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

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-062 Outline The NN system The NN system - data and phase shift analysis - data and phase shift analysis - theory: - theory: * phenomenological models * phenomenological models * chiral effective field theory (EFT) * chiral effective field theory (EFT) Three- and four-nucleon systems Three- and four-nucleon systems - data and conventional theory - data and conventional theory - chiral EFT: - chiral EFT: * three-nucleon forces * three-nucleon forces * four-nucleon forces * four-nucleon forces Summary and many more issues Summary and many more issues

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-063 The NN System

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-064 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] 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. np data up to 1300 MeV (≈ 20,000 data) of sufficient quality for PSA. Below 350 MeV, “high-precision” PSA ( χ ²/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 However, for χ ² calculations, 1992 data base too outdated; newer data base should be used that includes the IUCF pp spin correlation parameters and other new data. Below 350 MeV, “high-precision” PSA ( χ ²/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 However, for χ ² calculations, 1992 data base too outdated; newer data base should be used that includes the IUCF pp spin correlation parameters and other new data.

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-065 Are there still problems with some data below 350 MeV?

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-066 The np differential cross section controversy Bonner et al. versus Uppsala, Freiburg/PSI Bonner et al. versus Uppsala, Freiburg/PSI IUCF has resolved the issue by a very reliable absolute measurement at 194 MeV. IUCF has resolved the issue by a very reliable absolute measurement at 194 MeV. Bonner is right, Uppsala & Freiburg/PSI wrong. Bonner is right, Uppsala & Freiburg/PSI wrong. Nijmegen was right! Nijmegen was right!

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-067 Low-energy parameters All in a good shape except the neutron-neutron scattering length, a_nn All in a good shape except the neutron-neutron scattering length, a_nn pi- + d -> gamma + n +n pi- + d -> gamma + n +n a_nn = ± 0.27 ± 0.3 fm a_nn = ± 0.27 ± 0.3 fm nd breakup: nd breakup: a_nn = ± 0.13 ± 0.65 fm (TUNL) a_nn = ± 0.13 ± 0.65 fm (TUNL) a_nn = ± 0.69 ± 0.52 fm (v. Witch, Bonn) a_nn = ± 0.69 ± 0.52 fm (v. Witch, Bonn) To be compared with a_pp(w/o e.m.) = ± 0.3 fm

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-068 NN phenomenology: “High-Precision” Potentials χ²/datum ≈ 1 with regard to data base they were fit to Nijmegen (1994): Niijm-I, Nijm-II, Reid93 Nijmegen (1994): Niijm-I, Nijm-II, Reid93 Argonne (1995): AV18 Argonne (1995): AV18 CD-Bonn (1996, 2001) CD-Bonn (1996, 2001) Later additions to the club: Doleschall et al. (2003): highly non-local (triton binding w/o 3NF) Doleschall et al. (2003): highly non-local (triton binding w/o 3NF) Deltuva & Sauer (2003): “CD-Bonn + Delta” Deltuva & Sauer (2003): “CD-Bonn + Delta” J-matrix inverse scattering: Shirokov, Vary et al. (2005) J-matrix inverse scattering: Shirokov, Vary et al. (2005)

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-069 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). 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. Fundamental approaches were either not fundamental or not quantitative. In short: In short: The more quantitative, the less fundamental. The more quantitative, the less fundamental. The more fundamental, the less quantitative. The more fundamental, the less quantitative.

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0610 We need … a fundamental approach that produces a quantitative description of the nuclear force. a fundamental approach that produces a quantitative description of the nuclear force. A fundamental approach must necessarily be based upon QCD. A fundamental approach must necessarily be based upon QCD.

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0611 Describe Low-energy QCD in terms of an (chiral) effective field theory (EFT)

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0612 The organizational scheme “Power Counting” Chiral Perturbation Theory (ChPT)

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct N forces 3N forces4N forces Leading Order Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order Next-to Leading Order The Hierarchy of Nuclear Forces

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0614 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) 1994/96: v. Kolck and co-workers, first ChPT based NN potential at N2LO using cutoff regularization (r-space) : : - Robilotta and co-workers, 2-pi at N2LO - Robilotta and co-workers, 2-pi at N2LO : Kaiser et al., 2-pi at N2LO using HBChPT and DR : 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) 2000: Epelbaum et al. (“Bochum-Juelich” group), NN potential in momentum space at N2LO (HBChPT, DR) 2003: 2003: - Robilotta and co-workers 2-pi at N3LO in RBChPT - Robilotta and co-workers 2-pi at N3LO in RBChPT - Entem & Machleidt (“Idaho” group), first NN potential at N3LO (HBChPT, DR) - Entem & Machleidt (“Idaho” group), first NN potential at N3LO (HBChPT, DR) 2005: Epelbaum et al. (“Bochum-Juelich” group), NN potential at N3LO (HBChPT, SFR) 2005: Epelbaum et al. (“Bochum-Juelich” group), NN potential at N3LO (HBChPT, SFR)

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0615 What order do we need for sufficient precision?

