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Effective Field Theories of Light Nuclei

Explore the concepts of effective field theories and their application to different aspects of light nuclei, including shallow bound states and narrow resonances. Presented by U. van Kolck from the University of Arizona.

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Effective Field Theories of Light Nuclei

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  1. Effective FieldTheoriesof Light NucleiU. van KolckUniversity of ArizonaSupported in part by US DOE and Sloan Foundation Background by S. Hossenfelder

  2. Outline • Effective Field Theories • Shallow Bound States: and , and • Narrow Resonances: and • Outlook U. van Kolck, EFTs of Light Nuclei

  3. Wanted fDead sor s Alive QCDEXPLANATIONOFNUCLEARPHYSICS Reward understanding of gross features: Why is ? How large are few-nucleon forces? Why is isospin a good symmetry? … Beware coupling constants not small U. van Kolck, EFTs of Light Nuclei

  4. What is Effective? local underlying symmetries renormalization-group invariance U. van Kolck, EFTs of Light Nuclei

  5. normalization non-analytic, from loops “power counting” e.g. # loops L For Q ~ m, truncate consistently with RG invariance so as to allow systematic improvement (perturbation theory): U. van Kolck, EFTs of Light Nuclei

  6. Nuclear physics scales “His scales are His pride”, Book of Job (according to J. Friar) perturbative QCD ~1 GeV sum ? hadronic th with chiral symm / ~100 MeV sum ~30 MeV / sum nosmall coupling expansion in U. van Kolck, EFTs of Light Nuclei

  7. Nuclear EFTs pionful EFT • degrees of freedom: nucleons, pions (+ deltas, roper?, …) • symmetries: Lorentz, P, T, chiral • expansion in: non-relativistic multipole pion loop U. van Kolck, EFTs of Light Nuclei

  8. Weinberg ’79 Gasser + Leutwyler ’84 … Gasser, Sainio + Svarc ’87 Jenkins + Manohar ’91 … A= 0, 1: chiral perturbation theory nucleon dense but short-ranged Weinberg ’90, ’92 Rho ‘91 Ordonez + v.K. ’92 … Park, Min + Rho ’95 Beane, Lee + v.K. ‘95 … Kaplan, Savage + Wise ’98 … Beane, Bedaque, Savage + v.K. ’02 … Entem + Machleidt ’03 Epelbaum, Glockle + Meissner ’04 ... long-ranged but sparse A > 2: resummed chiral perturbation theory see talks by Kubodera, Park and Song U. van Kolck, EFTs of Light Nuclei

  9. cf. Bethe + Peierls ‘35 - overkillat lower energies! e.g. (real) bound state = deuteron (virtual) bound state multipole expansion of meson cloud: contact interactions among local nucleon fields U. van Kolck, EFTs of Light Nuclei

  10. pionless EFT • degrees of freedom: nucleons • symmetries: Lorentz, P, T • expansion in: non-relativistic multipole omitting spin, isospin U. van Kolck, EFTs of Light Nuclei

  11. v.K. ’97 ’99 Kaplan, Savage + Wise ’98 Gegelia ’98 = + … + if scattering length p, other waves effective range s wave but b.s. at U. van Kolck, EFTs of Light Nuclei

  12. Alternative: auxiliary field Kaplan ’97 v.K. ’99 sign integrate out auxiliary field: same Lag as before with = = + + … U. van Kolck, EFTs of Light Nuclei

  13. renormalization: s wave (next order) long-range physics: non-analytic in - unitarity short-range physics: analytic in - high momenta in loops - counterterms or E E U. van Kolck, EFTs of Light Nuclei

  14. Chen, Rupak + Savage ’99 fitted predicted Nijmegen PSA fitted predicted Nijmegen PSA U. van Kolck, EFTs of Light Nuclei

  15. = + + … + = U. van Kolck, EFTs of Light Nuclei

  16. naïve dimensional analysis Bedaque + v.K. ’97 Bedaque, Hammer + v.K. ’98 … no three-body force up to U. van Kolck, EFTs of Light Nuclei

  17. renormalization: quartet s wave Skornyakov + Ter-Martirosian ’60 Bedaque + v.K. ’97 Bedaque, Hammer + v.K. ‘98 different regulators U. van Kolck, EFTs of Light Nuclei

  18. naïve dimensional analysis Bedaque + v.K. ’97 Bedaque, Hammer + v.K. ’98 … no three-body force up to v.Oers + Seagrave ‘67 Dilg et al. ‘71 predicted U. van Kolck, EFTs of Light Nuclei

