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Nuclear Forces from Chiral EFT: The Unresolved Issues

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Abstract

In recent years, there has been substantial progress in the derivation of nuclear forces from chiral effective field theory (EFT). Accurate two-nucleon forces have been constructed at next-to-next-to-next-to-leading order (N3LO) and applied (together with three-nucleon forces at NNLO) to nuclear few- and many-body systems—with a good deal of success. This may suggest that the 80-year old nuclear force problem has finally been cracked. Not so! Some pretty basic issues are still unresolved. In this talk, I focus on the two most pressing ones, namely, subleading many-body forces and the proper renormalization of the two-nucleon potential.

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References

  1. Machleidt R.: The Meson theory of nuclear forces and nuclear structure. Adv. Nucl. Phys. 19, 189 (1989)

    Google Scholar 

  2. Weinberg S.: Phenomenological Lagrangians. Physica 96A, 327 (1979)

    ADS  Google Scholar 

  3. Gasser J., Leutwyler H.: Chiral perturbation theory to one loop. Ann. Phys. (N.Y.) 158, 142 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  4. Gasser J., Sainio M.E., Švarc A.: Nucleons with chiral Loops. Nucl. Phys. B 307, 779 (1988)

    Article  ADS  Google Scholar 

  5. Weinberg S.: Nuclear forces from chiral Lagrangians. Phys. Lett. B 251, 288 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  6. Weinberg S.: Effective chiral Lagrangians for nucleon–pion interactions and nuclear forces. Nucl. Phys. B 363, 3 (1991)

    Article  ADS  Google Scholar 

  7. Weinberg S.: Three-body interactions among nucleons and pions. Phys. Lett. B 295, 114 (1992)

    Article  ADS  Google Scholar 

  8. Ordóñez C., Ray L., van Kolck U.: Nucleon–nucleon potential from an effective chiral Lagrangian. Phys. Rev. Lett. 72, 1982 (1994)

    Article  ADS  Google Scholar 

  9. Ordóñez C., Ray L., van Kolck U.: Two-nucleon potential from chiral Lagrangians. Phys. Rev. C 53, 2086 (1996)

    Article  ADS  Google Scholar 

  10. van Kolck U.: Few-nucleon forces from chiral Lagrangians. Phys. Rev. C 49, 2932 (1994)

    Article  ADS  Google Scholar 

  11. van Kolck U.: Effective field theory of nuclear forces. Prog. Part. Nucl. Phys. 43, 337 (1999)

    Article  ADS  Google Scholar 

  12. Kaiser N., Brockmann R., Weise W.: Peripheral nucleon–nucleon phase shifts and chiral symmetry. Nucl. Phys. A 625, 758 (1997)

    Article  ADS  Google Scholar 

  13. Kaiser N., Gerstendörfer S., Weise W.: Peripheral NN-scattering: role of delta-excitation, correlated two-pion and vector meson exchange. Nucl. Phys. A 637, 395 (1998)

    Article  ADS  Google Scholar 

  14. Epelbaum E., Glöckle W., Meißner U.-G.: Nuclear forces from chiral Lagrangians using the method of unitary transformations (I): Formalism. Nucl. Phys. A 637, 107 (1998)

    Article  ADS  Google Scholar 

  15. Epelbaum E., Glöckle W., Meißner U.-G.: Nuclear forces from chiral Lagrangians using the method of unitary transformations (II): the two-nucleon system. Nucl. Phys. A 671, 295 (2000)

    Article  ADS  Google Scholar 

  16. Bedaque P.F., van Kolck U.: Effective field theory for few-nucleon systems. Ann. Rev. Nucl. Part. Sci. 52, 339 (2002)

    Article  ADS  Google Scholar 

  17. Entem D.R., Machleidt R.: Accurate nucleon–nucleon potential based upon chiral perturbation theory. Phys. Lett. B 524, 93 (2002)

    Article  ADS  Google Scholar 

  18. Entem D.R., Machleidt R.: Chiral 2π exchange at fourth order and peripheral NN scattering. Phys. Rev. C 66, 014002 (2002)

