R. Machleidt, University of Idaho Recent advances in the theory of nuclear forces and its relevance for the microscopic approach to dense matter

Outline Introduction Introduction Historical perspective – Historical perspective – The many-body problem and the nuclear force problem: two very different histories The many-body problem and the nuclear force problem: two very different histories The link between nuclear forces and QCD: chiral effective field theory (EFT) The link between nuclear forces and QCD: chiral effective field theory (EFT) EFT based nuclear forces and results EFT based nuclear forces and results The limitations of chiral EFT and the lasting significance of meson theory The limitations of chiral EFT and the lasting significance of meson theory Conclusions Conclusions R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai,

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Explain the properties of nuclear matter and finite nuclei in terms of the basic forces between the constituents. One of the most fundamental goals of theoretical nuclear physics:

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, This microscopic approach to nuclear structure and reactions, a.k.a. the ab initio approach, has two ingredients Many-body theory/methods Many-body theory/methods “Bare” nuclear forces “Bare” nuclear forces But note: The history of each ingredient is very different.

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Some many-body history

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 6 “Brueckner Theory” ≈1955

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 7 Coupled Cluster Theory ≈1958

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, The fundamental basis for today’s many- body methods was provided already 50 years ago. “The nuclear force” 50 years ago: Gammel- Thaler potential Only since ≈ A.D quantitative nuclear forces derived on fundamental grounds have been developed.

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, 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). 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. Fundamental approaches were either not fundamental or not quantitative. In short: In short: The more quantitative, the less fundamental. The more quantitative, the less fundamental. The more fundamental, the less quantitative. The more fundamental, the less quantitative.

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Therefore, we need … a fundamental approach that produces a quantitative description of the nuclear force. a fundamental approach that produces a quantitative description of the nuclear force. A fundamental approach must necessarily be based upon QCD. A fundamental approach must necessarily be based upon QCD.

The chiral effective field theory approach to nuclear forces Clear connection to QCD: via symmetries Clear connection to QCD: via symmetries Degrees of freedom relevant to (low- energy) nuclear physics: pions and nucleons Degrees of freedom relevant to (low- energy) nuclear physics: pions and nucleons Systematic expansion: Q/Λ Systematic expansion: Q/Λ Controlled error, predictive power. Controlled error, predictive power. Explains the empirically known hierarchy of nuclear forces Explains the empirically known hierarchy of nuclear forces R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai,

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 12 2N forces 3N forces4N forces Leading Order Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order Next-to Leading Order The Hierarchy of Nuclear Forces

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, The Hierarchy of Nuclear Forces 2N forces Leading Order Next-to Leading Order Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Phase shifts up to 300 MeV Red Line: N3LO Potential by Entem & Machleidt, PRC 68, (2003). Green dashed line: NNLO Potential, and blue dotted line: NLO Potential by Epelbaum et al., Eur. Phys. J. A19, 401 (2004).

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 15 N3LO Potential by Entem & Machleidt, PRC 68, (2003). NNLO and NLO Potentials by Epelbaum et al., Eur. Phys. J. A19, 401 (2004).

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, The Hierarchy of Nuclear Forces 2N forces Leading Order Next-to Leading Order Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order 4N forces

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 17 4NF at N3LO (leading order) Essentially negligible, as to be expected.

Interim summary 2NF o.k. 2NF o.k. 4NF (negligibly) small … 4NF (negligibly) small … R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai,

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, NF The Hierarchy of Nuclear Forces 2N forces 3N forces Leading Order Next-to Leading Order Next-to- Next-to Leading Order Next-to- Next-to- Next-to Leading Order The focus: The 3NF 4N forces

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Three-nucleon forces at N2LO TPE-3NF OPE-3NF Contact- 3NF No new parameters! One new parameter, D. 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.