  19. Bedaque, Hammer + v.K. ’99 ’00 Hammer + Mehen ’01 Bedaque et al. ‘03 unless U. van Kolck, EFTs of Light Nuclei

  20. renormalization: doublet s wave -I Danilov ’63 Bedaque, Hammer + v.K. ’99 ’00 different cutoffs SU(4) limit U. van Kolck, EFTs of Light Nuclei

  21. = + + + … + … + = + + U. van Kolck, EFTs of Light Nuclei

  22. renormalization: doublet s wave -I Danilov ’63 Bedaque, Hammer + v.K. ’99 ’00 different cutoffs SU(4) limit U. van Kolck, EFTs of Light Nuclei

  23. renormalization: doublet s wave -II Bedaque, Hammer + v.K. ’99 ’00 SU(4) limit Limit cycle ! U. van Kolck, EFTs of Light Nuclei

  24. Bedaque, Hammer + v.K. ’99 ’00 Hammer + Mehen ’01 Bedaque et al. ’03 … unless v.Oers + Seagrave ‘67 Kievsky et al. ‘96 (limit cycle!) fitted predicted Dilg et al. ‘71 U. van Kolck, EFTs of Light Nuclei

  25. renormalization: doublet s wave -III Bedaque, Hammer + v.K. ’99 ’00 outside EFT various cutoffs triton U. van Kolck, EFTs of Light Nuclei

  26. Phillips line Bedaque, Hammer + v.K. ’99 ’00 potential models varying experiment U. van Kolck, EFTs of Light Nuclei

  27. Effective FieldTheoriesof Light NucleiU. van KolckUniversity of ArizonaSupported in part by US DOE and Sloan Foundation Background by S. Hossenfelder

  28. Outline • Effective Field Theories • Shallow Bound States: and , and • Narrow Resonances: and • Outlook U. van Kolck, EFTs of Light Nuclei

  29. Extensions + four-nucleon system Platter, Hammer + Meissner ’04 Is the non-derivative four-nucleon force leading order? + nuclear matter on a spatial lattice Muller, Koonin, Seki + v.K. ’00 … Is nuclear matter within pionless EFT? + bosons and atomic systems • shallow molecules e.g., 4He dimer, trimer, tetramer • Feshbach resonances e.g., BECs in traps Bedaque, Hammer + v.K. ’99 ’00 … Bedaque, Braaten + Hammer ’01 … + limit cycles in other theories Glazek + Wilson ’02 … U. van Kolck, EFTs of Light Nuclei

  30. - many-body systems get complicated rapidly + (continue) focus on simpler halo nuclei one or more loosely-bound nucleons (near driplines) nucleon separation energy core excitation energy e.g. “ ” resonance at p n n n p n U. van Kolck, EFTs of Light Nuclei

  31. halo EFT • degrees of freedom: nucleons, cores • symmetries: Lorentz, P, T • expansion in: non-relativistic multipole simplest formulation: auxiliary fields for core + nucleon states e.g. U. van Kolck, EFTs of Light Nuclei

  32. Bertulani, Hammer + v.K. ’02 Bedaque, Hammer + v.K. ’03 spin transition operator U. van Kolck, EFTs of Light Nuclei

  33. reduced mass resonance at if and = + + … U. van Kolck, EFTs of Light Nuclei

  34. other waves: = + + … U. van Kolck, EFTs of Light Nuclei

  35. = U. van Kolck, EFTs of Light Nuclei

  36. Bedaque, Hammer + v.K. ’03 NNDC, BNL Haesner et al. ‘83 U. van Kolck, EFTs of Light Nuclei

  37. except at where = + + … enhanced by resum self-energy U. van Kolck, EFTs of Light Nuclei

  38. renormalization: p wave cannot resum without OOPS! without … ?! but U. van Kolck, EFTs of Light Nuclei

  39. Bertulani, Hammer + v.K. ’02 NNDC, BNL Haesner et al. ‘83 U. van Kolck, EFTs of Light Nuclei

  40. Bertulani, Hammer + v.K. ’02 PSA, Arndt et al. ’73 scatt length only U. van Kolck, EFTs of Light Nuclei

  41. Outlook • three-body bound states: e.g. • reactions, some of astrophysical interest: e.g. Hammer + v.K., in progress c.f. Bedaque, Hammer + v.K. ’99 but Borromean! c.f. Chen et al. ’00 new, systematic approach to physics near d r i p lines U. van Kolck, EFTs of Light Nuclei

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