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Isospin mixing in the 4 He ground state and the nucleon strange form factor

Dedicated to Adelchi. Isospin mixing in the 4 He 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. g. g. Z 0.

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Isospin mixing in the 4 He ground state and the 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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