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0616 How many parameters do we need?

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0617

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0618 Conclusion: At least, N3LO is needed Entem & Machleidt, PLB 524, 93 (2002)

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0619

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0620

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0621 Summary: χ ²/datum NLO: ≈ 100 NLO: ≈ 100 NNLO: ≈ 10 NNLO: ≈ 10 N3LO: ≈ 1 N3LO: ≈ 1 Great rate of convergence of ChPT! Great rate of convergence of ChPT!

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0622 np phase shifts of N3LO potentials red = Idaho, green = Bochum/Juelich

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct N and 4N systems Data base Data base Theory Theory

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0624  Present achievement of intermediate energies

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0625 Theory: The need for three-nucleon forces (3NF) is best established in the 3N system What 3NFs are there?

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0626 “Conventional” three-nucleon forces (3NF) Fujita-Miyazawa (1957) Fujita-Miyazawa (1957) Tucson-Melbourne Tucson-Melbourne (TM, 1979), (TM, 1979), TM99 (TM’) TM99 (TM’) Urbana IX (UIX, U9, 1995) Urbana IX (UIX, U9, 1995) Dynamical Delta model (“CD-Bonn+Delta”, Dynamical Delta model (“CD-Bonn+Delta”, “Hannover model” 2003) “Hannover model” 2003) Illinois (2001) Illinois (2001) Ggggggg     2-pi exchange 3NF P wave S wave Hannover NN model

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0627 “Illinois” 3NFs

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0628

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0629 Elastic 3N scattering

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0630

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0631

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0632  Failure? d  /d  ? (T p >200 MeV) nd elastic scattering measurements at E n =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

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0633

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0634

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0635  Failure? iT 11, T ij, PT  some successful, some not. confusing, chaotic! confusing, chaotic! Sekiguchi et al. NN only NN+3NF(TM99) AV18+3NF(U9) CDBonn+ △ Courtesy of H. Sakai

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0636 Breakup

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0637 Prediction by CD-Bonn + Delta, courtesy of A. Deltuva

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0638 The situation is, in part, chaotic. Try and error is not good enough. We need a systematic approach. ChPT!

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0639 The Hierarchy of Nuclear Forces 2N forces 3N forces Leading Order Next-to Leading Order Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0640 n-d at 3 MeV Ay puzzle at NLO and NNLO NLO, χ ²/dat≈100 NNLO χ²/dat≈15

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0641 Spin-Transfer Coefficients H.R. Amir-Ahmadi, Submitted to PRL Courtesy of N. Kalantar

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0642 Spin-Transfer Coefficients H.R. Amir-Ahmadi, Submitted to PRL Courtesy of N. Kalantar

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0643 Spin-Transfer Coefficients Courtesy of N. Kalantar

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0644 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. Conclusions from 2NF + 3NF NNLO calculations:

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0645 The Hierarchy of Nuclear Forces 2N forces 3N forces Leading Order Next-to Leading Order Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0646 Many new isospin structures; It’s being worked out by the Juelich group. The 3NF at N3LO

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0647 The 4N system

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0648 Courtesy of M. Viviani; latest data from TUNL.

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0649 Courtesy of M. Viviani; latest data from TUNL.

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0650 Courtesy of W. Tornow, data from TUNL, calculations by

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0651 Four-nucleon forces (4NF)

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0652 The Hierarchy of Nuclear Forces 2N forces 3N forces Leading Order Next-to Leading Order Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order 4N forces

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct NF at N3LO (leading order) Do not expect much for 4N scattering!

