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R. Machleidt University of Idaho

Nuclear forces from chiral EFT: The unfinished business. R. Machleidt University of Idaho. Outline. Nuclear forces from chiral EFT: Overview & achievements Are we done? No! Sub-leading many-body forces Proper renormalization of chiral forces Outlook: Will we ever be done?.

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R. Machleidt University of Idaho

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  1. Nuclear forces from chiral EFT: The unfinished business R. Machleidt University of Idaho

  2. Outline • Nuclear forces from chiral EFT: Overview & achievements • Are we done? No! • Sub-leading many-body forces • Proper renormalization of chiral forces • Outlook: Will we ever be done? The unfinished business Vietri, Italy, 22 May 2010

  3. The chiral EFT approach to nuclear forces • Clear connection to QCD: via symmetries • Degrees of freedom relevant to (low-energy) nuclear physics: pions and nucleons • Systematic expansion: Q/Λ • Controlled error, predictive power. • Explains the empirically known hierarchy of nuclear forces The unfinished business Vietri, Italy, 22 May 2010

  4. 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 The unfinished business Vietri, Italy, 22 May 2010

  5. 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 The unfinished business Vietri, Italy, 22 May 2010

  6. Phase shifts up to 300 MeV Red Line: N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003). Green dash-dotted line: NNLO Potential, and blue dashed line: NLO Potential by Epelbaum et al., Eur. Phys. J. A19, 401 (2004). LO NLO NNLO N3LO The unfinished business Vietri, Italy, 22 May 2010

  7. N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003). NNLO and NLO Potentials by Epelbaum et al., Eur. Phys. J. A19, 401 (2004). The unfinished business Vietri, Italy, 22 May 2010

  8. Applications of the chiral NN potential The unfinished business Vietri, Italy, 22 May 2010

  9. The unfinished business Vietri, Italy, 22 May 2010

  10. The unfinished business Vietri, Italy, 22 May 2010

  11. Chiral NN potential at N3LO underbinds by ~1MeV/nucleon. (Size extensivity at its best.) The unfinished business Vietri, Italy, 22 May 2010

  12. The unfinished business Vietri, Italy, 22 May 2010

  13. The unfinished business Vietri, Italy, 22 May 2010

  14. 4N 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 The unfinished business Vietri, Italy, 22 May 2010

  15. 4NF at N3LO (leading order) Essentially negligible, as to be expected. R. Machleidt The unfinished business Vietri, Italy, 22 May 2010 15

  16. Interim summary • 2NF o.k. (except for the issue of non-perturbative renormalization) • 4NF (negligibly) small … The unfinished business Vietri, Italy, 22 May 2010

  17. 3N forces 4N forces 3NF 2N forces Leading Order The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to Leading Order The focus: The 3NF Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order The unfinished business Vietri, Italy, 22 May 2010

  18. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) Next-to-Next-to-Next-to Leading Order (Q4) N4LO (Q5) R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 18 18

  19. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) Coon & Friar (1986) Next-to-Next-to-Next-to Leading Order (Q4) N4LO (Q5) R. Machleidt R. Machleidt R. Machleidt R. Machleidt The unfinished business Vietri, Italy, 22 May 2010 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 19 19 19 19

  20. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) The 3NF At N2LO : How well does it do? Next-to-Next-to-Next-to Leading Order (Q4) N4LO (Q5) R. Machleidt R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 20 20 20

  21. The unfinished business Vietri, Italy, 22 May 2010

  22. Calculating the properties of light nuclei usingchiral 2N and 3N forces “No-Core Shell Model “ Calculations by P. Navratil et al., LLNL The unfinished business Vietri, Italy, 22 May 2010

  23. Calculating the properties of light nuclei usingchiral 2N and 3N forces “No-Core Shell Model “ Calculations by P. Navratil et al., LLNL 2N (N3LO) force only The unfinished business Vietri, Italy, 22 May 2010

  24. Calculating the properties of light nuclei usingchiral 2N and 3N forces “No-Core Shell Model “ Calculations by P. Navratil et al., LLNL 2N (N3LO) +3N (N2LO) forces 2N (N3LO) force only R. Machleidt The unfinished business Vietri, Italy, 22 May 2010 24

  25. p-d 2NF+3NF Analyzing Power, Ay Calculations by the Pisa Group 2NF only The Ay puzzle is NOT solved by the 3NF at NNLO. p-3He The unfinished business Vietri, Italy, 22 May 2010

  26. Why do we need 3NFs beyond NNLO? • The 2NF is N3LO; • consistency requires that all contributions are at the same order. • There are unresolved problems in 3N, 4N scattering and nuclear structure. The unfinished business Vietri, Italy, 22 May 2010

  27. What’s there beyond NNLO? The unfinished business Vietri, Italy, 22 May 2010

  28. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) Next-to-Next-to-Next-to Leading Order (Q4) N4LO (Q5) R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 28 28

  29. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) Next-to-Next-to-Next-to Leading Order (Q4) N4LO (Q5) R. Machleidt R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 29 29 29

  30. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) Next-to-Next-to-Next-to Leading Order (Q4) N4LO (Q5) R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 30 30

