Halo Effective Field Theory

1. Halo Effective Field Theory U. van Kolck University of Arizona Supported in part by US DOE v. Kolck, Halo EFT Background by S. Hossenfelder

2. Hnning v. Kolck, Halo EFT

3. Outline • EFT • Nucleon-alpha system • Alpha-alpha system • Other systems • Outlook v. Kolck, Halo EFT

4. Nuclear physics scales expansion in perturbative QCD unknown; use brute force (lattice, …) ~1 GeV hadronic theory Chiral EFT ~100 MeV no small coupling constants! v. Kolck, Halo EFT

5. Fukugita et al. ‘95 triplet scattering length Lattice QCD: quenched cf. Beane et al ‘06 Beane, Bedaque, Savage + v.K. ’02 … EFT: (incomplete) NLO unitarity limit Deuteron binding energy Large deuteron size because New scale v. Kolck, Halo EFT

6. Nuclear physics scales expansion in perturbative QCD unknown; use brute force (lattice, …) ~1 GeV hadronic theory Chiral EFT ~100 MeV ~30 MeV Contact EFT no small coupling constants! v. Kolck, Halo EFT

7. All possible interactions allowed by gauge invariance Expansion in powers of distance scale of underlying distribution distance scale of interest v. Kolck, Halo EFT

8. pionless EFT • degrees of freedom: nucleons • symmetries: Lorentz, B, P, T • expansion in: non-relativistic multipole Kaplan ’97 v.K. ’99 simplest formulation: auxiliary field for two-nucleon bound states omitting spin, isospin v. Kolck, Halo EFT sign sign

9. Bedaque, Hammer + vK ’98, ’99, ‘00 Hammer, Platter + Meissner ’04 Stetcu, Barrett + v.K. ’07 … • describes structure and reactions of bound states -- deuteron, triton, alpha particle • can be extended to p-shell nuclei with No-Core Shell Model • makes evident new phenomena -- from one-parameter three-body force at LO: SO(4) invariance, limit-cycle behavior, Phillips line, Efimov spectrum First orders apply also to atoms from - many-body systems get complicated rapidly, just as for models v. Kolck, Halo EFT

10. new scale leads to proliferation of shallow states (near driplines): loosely bound nucleons around tightly bound cores core p n n p p n p n Halo/Cluster states p n separation energy core excitation energy v. Kolck, Halo EFT

11. e.g. resonance at resonance at bound state at resonance at resonance at bound state at resonance at resonance at v. Kolck, Halo EFT

12. halo EFT • degrees of freedom: nucleons, cores • symmetries: Lorentz, B, P, T • expansion in: non-relativistic multipole simplest formulation: auxiliary fields for core + nucleon states e.g. v. Kolck, Halo EFT

13. Bertulani, Hammer + v.K. ’02 Bedaque, Hammer + v.K. ’03 spin transition operator v. Kolck, Halo EFT

14. = + + … = reduced mass resonance at if and width = + + … v. Kolck, Halo EFT

15. other waves: = + + … v. Kolck, Halo EFT

16. etc. v. Kolck, Halo EFT

17. Bedaque, Hammer + v.K. ’03 NNDC, BNL Haesner et al. ‘83 v. Kolck, Halo EFT

18. except at where = + + … enhanced by resum self-energy v. Kolck, Halo EFT

19. Bertulani, Hammer + v.K. ’02 NNDC, BNL Haesner et al. ‘83 v. Kolck, Halo EFT

20. Bertulani, Hammer + v.K. ’02 PSA, Arndt et al. ’73 scatt length only v. Kolck, Halo EFT

21. Arndt et al ‘73 cf. consistent… v. Kolck, Halo EFT

22. Higa, Bertulani + v.K. in progress + electromagnetic interactions Sommerfeld parameter Coulomb transverse photons corrections = + + … + = + non-perturbative for v. Kolck, Halo EFT

23. = + pure Coulomb Coulomb/short-range interference Coulomb phase shift = = = + + … v. Kolck, Halo EFT

24. Higa, Hammer + v.K. ’08 deep non-perturbative Coulomb region! Sommerfeld factor = Landau-Smorodinsky function v. Kolck, Halo EFT Coulomb-corrected phase shift

25. = + + … unitarity limit in LO : renorm scale v. Kolck, Halo EFT “usual” fine-tuning?

26. = + + … exponentially suppressed since Coulomb “short-ranged”

27. Expansion around pole: exponential suppression v. Kolck, Halo EFT

28. Higa, Hammer + v.K. ‘08 ‘69 Extra fitting parameters none fitted with Wuestenbecker et al. ‘92 v. Kolck, Halo EFT

29. Higa, Hammer + v.K. ‘08 Rasche ‘67 cf. also, consistent… but fine-tuning of 1 in 10! v. Kolck, Halo EFT

30. Higa, Hammer + v.K. ‘08 Rasche ‘67 previous fine-tuning naturalness Extra fine-tuning of 1 in 100! Fine-tuning of 1 in a 1000 between strong and electromagnetic interactions!! v. Kolck, Halo EFT

31. Rotureau + v.K., in progress Next: three-body states Bedaque, Hammer + v.K., ‘98 Ando + Birse, ’10 Koenig + Hammer, ‘11 cf. in pionless EFT Main issue: three-body force in LO? : yes (preliminary) v. Kolck, Halo EFT

32. Other cores Rupak + Higa, ’11 Fernando, Higa + Rupak, in preparation field included for excited core state cf. in pionless EFT Chen, Rupak + Savage, ’99 Rupak, ‘00 Goal: one-parameter fit other s-, p-wave parameters fit to scattering data, binding energy v. Kolck, Halo EFT

33. Hammer + Phillips, ‘11 Coulomb dissociation of 11Be s-, p-wave parameters fit to binding energies, B(E1) transition strength v. Kolck, Halo EFT

34. Canham + Hammer, ’08, ’10 s-wave interaction with spin 0 at least one Efimov state (negative energies: virtual states) v. Kolck, Halo EFT

35. SM Forecast QCD lattice Extrapolates to realistically small Pionful EFT Faddeev* eqs, … Extrapolate to larger and larger Pionless EFT NCSM, … Halo/cluster EFT Low-energy reactions v. Kolck, Halo EFT