1 / 59

R. Machleidt, University of Idaho

2009 Mardi Gras “Special Symmetries and Ab Initio Methods for Light Nuclei” Workshop Louisiana State University, 18-20 February, 2009. The missing three-nucleon forces: Where are they?. R. Machleidt, University of Idaho. Outline.

sheri
Download Presentation

R. Machleidt, University of Idaho

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2009 Mardi Gras “Special Symmetries and Ab Initio Methods for Light Nuclei” Workshop Louisiana State University, 18-20 February, 2009 The missing three-nucleon forces: Where are they? R. Machleidt, University of Idaho

  2. Outline • Nuclear forces from Chiral Perturbation Theory (ChPT): Current status • The 3NF at N2LO • The 3NF at N3LO: Weak expectations • N4LO or Δ-isobars? • Summary Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  3. The ChPT 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  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 R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 4

  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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  6. Phase shifts up to 300 MeV Red Line: N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003). Green dashed line: NNLO Potential, and blue dotted line: NLO Potential by Epelbaum et al., Eur. Phys. J. A19, 401 (2004). Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  7. N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003). NNLO and NLO Potentials by Epelbaum et al., Eur. Phys. J. A19, 401 (2004). R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 7

  8. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  9. Deuteron wave functions of N3LO potentials red = Idaho, green = Bochum/Juelich Black lines = high-precision pots. R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 9

  10. Results from applications of chiral two-nucleon forces • Latest Coupled Cluster results for A≤48 using N3LO R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 10

  11. ? Chiral NN potential at N3LO underbinds by ~1MeV/nucleon. (Size extensivity at its best.) V_low-k R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 11

  12. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  13. 4NF at N3LO (leading order) Essentially negligible, as to be expected. R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 13

  14. Interim summary • 2NF o.k. (except for the issue of non-perturbative renormalization) • 4NF (negligibly) small … Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  15. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  16. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 16 16

  17. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 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 17 17 17 17

  18. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 18 18

  19. 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. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 20 20 20

  21. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 21

  22. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  23. Courtesy of M. Viviani; latest data from TUNL. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  24. n-d at 3 MeV Ay puzzle at NLO and NNLO (2NF+3NF) NLO The Ay puzzle is NOT solved by the 3NF at NNLO. NNLO R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 Recent Adv. in Th. of Nucl. Forces EXOCT07, Catania, 14-June-07 24

  25. 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. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  26. What 3NFs are generated by ChPT beyond NNLO? Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  27. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 27 27

  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 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 28 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 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 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) Time derivative N4LO (Q5) R. Machleidt Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 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) 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 31 31

  32. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  33. The ring diagrams From: Bernard, Epelbaum, Krebs, Meissner, PRC 77, 064004 (2008) Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  34. 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) Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  35. 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. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  36. What now? Go to the next order! Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  37. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 37 37 37

  38. What to expect from those N4LO 1-loop diagrams? Compare to “similar” 2NF diagrams. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  39. ✗Small Corresponding 2NF contributions 2π 1-loop lead. vert. 1-loop One ci vert. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  40. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  41. ✗Small Corresponding 2NF contributions 2π 3π Small 1-loop lead. vert. Kaiser (2000) Large!! 1-loop One ci vert. Kaiser (2001) R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 Chiral 3NF beyond N2LO PNuT Seminar, UA, 11-06-08 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 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. Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  44. pi-N Lagrangian with two derivatives(“next-to-leading” order) Bernard et al. ‘97 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  45. Chiral 2NF Δ less Additional in Δ full Leading Order Ordonez ’94, Kaiser ‘98 The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to Leading Order Krebs ‘07 Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 45

  46. Δ-full theory Raises NLO, Better convergence R. Machleidt Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 46

  47. The 3NF in the Δ-full theory Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  48. 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 Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09 48 48 48 48 48

  49. However, there is a however … • For reasons of consistency, the 2NF must then also include Δ’s---up to N3LO! • So, what does that look like? Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

  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) Missing 3NFs: Where are they? Mardi Gras, LSU, 02-18-09

More Related