The nucleon-nucleon interaction in the chiral expansion

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

Girlanda, Kievsky, Viviani, PRC 84, 014001 (2011) 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) R. Machleidt NN up to N5LO CD2015, Pisa, June 30, 2015

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

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

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

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

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

Entem, Kaiser, Machleidt, Nosyk, N4LO 2NF Contributions Entem, Kaiser, Machleidt, Nosyk, PRC 91, 014002 (2015) R. Machleidt NN up to N5LO CD2015, Pisa, June 30, 2015

N4LO effects on NN scattering in peripheral partial waves From Entem, Kaiser, Machleidt, Nosyk, PRC 91, 014002 (2015) R. Machleidt NN up to N5LO CD2015, Pisa, June 30, 2015

Using LECs from pi-N Analysis at order four. From Entem, Kaiser, Machleidt, Nosyk, PRC 91, 014002 (2015) R. Machleidt NN up to N5LO CD2015, Pisa, June 30, 2015

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

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

Entem, Kaiser, Machleidt, Nosyk, N5LO 2NF Contributions Entem, Kaiser, Machleidt, Nosyk, arXiv:1505.03562 (May 2015)

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

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

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

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

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

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

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