  31. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) ✗ ✗ ✗ ✗ Next-to-Next-to-Next-to Leading Order (Q4) Time derivative N4LO (Q5) R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 31

  32. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) ✗ ✗ ✗ ✗ Next-to-Next-to-Next-to Leading Order (Q4) 1-loop lead. vert. N4LO (Q5) R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 32 32

  33. The 3NF at N3LO explicitly One-loop, leading vertices Ishikawa & Robilotta, PRC 76, 014006 (2007) Bernard, Epelbaum, Krebs, Meissner, PRC 77, 064004 (2008) In progress The unfinished business Vietri, Italy, 22 May 2010

  34. The ring diagrams From: Bernard, Epelbaum, Krebs, Meissner, PRC 77, 064004 (2008) The unfinished business Vietri, Italy, 22 May 2010

  35. Proton-deuteron elastic scattering Black line: 2NF only Red dashed line: 2NF + 3NF(N2LO+2πN3LO) ≈ 2NF + 3NF(N2LO) The 2πN3LO 3NF is negligible. From: Ishikawa & Robilotta, PRC 76, 014006 (2007) The unfinished business Vietri, Italy, 22 May 2010

  36. Interim balance • The 3NF at N3LO may be generally weak. • Reason: only “leading” vertices are involved, which are known to be weak (e.g., from NN). • Thus, the 3NF at N3LO may not solve any of the outstanding problems. The unfinished business Vietri, Italy, 22 May 2010

  37. What now? Go to the next order! The unfinished business Vietri, Italy, 22 May 2010

  38. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) ✗ ✗ ✗ ✗ Next-to-Next-to-Next-to Leading Order (Q4) 1-loop lead. vert. N4LO (Q5) 1-loop one ci vert. R. Machleidt R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 38 38 38

  39. What to expect from those N4LO 1-loop diagrams? Compare to “similar” 2NF diagrams. The unfinished business Vietri, Italy, 22 May 2010

  40. ✗Small Corresponding 2NF contributions 2π 1-loop lead. vert. 1-loop One ci vert. The unfinished business Vietri, Italy, 22 May 2010

  41. ✗Small Corresponding 2NF contributions 2π 3π Small 1-loop lead. vert. Kaiser (2000) Large!! 1-loop One ci vert. Kaiser (2001) R. Machleidt The unfinished business Vietri, Italy, 22 May 2010 41

  42. The chiral 3NF ✗ Leading Order (Q0) Basic Diagrams (1/M)n corrections Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) ✗ ✗ ✗ ✗ Next-to-Next-to-Next-to Leading Order (Q4) 1-loop lead. vert. Large!! N4LO (Q5) 1-loop one ci vert. R. Machleidt R. Machleidt R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 42 42 42 42

  43. So, we will have to go to N4LO!? • No, not necessarily. • There is an alternative: go to N3LO, but include Δ(1232) isobars explicitly. The unfinished business Vietri, Italy, 22 May 2010

  44. The 3NF in the “Δ-full” theory The unfinished business Vietri, Italy, 22 May 2010

  45. The chiral 3NF: Δ-less vs. Δ-full ✗ Leading Order (Q0) Δ less Additional in Δ full Next-to Leading Order (Q2) The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to-Next-to Leading Order (Q3) Next-to-Next-to-Next-to Leading Order (Q4) 1-loops with Δ e.g., Illinois N4LO (Q5) R. Machleidt R. Machleidt R. Machleidt R. Machleidt R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 The unfinished business Vietri, Italy, 22 May 2010 45 45 45 45 45

  46. However, there is a however … • For reasons of consistency, the 2NF must then also include Δ’s, up to N3LO! • It will be a big mess! The unfinished business Vietri, Italy, 22 May 2010

  47. Conclusions • Substantial advances in chiral nuclear forces during the past decade. The major milestone of the decade: “high precision” NN pots. at N3LO, successful in nuclear structure. But there are still issues: • 3NFs beyond N2LO are needed! • The 3NF at N3LO of the Δ-less theory may be weak and useless. • This calls for further 3NF contributions: - Δ-less N4LO or - Δ-full N3LO, they will be large, but none will be easy. • ChPT of nuclear forces has been fairly easy and straightforward, so far; but what’s left won’t be easy, no matter how you do it. The unfinished business Vietri, Italy, 22 May 2010

  48. The End The unfinished business Vietri, Italy, 22 May 2010

  49. Three-nucleon forces at N2LO TPE-3NF No new parameters! OPE-3NF One new parameter, D. Contact-3NF 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. The unfinished business Vietri, Italy, 22 May 2010

  50. The chiral 2NF: Δ-less vs. Δ-full Additional in Δ full Leading Order Δ less Ordonez ’94, Kaiser ‘98 The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to Leading Order Krebs ‘07 Next-to-Next-to Leading Order + 1/M corrections, Kaiser ’98: large? Next-to-Next-to-Next-to Leading Order 2pi & 3pi 2-loops with Δ N4LO (Q5) The unfinished business Vietri, Italy, 22 May 2010

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