    Article  ADS  Google Scholar 

  19. Entem D.R., Machleidt R.: Accurate charge-dependent nucleon–nucleon potential at fourth order of chiral perturbation theory. Phys. Rev. C 68, 041001 (2003)

    Article  ADS  Google Scholar 

  20. Machleidt R., Entem D.R.: Towards a consistent approach to nuclear structure: EFT of two- and many-body forces. J. Phys. G: Nucl. Part. Phys. 31, S1235 (2005)

    Article  ADS  Google Scholar 

  21. Epelbaum E., Glöckle W., Meißner U.-G.: The two-nucleon system at next-to-next-to-next-to-leading order. Nucl. Phys. A 747, 362 (2005)

    Article  ADS  Google Scholar 

  22. Machleidt, R.: Nuclear forces from chiral effective field theory. arXiv:0704.0807 [nucl-th]

  23. Machleidt R., Entem D.R.: Nuclear forces from chiral EFT: the unfinished business. J. Phys. G: Nucl. Part. Phys. 37, 064041 (2010)

    Article  ADS  Google Scholar 

  24. Machleidt R., Holinde K., Elster Ch.: The Bonn Meson-exchange model for The nucleon–nucleon interaction. Phys. Rep. 149, 1 (1987)

    Article  Google Scholar 

  25. Weinberg, S.: Effective field theory, past and future. arXiv:0908.1964 [hep-th]

  26. Kaplan D.B., Savage M.J., Wise M.B.: Nucleon–nucleon scattering from effective field theory. Nucl. Phys. B 478, 629 (1996)

    Article  ADS  Google Scholar 

  27. Kaplan D.B., Savage M.J., Wise M.B.: A new expansion for nucleon–nucleon interactions. Phys. Lett. B 424, 390 (1998)

    Article  ADS  Google Scholar 

  28. Kaplan D.B., Savage M.J., Wise M.B.: Two-nucleon system from effective field theory. Nucl. Phys. B 534, 329 (1998)

    Article  ADS  Google Scholar 

  29. Nogga A., Timmermans R.G.E., van Kolck U.: Renormalization of one-pion exchange and power counting. Phys. Rev. C 72, 054006 (2005)

    Article  ADS  Google Scholar 

  30. Yang C.-J., Elster Ch., Phillips D.R.: Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory. Phys. Rev. C 77, 014002 (2008)

    Article  ADS  Google Scholar 

  31. Yang C.-J., Elster Ch., Phillips D.R.: Subtractive renormalization of the chiral potentials up to next-to-next-to-leading order in higher NN partial waves. Phys. Rev. C 80, 034002 (2009)

    Article  ADS  Google Scholar 

  32. Yang C.-J., Elster Ch., Phillips D.R.: Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves. Phys. Rev. C 80, 044002 (2009)

    Article  ADS  Google Scholar 

  33. Pavon Valderrama M., Ruiz Arriola E.: Renormalization of the NN interaction with a chiral two-pion exchange potential. II. Noncentral phases. Phys. Rev. C 74, 064004 (2006)

    Article  ADS  Google Scholar 

  34. Pavon Valderrama M., Ruiz Arriola E.: Erratum. Phys. Rev. C 75, 059905 (2007)

    Article  ADS  Google Scholar 

  35. Entem D.R., Ruiz Arriola E., Pavón Valderrama M., Machleidt R.: Renormalization of chiral two-pion exchange NN interactions: momentum space versus coordinate space. Phys. Rev. C 77, 044006 (2008)

    Article  ADS  Google Scholar 

  36. Long B., van Kolck U.: Renormalization of singular potentials and power counting. Ann. Phys. (N.Y.) 323, 1304 (2008)

    Article  MATH  ADS  Google Scholar 

  37. Valderrama, M.P.: Perturbative Renormalizability of chiral two pion exchange in nucleon–nucleon scattering. arXiv:0912.0699 [nucl-th]

