Ottobre 2006 Grand angular q.n.

  15. 4 3 1 2 HH method (2) Fabre de la Ripelle, 1983 • Expansion of the wave function • Rainal-Revai coefficients • Matrix elements of the interaction Cortona Ottobre 2006

  16. HH method (3) • Fourier transform • Usual choice: Lagrange polynomials Cortona Ottobre 2006

  17. r B A HH method (4) • Bound state • Rayleigh-Ritz variational principle • Boundary conditions: • Scattering states • Kohn variational principle • Boundary conditions: Cortona Ottobre 2006

  18. Convergence Cortona Ottobre 2006

  19. Binding energy (MeV) 3H binding energy Cortona Ottobre 2006 F: Nogga et al, PRC65, 054003 (2002); Deltuva et al, PRC68, 024005 (2003) NCSM: Navratil & Barret, PRC59, 014311 (2004)

  20. 4He binding energy Cortona Ottobre 2006 FY: Nogga et al, PRC 65, 054003 (2002) NCSM: Navratil & Barret, PRC 59, 014311 (2004)

  21. T>0 components (1) • Previous estimates of PT=1: • [Ramavataram et al, 1994] – based on an approx 4He w.f. • PT=10.0007% : RT=1 was estimated to be negligible • Current estimates of PT=13 to 5 times larger Cortona Ottobre 2006

  22. T>0 components (2) • Origin of the T>0 components Cortona Ottobre 2006

  23. 4He FF (1) Q2=0.0772 GeV2 q1.4 fm-1 PRELIMINARY Cortona Ottobre 2006

  24. K. Aniol, QNP06 Madrid June 2006 4He FF (2) Preliminary HAPPEX estimate @ Q2=0.0772 GeV2 (q1.4fm-1): ALR = +6.43  0.23 (stat)  0.22 (syst) ppm Rs-1.08 RT=1= 0.009  0.03 PRELIMINARY Cortona Ottobre 2006 In agreement with recent lattice calculations GEs= 0.001 0.004 [Leinweber et al, hep-lat/0601025]

  25. Summary • Current models predict a non-negligible contribution of the T>0 components to the LR asymmetry • GEs is currently predicted (at low Q2) to be very small • The next generation of the HAPPEX-He experiment could measure … RT=1 • CSB in NN interaction is of maior interest • d+d4He+0 at IUCF Cortona Ottobre 2006

  26. We’d like to invite everybody to the EUROPEAN FEW BODY CONFERENCE XX PISA (Italy) preregistration: http://www.pi.infn.it/efb20 10-15 September 2007 Cortona Ottobre 2006

  27. AV18 NN potentials in p-space Cortona Ottobre 2006

  28. AV18 NN potentials in p-space CD BONN  very long tail Cortona Ottobre 2006

  29. AV18 AV18 N3LO NN potentials in p-space CD BONN CD BONN  very long tail VN3LO(k,k’)0 for k,k’>5 fm-1 Cortona Ottobre 2006

  30. AV18 N3LO NN potentials in p-space CD BONN  very long tail VN3LO(k,k’)0 for k,k’>5 fm-1 Vlow-k(k,k’)=0 for k,k’>2.1 fm-1 Cortona Ottobre 2006 Vlow-k

  31. Deuton wave function • In r-space: 3S1 wave Cortona Ottobre 2006 0 2.5 5.0 7.5 10.0 12.5 15.0 r (fm)

  32. Deuton wave function • In p-space: 3S1 wave Cortona Ottobre 2006

  33. NN potentials in r-space Cortona Ottobre 2006

  34. V(r,r’)=<3S1|V(r,r’)| 3S1 > NN potentials in r-space: N3LO Cortona Ottobre 2006

  35. V(r,r’)=<3S1|V(r,r’)| 3S1 > NN potentials in r-space: Vlow-k Cortona Ottobre 2006

  36. A=4 scattering • p-3He, p-3H, d-d,… • 3N force effect? • Fusion • Theoretical methods still under development • Faddeev-Yakubovsky [Lazauskas & Carbonell, 2004] [Fonseca, 1999, Deltuva & Fonseca, work in progress] • Variational – HH [MV et al, 2006] • Resonating Group Model[Pfitzinger, Hofmann & Hale, 2001] Cortona Ottobre 2006

  37. A=4 scattering with the N3LO potential • n-t scattering lenghts [fm] • Experimental situation • Theoretical calculations FY: Lazauskas & Carbonell, 2004 Cortona Ottobre 2006 PRELIMINARY

  38. n-t scattering lengths (expt) =1.700.03 b [Phillips et al, 1980] Coherent scattering length ac=3.590.02 fm [Rauch et al, 1985] ac=3.6070.017 fm [Hale et al, 1990] Cortona Ottobre 2006

  39. n-t scattering lengths (expt) =1.700.03 b [Phillips et al, 1980] Coherent scattering length ac=3.590.02 fm [Rauch et al, 1985] ac=3.6070.017 fm [Hale et al, 1990] AV18UIX Cortona Ottobre 2006

  40. as at n-t scattering lengths Rauch et al, 1985 (I) PRELIMINARY Hale et al, 1990 Cortona Ottobre 2006

  41. as at n-t scattering lengths Rauch et al, 1985 (I) PRELIMINARY Hale et al, 1990 Cortona Ottobre 2006

  42. p-t scattering at low energies (1) Isospin state T=1/2,Tz=+1/2 Isospin state T=1/2,Tz=-1/2 r 3H p The “internal” part contains T=0 and T=1 isospin channels Cortona Ottobre 2006

  43. p-t scattering at low energies (2) • Triplet phase shift [deg] • Ecm=0.1 MeV N3LO FY: Lazauskas & Carbonell, 2004 Cortona Ottobre 2006 PRELIMINARY PRELIMINARY

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