The theory of nuclear forces: Is the never-ending ending story coming to an end? R. Machleidt University of Idaho

The theory of nuclear forces: Is the never-ending ending story coming to an end? University of Idaho

What s left to say? Put the recent progress into a wider perspective. Fill in some missing details. Draw a general balance. 2

Outline Historical perspective ChPT: : What order? NN potentials at N3LO The LECs and NN Results from applications in few- and many-body problems Conclusions and outlook 3

History of Nuclear Forces: Phase I 1930 s The first pion period Chadwick (1932): Neutron Heisenberg (1932): First Phenomenology (Isospin) Yukawa (1935): Meson Hypothesis 1940 s 1950 s Pion Theories Discovery of the pion in cosmic ray (1947) and in the Berkeley Cyclotron Lab (1948). Nobel prize awarded to Yukawa (1949). In analogy to Quantum-Electro-Dynamics (QED) which uses the gamma, construct a Quantum Field Theory for the nuclear force which uses the pion. The first pion period: One-Pion-Exchange (OPE): o.k. Multi-pion exchanges: Disaster! results in a disaster 4

Phase II: The meson period 1960 s Heavy mesons are discovered: σ ( 600), ρ(770), ω(782)... Many pions = multi-pion resonances: One-Boson-Exchange Model: Great success! Refined Meson Theories 1970 s Sophisticated models for two-pion exchange: Paris Potential (Lacombe et al., PRC 21, 861 (1980)) Bonn potential (Machleidt et al., Phys. Rep. 149, 1 (1987)) 5

The exponential tail of phase II (or the epigone period of meson theory) 1980 s Nijmegen: We need more precision!!! A χ²/dat 2 is not good enough, it has to be 1.0 1993: The high-precision Nijmegen phase shift analysis 1990 s 1994-2001: High-precision NN potentials: Nijmegen I, II, 93, Reid93 (Stoks et al. 1994) Argonne V18 (Wiringa et al, 1995) CD-Bonn (Machleidt et al. 1996, 2001) All have χ²/dat 1. 6

The CRUX of NN potential development up to about 2000 There are many quantitative NN potentials which are, however, not fundamental (the latest are the high- precision potentials developed in the 1990s). Fundamental approaches were either not fundamental or not quantitative. In short: The more quantitative, the less fundamental. The more fundamental, the less quantitative. 7

We need a fundamental approach that produces a quantitative description of the nuclear force. A fundamental approach must necessarily be based upon QCD. 8

Phase III: The QCD/EFT period 1980 s Nijmegen: Nuclear physicists We need discover more precision!!! QCD: Quark cluster models. 1990 s 1993: Nuclear The physicists high-precision discover Nijmegen Effective phase shift Field analysis Theory (EFT): 1994-2001: High-precision NN potentials: Weinberg (1990); Ordonez, Ray, van Kolck Nijmegen I, II, 93, Reid93; (1994/96). - 2006 Argonne V18; Another pion theory ; but now right: constrained CD-Bonn. by chiral symmetry The second pion period: No disaster! 9

Main milestones for NN potential development in chiral perturbation theory (ChPT( ChPT) 1994/96: v. Kolck and co-workers, first ChPT based NN potential at N2LO using cutoff regularization (r-space) 1994-1997: 1997: - Robilotta and co-workers, 2-pi 2 at N2LO - 1997: Kaiser et al., 2-pi 2 at N2LO using HBChPT and DR 2000: Epelbaum et al. ( Bochum Bochum-Juelich group), NN potential in momentum space at N2LO (HBChPT( HBChPT,, DR) 2003: - Robilotta and co-workers 2-pi 2 at N3LO in RBChPT - Entem & Machleidt ( Idaho group), first NN potential at N3LO (HBChPT,, DR) 2005: Epelbaum et al. ( Bochum Bochum-Juelich group), NN potential at N3LO (HBChPT,, SFR) 10

The orders of ChPT are 0 Leading order (LO), Q Next-to to-leading order (NLO), 2 Q 3 Next-to to-next-to-leading order (NNLO), Q Next-to to-next-to-next-to-leading order (N3LO), Q 4 11

2N forces 3N forces 4N forces Leading Order Next-to Leading Order The Hierarchy of Nuclear Forces Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order 12

What order do we need for sufficient precision? 13

Believe it or not, in answering this question, the epigonic high-precision potentials of the 1990 s can help us here. 14

How many parameters do we need? 15

Conclusion: At least, N3LO is needed Entem & Machleidt, PLB 524, 93 (2002) 17

np phase shifts: red = Idaho, green = Bochum/Juelich, black = CD-Bonn 20

Conclusion: Fitting phase shifts is not good enough. You have to make a direct comparison with the NN data. 21

Deuteron wave functions of N3LO potentials red = Idaho, green = Bochum/Juelich Black lines = high-precision pots. 23

The Low Energy Constants (LECs) 24

(2) : L πn (3) : L πn All the same 25

Perturbative amplitude at N2LO using c_3 = - 4.78 Nijmegen: N2LO 2-pi r-space potential cutoff at r = 1.6 fm using c_3 = - 4.78 26

(2) : L πn (3) : L πn All the same 27

Results from applications of the Idaho N3LO Potential in microscopic nuclear structure calculations 28

relative to the closest doubly magic core. 30

Calculating the properties of light nuclei using chiral 2N and 3N forces No-Core Shell Model Calculations by P. Navratil et al., LLNL 2N (N3LO) +3N (N2LO) forces 2N (N3LO) force only 31

Microscopic nuclear structure, cont d No-Core Shell Model Calculations by P. Navratil et al., LLNL 2N (N3LO) +3N (N2LO) 2N (N3LO) force only forces 32

Summary Chiral EFT IS fundamental (QCD based) and quantitative. At N3LO, some accurate NN potentials have been developed (but, watch it, not all N3LO pots. are accurate!). Two- and many-forces are created on an equal footing. Current results in nuclear structure including the 3NF at N2LO are encouraging (however, the N-d N A_y puzzle is not solved!). 33

Open issues, problems The 3NF at N3LO: Will it solve the N-d N A_y puzzle,, will it further improve the spectra of light nuclei,? Do we need to go to N4LO, N5LO,? - Not necessary for NN and if, then we have to go to N5LO - to get more contacts. Contacts at N5LO no problem, but the 2-pi, 2 3-pi, 3 and 4-pi 4 contributions will be a nightmare! 34

Illinois 3NFs N4LO and N5LO (in a theory w/o explicit Deltas) N2LO 3NFs 37

The never-ending story is converging 39

The End 40