R. Machleidt University of Idaho Current status & current - - PowerPoint PPT Presentation
2017 ICNT Program at FRIB, FRIB-MSU, East Lansing, Michigan, March 22 April 12, 2017 R. Machleidt University of Idaho Current status & current issues How to address the open issues? Consistent interactions up to N4LO Keeping
University of Idaho
2017 ICNT Program at FRIB, FRIB-MSU, East Lansing, Michigan, March 22 – April 12, 2017
§Current status & current issues §How to address the open issues? §Consistent interactions up to N4LO §Keeping the error budget low §Conclusions
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hadrons.
van der Waals forces)
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soft scale: Q ≈ mπ , hard scale: Λχ ≈ mρ ; pions and nucleons are relevant d.o.f.
with ν bounded from below.
symmetries of low-energy QCD, particularly, chiral symmetry which is spontaneously broken.
(i) NN potential perturbatively (ii) apply nonpert. in LS equation. (Weinberg)
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Chiral nuclear forces PKU-CUSTIPEN, August 2, 2015
§ There has been some success (ground state of 10B, drip
lines, nuclear matter saturation, orbit evolution, etc.), but some persistent problems remain.
§ In the few-body sector: Ay puzzle, N-d break-up, …
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N4LO TRIUMF, Feb. 18, 2015 10
N-d Ay calculations by Witala et al.
2N (N3LO) force only
2N (N3LO) +3N (N3LO) forces
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§ Current status: 2NFs and 3NFs up to N3LO are applied in
nuclear few- and many-body systems.
§ In general, quite a bit of success, but some persistent
problems remain.
§ In the few-body sector: Ay puzzle, N-d break-up, … § Light nuclei: Spectra not perfect.
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From Roth
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§ Current status: 2NFs and 3NFs up to N3LO are applied in
nuclear few- and many-body systems.
§ In general, quite a bit of success, but some persistent
problems remain.
§ In the few-body sector: Ay puzzle, N-d break-up, … § Light nuclei: Spectra not perfect. § The radii of nuclei
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NNLO_sat N3LO
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§ Current status: 2NFs and 3NFs up to N3LO are applied in
nuclear few- and many-body systems.
§ In general, quite a bit of success, but some persistent
problems remain.
§ In the few-body sector: Ay puzzle, N-d break-up, … § Light nuclei: Spectra not perfect. § The radii of nuclei § Overbinding of intermediate-mass nuclei
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From Hergert et al., PRC 90, 041302 (2014).
Oxygen Calcium
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From Hergert
Oxygen
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§ Current status: 2NFs and 3NFs up to N3LO are applied in
nuclear few- and many-body systems.
§ In general, quite a bit of success, but some persistent
problems remain.
§ In the few-body sector: Ay puzzle, N-d break-up, … § Light nuclei: Spectra not perfect. § The radii of nuclei § Overbinding of intermediate-mass nuclei § Convergence of the chiral expansion in the many-body
system
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Chiral nuclear forces PKU-CUSTIPEN, August 2, 2015
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Ekstroem et al., 2013+ Carlsson et al., 2016 NNLOopt NNLOsat NNLOsep NNLOsim
Piarulli et al., 2015+ Local potentials.
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Chiral nuclear forces PKU-CUSTIPEN, August 2, 2015
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1-loop graphs: 5 topologies
2PE 2PE-1PE Ring Contact-1PE Contact-2PE
Krebs et al. (2012, 2013)
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1-loop graphs: 5 topologies
2PE 2PE-1PE Ring Contact-1PE Contact-2PE
Krebs et al. (2012, 2013)
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1-loop graphs: 5 topologies
2PE 2PE-1PE Ring Contact-1PE Contact-2PE
Krebs et al. (2012, 2013)
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1-loop graphs: 5 topologies
2PE 2PE-1PE Ring Contact-1PE Contact-2PE
Krebs et al. (2012, 2013)
3NF contacts at N4LO
Girlanda, Kievsky, Viviani, PRC 84, 014001 (2011)
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1-loop graphs: 5 topologies
2PE 2PE-1PE Ring Contact-1PE Contact-2PE
Krebs et al. (2012, 2013)
3NF contacts at N4LO
Girlanda, Kievsky, Viviani, PRC 84, 014001 (2011)
All possible 20 isospin-spin-momentum/position structures occur in the 3NF at N4LO!
