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Session 1: NN and many-body interactions: chiral perturbation theory; effective interactions

SURA Workshop on the Physics of Nucleons and Nuclei Washington, DC, 16-17 October 2006. Session 1: NN and many-body interactions: chiral perturbation theory; effective interactions. R. Machleidt University of Idaho. Reviewer’s presentation (theory). Outline. The NN system

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Session 1: NN and many-body interactions: chiral perturbation theory; effective interactions

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  1. SURA Workshop on the Physics of Nucleons and Nuclei Washington, DC, 16-17 October 2006 Session 1: NN and many-body interactions:chiral perturbation theory;effective interactions R. Machleidt University of Idaho Reviewer’s presentation (theory)

  2. Outline • The NN system - data and phase shift analysis - theory: * phenomenological models * chiral effective field theory (EFT) • Three- and four-nucleon systems - data and conventional theory - chiral EFT: * three-nucleon forces * four-nucleon forces • Summary and many more issues Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  3. The NN System Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  4. NN data base • pp data up to 3000 MeV (≈40,000 data) of sufficient quality to allow PSA (SATURN II, Saclay, and COSY, Juelich, (“EDDA” group) data are crucial) [analysis by Arndt, Strakowski, Workman, GWU/VPI] • np data up to 1300 MeV (≈ 20,000 data) of sufficient quality for PSA. • Below 350 MeV, “high-precision” PSA (χ²/datum ≈ 1) by Nijmegen group (PWA93). Since 1994, Nijmegen has announced new PWA up to 500 MeV, but not published. PWA93 is used in all NN potential constructions and is good enough. However, for χ² calculations, 1992 data base too outdated; newer data base should be used that includes the IUCF pp spin correlation parameters and other new data. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  5. Are there still problems with some data below 350 MeV? Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  6. The np differential cross section controversy • Bonner et al. versus Uppsala, Freiburg/PSI • IUCF has resolved the issue by a very reliable absolute measurement at 194 MeV. • Bonner is right, Uppsala & Freiburg/PSI wrong. • Nijmegen was right! Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  7. Low-energy parameters • All in a good shape except the neutron-neutron scattering length, a_nn • pi- + d -> gamma + n +n a_nn = -18.93 ± 0.27 ± 0.3 fm • nd breakup: a_nn = -18.72 ± 0.13 ± 0.65 fm (TUNL) a_nn = -16.50 ± 0.69 ± 0.52 fm (v. Witch, Bonn) To be compared with a_pp(w/o e.m.) = -17.3 ± 0.3 fm Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  8. NN phenomenology: “High-Precision” Potentialsχ²/datum ≈ 1 with regard to data base they were fit to • Nijmegen (1994): Niijm-I, Nijm-II, Reid93 • Argonne (1995): AV18 • CD-Bonn (1996, 2001) Later additions to the club: • Doleschall et al. (2003): highly non-local (triton binding w/o 3NF) • Deltuva & Sauer (2003): “CD-Bonn + Delta” • J-matrix inverse scattering: Shirokov, Vary et al. (2005) Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  9. The CRUX of NN potential development up to about 2000 • There are many quantitative NN potentials which are, however, not fundamental (the latest are the “high-precision potentials” developed in the 1990s). • Fundamental approaches were either not fundamental or not quantitative. • In short: The more quantitative, the less fundamental. The more fundamental, the less quantitative. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  10. We need … • a fundamental approach that produces a quantitative description of the nuclear force. • A fundamental approach must necessarily be based upon QCD. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  11. Describe Low-energy QCD in terms of an (chiral) effective field theory (EFT) Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  12. The organizational scheme “Power Counting” Chiral Perturbation Theory (ChPT) Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  13. 3N forces 4N forces 2N forces Leading Order The Hierarchy of Nuclear Forces Next-to Leading Order Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  14. Main milestones for NN potential development in chiral perturbation theory (ChPT) • 1994/96: v. Kolck and co-workers, first ChPT based NN potential at N2LO using cutoff regularization (r-space) • 1994-1997: - Robilotta and co-workers, 2-pi at N2LO - 1997: Kaiser et al., 2-pi at N2LO using HBChPT and DR • 2000: Epelbaum et al. (“Bochum-Juelich” group), NN potential in momentum space at N2LO (HBChPT, DR) • 2003: - Robilotta and co-workers 2-pi at N3LO in RBChPT - Entem & Machleidt (“Idaho” group), first NN potential at N3LO (HBChPT, DR) • 2005: Epelbaum et al. (“Bochum-Juelich” group), NN potential at N3LO (HBChPT, SFR) Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  15. What order do we need for sufficient precision? Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  16. How many parameters do we need? Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  17. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  18. Conclusion: At least, N3LO is needed Entem & Machleidt, PLB 524, 93(2002) Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  19. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  20. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  21. Summary: χ²/datum • NLO: ≈ 100 • NNLO: ≈ 10 • N3LO: ≈ 1 Great rate of convergence of ChPT! Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  22. np phase shifts of N3LO potentials red = Idaho, green = Bochum/Juelich Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  23. 3N and 4N systems • Data base • Theory Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  24. Present achievement of experiments @ intermediate energies Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  25. Theory: The need for three-nucleon forces (3NF) is best established in the 3N system What 3NFs are there? Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  26. Ggggggg 2-pi exchange 3NF p D p p p P wave S wave Hannover NN model “Conventional” three-nucleon forces (3NF) • Fujita-Miyazawa (1957) • Tucson-Melbourne (TM, 1979), TM99 (TM’) • Urbana IX (UIX, U9, 1995) • Dynamical Delta model (“CD-Bonn+Delta”, “Hannover model” 2003) • Illinois (2001) Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  27. “Illinois” 3NFs Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  28. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  29. Elastic 3N scattering Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  30. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  31. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  32. Failure? d/d ? (Tp>200 MeV) nd elastic scattering measurements at En=250MeV Calc. even including 3NF still underestimate the data by 50% ! Relativistic calc. by Witala improve the fit only at θcm > 160 deg. but not enough. Courtesy of H. Sakai Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  33. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  34. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  35. NN only NN+3NF(TM99) AV18+3NF(U9) CDBonn+△ iT11, Tij, PT  some successful, some not. confusing, chaotic! • Failure? Courtesy of H. Sakai Sekiguchi et al. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  36. Breakup Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  37. Prediction by CD-Bonn + Delta, courtesy of A. Deltuva Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  38. The situation is, in part, chaotic. Try and error is not good enough. We need a systematic approach. ChPT! Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  39. 3N forces 2N forces Leading Order The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to Leading Order Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  40. n-d at 3 MeV Ay puzzle at NLO and NNLO NLO, χ²/dat≈100 NNLO χ²/dat≈15 Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  41. Spin-Transfer Coefficients H.R. Amir-Ahmadi, Submitted to PRL Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06 Courtesy of N. Kalantar

  42. Spin-Transfer Coefficients H.R. Amir-Ahmadi, Submitted to PRL Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06 Courtesy of N. Kalantar

  43. Spin-Transfer Coefficients Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06 Courtesy of N. Kalantar

  44. Conclusions from 2NF + 3NF NNLO calculations: • Uncertainties at NNLO very large, comparison with • data inconclusive. Note that the uncertainty is due to • the large χ²/dat ≈ 15 of the 2NF. • As far as one can tell, 3NF at NNLO not any • better than conventional 3NF’s. • Calculations applying the 3NF at NNLO were not • conducted in a smart and useful way. • Better: use 2NF at N3LO (χ²/dat ≈ 1!) • + 3NF at NNLO. Less uncertain, more conclusive. • In any case: • the 3NF at N3LO is needed. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  45. 3N forces 2N forces Leading Order The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to Leading Order Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  46. The 3NF at N3LO Many new isospin structures; It’s being worked out by the Juelich group. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  47. The 4N system Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  48. Courtesy of M. Viviani; latest data from TUNL. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  49. Courtesy of M. Viviani; latest data from TUNL. Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

  50. Courtesy of W. Tornow, data from TUNL, calculations by Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-06

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