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 21 Results from applications of chiral nuclear forces Nuclear matter in the Brueckner pair approximation Nuclear matter in the Brueckner pair approximation Ground state of finite nuclei with A≤48 using Coupled Cluster theory Ground state of finite nuclei with A≤48 using Coupled Cluster theory Spectra of light nuclei using the no-core shell model Spectra of light nuclei using the no-core shell model

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Nuclear matter [from Bogner et al. (2009)]

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 23 Chiral NN potential at N 3 LO underbinds by ~1MeV/nucleon. (Size extensivity at its best.) Nucleus  E / A [MeV] 4 He1.08 (0.73 FY ) 16 O Ca Ca Ni1.21

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 24 Calculating the properties of light nuclei using chiral 2N and 3N forces 2N (N3LO) +3N (N2LO) forces “No-Core Shell Model “ Calculations by P. Navratil et al., LLNL 2N (N3LO) force only

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, How does the chiral EFT approach To nuclear forces compare To the conventional approach (Meson Theory)?

OPE R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 26 ChPT Conventional meson theory TPE Short range “Contacts”

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, What are contact terms? Contact terms take care of the short range contributions. Consider the contribution from the exchange of a heavy meson ++ +…+…

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, OPE R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt 28 ChPT Conventional meson theory TPE Short range σ ρ “Contacts”

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Question: When everything is so equivalent to conventional meson theory, why not just use conventional meson theory? Answer: In ChPT, there is an organizational scheme (“power counting”) that allows to estimate the size of the various contributions and the error. This applies also to contributions from many-body forces. In conventional meson theory, we don’t have this.

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, However, there is a “However”!

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Phase shifts up to 300 MeV Red Line: N3LO Potential by Entem & Machleidt, PRC 68, (2003). Green dashed line: NNLO Potential, and blue dotted line: NLO Potential by Epelbaum et al., Eur. Phys. J. A19, 401 (2004).

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, red = Idaho N3LO, green = Juelich N3LO, black = CD-Bonn

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, pp TOTAL CROSS SECTIONS LOW INTER- MEDIATE HIGH ChPT Meson land pQCD

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, INTERMEDIATE ENERGIES above about 0.4 MeV Too high for ChPT Too high for ChPT Too low for perturbative QCD (pQCD) Too low for perturbative QCD (pQCD) Lattice QCD Lattice QCD … not very practical … not very practical But there is a well-established model – But there is a well-established model – the relativistic meson model the relativistic meson model

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, Conclusions

R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai, After 70 years of struggle, we have now a proper theory of nuclear forces that is based upon the fundamental theory of strong interactions, QCD. It is chiral effective field theory in which the pion plays a fundamental role. Thus, the original Yukawa idea of just ONE MESON which makes the nuclear force is re- instated, but with some refinements (chiral symmetry). The circle of history is closing. After 70 years of struggle, we have now a proper theory of nuclear forces that is based upon the fundamental theory of strong interactions, QCD. It is chiral effective field theory in which the pion plays a fundamental role. Thus, the original Yukawa idea of just ONE MESON which makes the nuclear force is re- instated, but with some refinements (chiral symmetry). The circle of history is closing. Based upon chiral perturbation theory (ChPT), quantitative NN potentials have been successfully developed and are available for nuclear structure applications. Based upon chiral perturbation theory (ChPT), quantitative NN potentials have been successfully developed and are available for nuclear structure applications. In ChPT, two- and many-body forces are generated on an equal footing. Many-body forces are predicted to be much smaller than two-body forces, consistent with experience. In ChPT, two- and many-body forces are generated on an equal footing. Many-body forces are predicted to be much smaller than two-body forces, consistent with experience. The theory is fundamental AND quantitative! The theory is fundamental AND quantitative! A new era of microscopic nuclear structure has started. A new era of microscopic nuclear structure has started.

However.. Chiral EFT is a LOW-ENERGY theory, restricted to momenta below ≈ 400 MeV/c Chiral EFT is a LOW-ENERGY theory, restricted to momenta below ≈ 400 MeV/c O.k. for normal nuclear densities. O.k. for normal nuclear densities. Too low for dense matter. Too low for dense matter. At intermediate energies “meson theory” remains the only valid model. At intermediate energies “meson theory” remains the only valid model. R. Machleidt Theory of Nuclear Forces... IWND09, Shanghai,