5/20/2015v. Kolck, Halo EFT1 Background by S. Hossenfelder Halo Effective Field Theory U. van Kolck University of Arizona Supported in part by US DOE

5/20/2015v. Kolck, Halo EFT2 Hnning

5/20/2015v. Kolck, Halo EFT3 Outline  EFT  Nucleon-alpha system  Alpha-alpha system  Other systems  Outlook

5/20/2015v. Kolck, Halo EFT4 Nuclear physics scales expansion in perturbative QCD ~1 GeV ~100 MeV hadronic theory Chiral EFT unknown; use brute force (lattice, …) no small coupling constants!

5/20/2015v. Kolck, Halo EFT5 triplet scattering length Deuteron binding energy Fukugita et al. ‘95 Lattice QCD: quenched EFT: (incomplete) NLO Beane, Bedaque, Savage + v.K. ’02 … Large deuteron size because cf. Beane et al ‘06 unitarity limit New scale

5/20/2015v. Kolck, Halo EFT6 Nuclear physics scales expansion in perturbative QCD ~1 GeV ~100 MeV ~30 MeV hadronic theory Contact EFT Chiral EFT unknown; use brute force (lattice, …) no small coupling constants!

5/20/2015v. Kolck, Halo EFT7 Expansion in powers of distance scale of underlying distribution distance scale of interest All possible interactions allowed by gauge invariance

5/20/2015v. Kolck, Halo EFT8 pionless EFT degrees of freedom: nucleons symmetries: Lorentz, B, P, T expansion in: multipole non-relativistic simplest formulation: auxiliary field for two-nucleon bound states Kaplan ’97 v.K. ’99 sign omitting spin, isospin sign

5/20/2015v. Kolck, Halo EFT9 First orders apply also to atoms from 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 Bedaque, Hammer + vK ’98, ’99, ‘00 Hammer, Platter + Meissner ’04 Stetcu, Barrett + v.K. ’07 … - many-body systems get complicated rapidly, just as for models

5/20/2015v. Kolck, Halo EFT10 Halo/Cluster states loosely bound nucleons around tightly bound cores new scale leads to proliferation of shallow states (near driplines): separation energy core excitation energy p n n n p p p n n p core

5/20/2015v. Kolck, Halo EFT11 resonance at e.g. resonance at bound state at resonance at bound state at resonance at

5/20/2015v. Kolck, Halo EFT12 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.

5/20/2015v. Kolck, Halo EFT13 Bertulani, Hammer + v.K. ’02 Bedaque, Hammer + v.K. ’03 spin transition operator

5/20/2015v. Kolck, Halo EFT14 = + + … = reduced mass resonance at andif + + … = width

5/20/2015v. Kolck, Halo EFT15 other waves: + + … =

5/20/2015v. Kolck, Halo EFT16 etc.

5/20/2015v. Kolck, Halo EFT17 Bedaque, Hammer + v.K. ’03 Haesner et al. ‘83 NNDC, BNL

5/20/2015v. Kolck, Halo EFT18 except atwhere ++ …= enhanced byresum self-energy

5/20/2015v. Kolck, Halo EFT19 Bertulani, Hammer + v.K. ’02 Haesner et al. ‘83 NNDC, BNL

5/20/2015v. Kolck, Halo EFT20 Bertulani, Hammer + v.K. ’02 PSA, Arndt et al. ’73 scatt length only

5/20/2015v. Kolck, Halo EFT21 Arndt et al ‘73 cf. consistent…

5/20/2015v. Kolck, Halo EFT22 + electromagnetic interactions Coulomb Sommerfeld parameter corrections transverse photons Higa, Bertulani + v.K. in progress = … =+ non-perturbative for

5/20/2015v. Kolck, Halo EFT23 = Coulomb phase shift = + pure Coulomb Coulomb/short-range interference = + + … =

5/20/2015v. Kolck, Halo EFT24 Higa, Hammer + v.K. ’08 deep non-perturbative Coulomb region! Sommerfeld factor = Landau-Smorodinsky function Coulomb-corrected phase shift

5/20/2015v. Kolck, Halo EFT … = unitarity limit in LO : renorm scale “usual” fine-tuning?

5/20/ since Coulomb “short-ranged” + + … = exponentially suppressed

5/20/2015v. Kolck, Halo EFT27 Expansion around pole: exponential suppression

5/20/2015v. Kolck, Halo EFT28 Higa, Hammer + v.K. ‘08 fitted with Extra fitting parameters none Wuestenbecker et al. ‘92 ‘69

5/20/2015v. Kolck, Halo EFT29 Rasche ‘67 Higa, Hammer + v.K. ‘08 cf. consistent… fine-tuning of 1 in 10! but also,

5/20/2015v. Kolck, Halo EFT30 naturalness Fine-tuning of 1 in a 1000 between strong and electromagnetic interactions!! Higa, Hammer + v.K. ‘08 previous fine-tuning Extra fine-tuning of 1 in 100! Rasche ‘67

5/20/2015v. Kolck, Halo EFT31 Next: three-body states Rotureau + v.K., in progress Main issue: three-body force in LO? cf. in pionless EFT Bedaque, Hammer + v.K., ‘98 Ando + Birse, ’10 Koenig + Hammer, ‘11 : yes (preliminary)

5/20/2015v. Kolck, Halo EFT32 Other cores Rupak + Higa, ’11 Fernando, Higa + Rupak, in preparation cf. in pionless EFT Chen, Rupak + Savage, ’99 Rupak, ‘00 other s-, p-wave parameters fit to scattering data, binding energy one-parameter fit Goal: field included for excited core state

5/20/2015v. Kolck, Halo EFT33 Hammer + Phillips, ‘11 Coulomb dissociation of 11Be s-, p-wave parameters fit to binding energies, B(E1) transition strength

5/20/2015v. Kolck, Halo EFT34 Canham + Hammer, ’08, ’10 with spin 0 s-wave interaction at least one Efimov state (negative energies: virtual states)

5/20/2015v. Kolck, Halo EFT35 Forecast QCD Pionful EFT lattice Pionless EFT Halo/cluster EFT Extrapolates to realistically small Low-energy reactions SM Extrapolate to larger and larger NCSM, … Faddeev* eqs, …