1. The nucleon-nucleon interaction in the chiral expansion
up to sixth order
in the chiral expansion
R. Machleidt
University of Idaho 1

2. Support by the US Department of Energy (DOE)
Co-workers
N. Kaiser, Technical University of Munich
D. Entem, University of Salamanca, Spain
Y. Nosyk, University of Idaho
Support by the US Department of Energy (DOE)
is acknowledged.
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

3. Outline Introduction Current status of chiral nuclear forces
Beyond N3LO
Outlook
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

4. R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

5. R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

6. Evaluation of current status.
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 (cf. talk by H. Witala).
Light nuclei: Spectra not perfect.
Intermediate nuclei: Overbinding.
Convergence of the chiral expansion in the many-body system? Not converged at N3LO (cf. plenary talk by F. Sammarruca).
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

7. What can we expect from N4LO?
Because of the problems just pointed out, improvement of current nuclear forces is called for.
How?
Go to next order!
That is: Turn to N4LO.
What can we expect from N4LO?
Does N4LO have anything to offer we were not offered before?
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

8. R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

9. 1-loop graphs: 5 topologies
2PE PE-1PE Ring Contact-1PE Contact-2PE
Krebs et al. (2012, 2013)
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

10. 1-loop graphs: 5 topologies
2PE PE-1PE Ring Contact-1PE Contact-2PE
Krebs et al. (2012, 2013)
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

11. Girlanda, Kievsky, Viviani, PRC 84, 014001 (2011)
1-loop graphs: 5 topologies
2PE PE-1PE Ring Contact-1PE Contact-2PE
Krebs et al. (2012, 2013)
3NF contacts
at N4LO
Girlanda, Kievsky, Viviani, PRC 84, (2011)
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

12. Epelbaum et al., Eur. Phys. J. A51, 26 (2015)
All possible 20 isospin-spin-momentum/position structures occur in the 3NF at N3LO!
Epelbaum et al., Eur. Phys. J. A51, 26 (2015)
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

13. R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

14. What can we expect from N4LO?
Because of the problems demonstrated, improvement of current nuclear forces indicated
How?
Go to next order!
That is: Turn to N4LO.
What can we expect from N4LO?
Does N4LO have anything to offer we were not offered before?
Oh yes! All 3NFs you have ever dreamed of!
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

15. What else is there at N4LO?
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

16. R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

17. Entem, Kaiser, Machleidt, Nosyk,
N4LO 2NF
Contributions
Entem, Kaiser, Machleidt, Nosyk,
PRC 91, (2015)
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

18. N4LO effects on NN scattering in peripheral partial waves
From Entem, Kaiser, Machleidt, Nosyk, PRC 91, (2015)
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

19. Using LECs from pi-N Analysis at order four. From Entem, Kaiser,
Machleidt, Nosyk,
PRC 91,
(2015)
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

20. How about convergence? NN up to N5LO CD2015, Pisa, June 30, 2015
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

21. R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

22. Entem, Kaiser, Machleidt, Nosyk,
N5LO 2NF Contributions
Entem, Kaiser, Machleidt, Nosyk,
arXiv: (May 2015)

23. R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

24. R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

25. Convergence at N5LO NN up to N5LO CD2015, Pisa, June 30, 2015
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

26. Conclusions N3LO won’t solve all our problems.
Turn to N4LO: Complete set of 3NFs and new 3NF contacts.
2NF at N4LO very quantitative including the peripheral waves (N4LO NN pots becoming available).
Convergence at N5LO
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

27. Map of Chartered and Unchartered Waters
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

28. Map of Chartered and Unchartered Waters
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015

29. The End
R. Machleidt
NN up to N5LO CD2015, Pisa, June 30, 2015