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Nuclear Forces - Lecture 4 -

12th CNS International Summer School (CNSSS13) 28 August to 03 September 2013 -- CNS Wako Campus . Nuclear Forces - Lecture 4 -. Nuclear Forces from Chiral EFT. R. Machleidt University of Idaho. Nuclear Forces - Overview of all lectures -. Lecture 1: History, facts, and phenomenology

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Nuclear Forces - Lecture 4 -

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  1. 12th CNS International Summer School (CNSSS13) 28 August to 03 September 2013 -- CNS Wako Campus Nuclear Forces- Lecture 4 - Nuclear Forces from Chiral EFT R. Machleidt University of Idaho Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  2. Nuclear Forces- Overview of all lectures - • Lecture 1: History, facts, and phenomenology • Lecture 2: The meson theory of nuclear forces • Lecture 3: QCD and nuclear forces; effective field theory (EFT) for low-energy QCD • Lecture 4: Nuclear forces from chiral EFT Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  3. Lecture 4: Nuclear Forces from EFT • Summary of basic arguments in favor of an EFT • The Hierarchy of nuclear forces • The new generation of chiral NN potentials • Beyond the two-nucleon force: 3NFs • Applications in nuclear structure • More on many-nucleon forces • Conclusions Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  4. From QCD to nuclear physics via chiral EFT (in a nutshell) • QCD at low energy is strong. • Quarks and gluons are confined into colorless hadrons. • Nuclear forces are residual forces (similar to van der Waals forces) • Separation of scales R. Machleidt Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  5. Calls for an EFT • soft scale: Q ≈ mπ ,hard scale: Λχ ≈ mρ ; pions and nucleon relevant d.o.f. • Low-energy expansion: (Q/Λχ)ν • with ν bounded from below. • Most general Lagrangian consistent with all symmetries of low-energy QCD, particularly, chiral symmetry which is spontaneously broken. • Weakly interacting Goldstone bosons = pions. • π-π and π-N perturbatively • NN has bound states: • (i) NN potential perturbatively • (ii) apply nonpert. in LS equation. • (Weinberg) Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  6. 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

  7. 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 7

  8. NN 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 Nuclear Forces - Lecture 4 NF from EFT (CNSSS13) 8

  9. N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003). NNLO and NLO Potentials by Epelbaum et al., Eur. Phys. J. A19, 401 (2004). Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  10. Summary: χ²/datum • NLO: ≈ 100 • NNLO: ≈ 10 • N3LO: ≈ 1 • Great rate of convergence of ChPT! Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  11. Parameters • pi-pi Lagrangian: • pi-N Lagrangians: • N-N Lagrangian (“Contacts”): 2+7+15=24 essentially free parameters. The free parameters are used to adjust the potential to the empirical NN phase shifts and data. No free parameters. no free parameters. In principal fixed by pi-N data; but cf. Table on next slide. 4 parameters. 4 parameters. Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  12. Parameters, cont’dpi-N Lagrangian parameters Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  13. Parameters, cont’d.# of contact parameters compared to phenomenological fits Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  14. How does the chiral EFT approach compare to conventional meson theory? Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  15. Main differences • Chiral perturbation theory (ChPT) is an expansion in terms of small momenta. • Meson theory is an expansion in terms of ranges (masses). Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  16. The nuclear force in the meson picture Short Inter- mediate Long range Taketani, Nakamura, Sasaki (1951): 3 ranges Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  17. 2N forces Leading Order Next-to Leading Order Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  18. ChPT Conventional meson theory OPE TPE Short range Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  19. Question: When everything is so equivalent to conventional meson theory, why not continue to use conventional meson theory? • Chiral EFT claims to be a theory, while “meson theory” is a model. • Chiral EFT has a clear connection to QCD, while the QCD-connection of the meson model is more hand-woven. • In ChPT, there is an organizational scheme (“power counting”) that allows to estimate the size of the various contributions and the uncertainty at a given order (i.e., the size of the contributions we left out). • Two- and many-body force contributions are generated on an equal footing in ChPT. Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  20. Three-nucleon forces (3NF) Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  21. 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 3NF at NNLO; used so far. Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  22. Now, showing only 3NF diagrams. The 3NF at NNLO; used so far. Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  23. Three-nucleon forces at NNLO 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. Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  24. Calculating the properties of light nuclei usingchiral 2N and 3N forces “No-Core Shell Model “ Calculations by P. Navratil et al., LLNL Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  25. 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 R. Machleidt Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  26. 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 Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  27. Oxygen Calcium R. Machleidt Nuclear Forces - Lecture 4 NF from EFT (CNSSS13) 27