Epelbaum et al., Eur. Phys. J. A51, 26 (2015)
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N4LO 2NF Contributions
Entem, Kaiser, Machleidt, Nosyk, PRC 91, 014002 (2015)
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Entem, Kaiser, Machleidt, Nosyk, arXiv:1505.03562 (May 2015)
Entem, Kaiser, Machleidt, Nosyk, PRC 92, 064001 (2015)
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From Entem, Kaiser, Machleidt, Nosyk, PRC 91, 014002 (2015)
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Converged at N4LO
From Entem, Kaiser, Machleidt, Nosyk, PRC 92, 064001 (2015)
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And that first and above all requires High-quality NN potentials, Constructed consistently through all orders.
§ Use π-N LECs determined in π-N analysis with the
highest possible precision: Roy-Steiner Analysis (Hoferichter et al., PRL 115, 192301 (2015)).
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§ Set of coupled partial-wave dispersion relations
constraint by analyticity, unitarity, and crossing symmetry.
§ Additional crucial constraint: High-accuracy π-N
scattering lengths extracted from pionic atoms.
§ Matching to π-N LECs done in the subthreshold region,
which is best for nuclear forces.
§ Comprehensive error analysis. § Small errors.
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(Hoferichter et al., PRL 115, 192301 (2015))
Very small errors!
§ One had to assume that, e.g., c3 ≅ 3.4 – 6.0 § Leading to a huge uncertainty for the 3NF
contribution.
§ Inconsistency with c3 used in the NN interaction. § This is all over now! § Uncertainty of the NN interaction due to the
uncertainty in ci’s absolutely negligible.
§ Uncertainty of the 3NF contribution due to the
uncertainty in ci’s : negligible as compared to truncation error.
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§ Use π-N LECs determined in π-N analysis with the
highest possible precision: Roy-Steiner Analysis (Hoferichter et al., PRL 115, 192301 (2015)).
§ NN potentials are fit to NN data (and not to phase
shifts) using all NN data below pion production threshold published up to December 2016.
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(Includes ct’s In F-waves.)
2016 NN data base
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Reproduction of the NN Data
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40 80 120 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
1S0
20 40 60 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
3P0
10 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
1P1
10 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
3P1
100 200 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
3S1
10 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
3D1
5 10 Mixing Parameter (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
ε1
5 10 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
1D2
10 20 30 40 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
3D2
10 20 30 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
3P2
Mixing Parameter (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
ε2
4 8 Phase Shift (deg) 100 200 300 400
LO NLO NNLO N3LO N4LO
3D3
Neutron-Proton Phase Shifts
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2.5 5 Mixing Parameter (deg) 100 200 300 400
450 500 550
ε1
5 10 Phase Shift (deg) 100 200 300 400
450 500 550
1D2
10 20 30 40 Phase Shift (deg) 100 200 300 400
450 500 550
3D2
5 10 15 20 Phase Shift (deg) 100 200 300 400
450 500 550
3P2
Mixing Parameter (deg) 100 200 300 400
450 500 550
ε2
2.5 5 7.5 Phase Shift (deg) 100 200 300 400
450 500 550
3D3
2 4 6 Mixing Parameter (deg) 100 200 300 400
450 500 550
ε1
4 8 12 16 Phase Shift (deg) 100 200 300 400
450 500 550
1D2
10 20 30 40 Phase Shift (deg) 100 200 300 400
450 500 550
3D2
10 20 Phase Shift (deg) 100 200 300 400
450 500 550
3P2
1 Mixing Parameter (deg) 100 200 300 400
450 500 550
ε2
2 4 6 8 Phase Shift (deg) 100 200 300 400
450 500 550
3D3
Cutoff Variations NNLO N4LO
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The Potentials are non-local and soft
§ Concerning the ab initio explanation of intermediate and heavy
nuclei we are faced with tough issues.
§ But, let’s not (yet) give up on the systematic use of chiral EFT. § This requires order-by-order calculations up to N4LO using
consistent 2NF and 3NF (and 4NF).
§ For this purpose, we have constructed a family of NN
potentials that keeps the error budget as low as possible: Essentially no uncertainties in the π-N LECs (Roy-Steiner!), Accurate fit to the 2016 NN data base (≅5000 data).
§ The NN potentials are relatively soft and require less 3NF as
compared to some other chiral NN potentials that are floating around (like, locals, “semi-locals”).
§ Systematic calculations with different families of chiral
interactions may hopefully give us clues for how to solve the remaining problems.
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But, one farther day,
will come. Be patient.