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0654 Summary The NN system The NN system - data and phase shift analysis below 350 MeV o.k.; - data and phase shift analysis below 350 MeV o.k.; a_nn is a problem. a_nn is a problem. - theory: chiral EFT at N3LO has provided some NN potentials - theory: chiral EFT at N3LO has provided some NN potentials of high precision; in the moment, no need to go to higher of high precision; in the moment, no need to go to higher orders; open issue: Is Weinberg counting consistent? orders; open issue: Is Weinberg counting consistent? Three- and four-nucleon systems Three- and four-nucleon systems - comparison of data with conventional theory: lots of - comparison of data with conventional theory: lots of problems with spin observables! More data always problems with spin observables! More data always welcome, but present data pose already enough problems. welcome, but present data pose already enough problems. Systematic approach is needed! Systematic approach is needed! - chiral EFT: 3NF at N2LO doesn’t solve any of those - chiral EFT: 3NF at N2LO doesn’t solve any of those problems; 3NF at N3LO is needed and under construction. problems; 3NF at N3LO is needed and under construction. 4NF: has been derived and is small. 4NF: has been derived and is small.

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0655 Some subtleties concerning 2NF and 3NF I couldn’t elaborate on ChPT predicts a large variety of isospin-breaking corrections to the 2NF and 3NF; Kaiser (pi- gamma, 2pi-gamma; 2006); Epelbaum & Meissner (2005). ChPT predicts a large variety of isospin-breaking corrections to the 2NF and 3NF; Kaiser (pi- gamma, 2pi-gamma; 2006); Epelbaum & Meissner (2005). This should be tested in high-precision calculations/experiments. This should be tested in high-precision calculations/experiments.

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0656 Lots of other topics/issues Few- nucleon systems at very low energy, pion-less EFT, “Universality” [Dan Phillips] Few- nucleon systems at very low energy, pion-less EFT, “Universality” [Dan Phillips] Low energy NN interactions, V_low-k [Achim Schwenk] Low energy NN interactions, V_low-k [Achim Schwenk] NN interaction at high energies (relativistic meson theory): problems with spin observables above 1.5 GeV (“EDDA” data, Cosy, Juelich) [Charlotte Elster] NN interaction at high energies (relativistic meson theory): problems with spin observables above 1.5 GeV (“EDDA” data, Cosy, Juelich) [Charlotte Elster] Systematic study of parity-violating nuclear forces in chiral EFT (Zhu, Maekawa, Holstein, Ramsey-Musolf, v. Kolck, 2005), 1-pi, 2-pi. Systematic study of parity-violating nuclear forces in chiral EFT (Zhu, Maekawa, Holstein, Ramsey-Musolf, v. Kolck, 2005), 1-pi, 2-pi. Electroweak operators consistent with nuclear forces (Park, Min, Rho; Dan Phillips; NNLO); needed to N3LO. Electroweak operators consistent with nuclear forces (Park, Min, Rho; Dan Phillips; NNLO); needed to N3LO. Hyperon-nucleon interactions in chiral EFT (Juelich, 2006): LO (one-boson-exchange) works already well. More data are needed (most data from bubble chamber experiments from the 1960’s, Filthuth et al.) Hyperon-nucleon interactions in chiral EFT (Juelich, 2006): LO (one-boson-exchange) works already well. More data are needed (most data from bubble chamber experiments from the 1960’s, Filthuth et al.)

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0657 Hyperon-nucleon interactions in chiral three-flavor EFT by the Juelich Group (Polinder, Haidenbauer, Meissner, 2006)

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0658 Results We need better data!

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0659 Lots of other topics/issues, cont’d. Quark mass dependence of the nuclear force; Quark mass dependence of the nuclear force; - time-dependence of fundamental couplings in - time-dependence of fundamental couplings in the NN sector, changes to primordial the NN sector, changes to primordial nucleosynthesis; nucleosynthesis; - extrapolation to lattice “data” (next item). - extrapolation to lattice “data” (next item). Connecting (lattice) QCD with chiral EFT (Session 2) Connecting (lattice) QCD with chiral EFT (Session 2) … more … … more …

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0660 The End

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0661 Appendix

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0662

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0663 Deuteron wave functions of N3LO potentials red = Idaho, green = Bochum/Juelich Black lines = high-precision pots.

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0664 At N3LO, F-waves have no contacts and are not great. red = Idaho, green = Bochum/Juelich

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0665

R. Machleidt Review: NN and Many-Body Int. SURA Workshop, DC, 16-Oct-0666 Three-nucleon forces at N2LO TPE-3NF OPE-3NF Contact- 3NF No new parameters! One new parameter, D. One new parameter, E. Strategy: Adjust D and E to two few-nucleon observables, e.g., the triton and alpha-particle binding energies. Then predict properties of other light nuclei.