  28. p-d Analyzing Power Ay 2NF+3NF Calculations by the Pisa Group 2NF only The Ay puzzle is NOT solved by the 3NF at NNLO. p-3He 2NF+3NF 2NF only Nuclear Forces - Lecture 4 NF from EFT (CNSSS13) 28

  29. And so, we need 3NFs beyond NNLO, because … • The 2NF is N3LO; • consistency requires that all contributions are included up to the same order. • There are unresolved problems in 3N and 4N scattering, and nuclear structure. Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  30. The 3NF at NNLO; used so far. Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  31. The 3NF at NNLO; used so far. Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  32. Apps of N3LO 3NF: Triton: Skibinski et al., PRC 84, 054005 (2011). Not conclusive. Neutron matter: Hebeler, Schwenk and co-workers, PRL 110, 032504 (2013). Not small!(?) N-d scattering (Ay): Witala et al. Small! The 3NF at NNLO; used so far. Small?

  33. N-d Ay calculations by Witala et al. R. Machleidt Nuclear Forces - Lecture 4 NF from EFT (CNSSS13) Chiral EFT of Nucl. Forces INPC 2013, Florence, 06/05/2013 33

  34. The 3NF at NNLO; used so far. Small? Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  35. The 3NF at NNLO; used so far. Small? 1-loop graphs: 5 topologies 2PE 2PE-1PE Ring Contact-1PE Contact-2PE Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  36. The 3NF at NNLO; used so far. Small? 1-loop graphs: 5 topologies 2PE 2PE-1PE Ring Contact-1PE Contact-2PE R. Machleidt Nuclear Forces - Lecture 4 NF from EFT (CNSSS13) Nuclear Forces - Lecture 4 NF from EFT (CNSSS13) 36

  37. The 3NF at NNLO; used so far. Small? Large?! Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  38. The 3NF at NNLO; used so far. Small? Large?! Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  39. 3NF contacts at N4LO Girlanda, Kievsky, Viviani, PRC 84, 014001 (2011) The 3NF at NNLO; used so far. Small? Large?! Spin-Orbit Force! Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  40. The 3NF at NNLO; used so far. Small? Large?! Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  41. A realistic, investigational approach: • use Δ-less The 3NF at NNLO; used so far. • include NNLO 3NF • skip N3LO 3NF Small? • at N4LO start with • contact 3NF, use • one term at a time, • e.g. spin-orbit • that may already • solve some of your • problems. Large?! Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  42. Current problems with chiral 3NFs • “Explosion” of 3NFs at higher orders. • For the time being, deal with it selectively. Do not try “complete” calculations. • Many open questions • Will the chiral 3NF converge with increasing order? • (This is quite in contrast to the chiral 2NF, where things are under control.) Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  43. Four-nucleon forces (4NF) Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  44. 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 4N forces Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  45. 4NF at N3LO (leading order) Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  46. Conclusions • After 80 years of struggle, we have now a proper theory for nuclear forces that is based upon the fundamental theory of strong interactions, QCD. It is chiral effective field theory for low-energy QCD, in which the pion plays a fundamental role (Goldstone boson). Thus, the original Yukawa idea that there is ONE MESON that makes the nuclear force is re-instated. But as compared to the early attempts, a crucial constraint has been added: chiral symmetry generates and controls pion-exchanges. • Based upon chiral perturbation theory (ChPT), quantitative NN potentials have been successfully developed (at N3LO) and are applied in nuclear structure calculations. • In ChPT, two- and many-body forces are generated on an equal footing. Concerning the 3NF, there are still some open issues including its order-by-order convergence. • A new and exciting era has started for microscopic nuclear structure! Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

  47. The End Thank you all for listening patiently, And thank you to the organizers! Review article: R. Machleidt and D.R. Entem, Chiral Effective Field Theory and Nuclear Forces, Physics Reports 503, 1 (2011). Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

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