  38. Machleidt R., Liu P., Entem D.R., Arriola E.R.: Renormalization of the leading-order chiral nucleon–nucleon interaction and bulk properties of nuclear matter. Phys. Rev. C 81, 024001 (2010)

    Article  ADS  Google Scholar 

  39. Brandow B.H.: Linked-cluster expansion for the nuclear many-body problem. Rev. Mod. Phys. 39, 771 (1967)

    Article  ADS  Google Scholar 

  40. Day B.D.: Elements of the Brueckner–Goldstone theory of nuclear matter. Rev. Mod. Phys. 39, 719 (1967)

    Article  ADS  Google Scholar 

  41. Bethe H.A.: Theory of nuclear matter. Ann. Rev. Nucl. Sci. 21, 93 (1971)

    Article  ADS  Google Scholar 

  42. Day B.D., Wiringa R.B.: Brueckner-Bethe and variational calculations of nuclear matter. Phys. Rev. C 32, 1057 (1985)

    Article  ADS  Google Scholar 

  43. Lepage, G.P.: How to renormalize the Schrödinger equation. arXiv:nucl-th/9706029

  44. Epelbaum E. et al.: Three-nucleon forces from chiral effective field theory. Phys. Rev. C 66, 064001 (2002)

    Article  ADS  Google Scholar 

  45. Epelbaum E.: Four-nucleon force in chiral effective field theory. Phys. Lett. B 639, 456 (2006)

    Article  ADS  Google Scholar 

  46. Epelbaum E.: Four-nucleon force using the method of unitary transformation. Eur. Phys. J. A 34, 197 (2007)

    Article  ADS  Google Scholar 

  47. Rozpedzik D. et al.: A first estimation of chiral four-nucleon force effects in 4He. Acta Phys. Polon. B 37, 2889 (2006)

    ADS  Google Scholar 

  48. Yang S.N., Glöckle W.: Three-body mesonic retardation effects. Phys. Rev. C 33, 1774 (1986)

    Article  ADS  Google Scholar 

  49. Coon S.A., Friar J.L.: Retardation effects in two-pion-exchange three-nucleon forces. Phys. Rev. C 34, 1060 (1986)

    Article  ADS  Google Scholar 

  50. Kalantar-Nayestanaki, N., et al.: The three-nucleon system as a laboratory for nuclear physics: the need for 3N forces. Nucl. Phys. News 17, 22 (2007). arXiv:nucl-th/0703089; and references therein

    Google Scholar 

  51. Viviani M., Kievsky A., Girlanda L.E., Marcucci L., Rosati S.: Neutron–triton elastic scattering. Few Body Syst. 45, 119 (2009)

    Article  ADS  Google Scholar 

  52. Marcucci L.E., Kievsky A., Girlanda L., Rosati S., Viviani M.: N-d elastic scattering using the hyperspherical harmonics approach with realistic local and nonlocal interactions. Phys. Rev. C 80, 034003 (2009)

    Article  ADS  Google Scholar 

  53. Navratil P., Gueorguiev V.G., Vary J.P., Ormand W.E., Nogga A.: Structure of A = 10–13 Nuclei with two- plus three-nucleon interactions from chiral effective field theory. Phys. Rev. Lett. 99, 042501 (2007)

    Article  ADS  Google Scholar 

  54. Hagen G. et al.: Coupled-cluster theory for three-body Hamiltonians. Phys. Rev. C 76, 034302 (2007)

    Article  ADS  Google Scholar 

  55. Otsuka T. et al.: Three-body forces and the limit of oxygen isotopes. Phys. Rev. Lett. 105, 032501 (2010)

    Article  ADS  Google Scholar 

  56. Bogner S.K. et al.: Is nuclear matter perturbative with low-momentum interactions?. Nucl. Phys. A 763, 59 (2005)

    Article  ADS  Google Scholar 

  57. Bogner, S.K., et al.: Nuclear matter from chiral low-momentum interactions. arXiv:0903.3366 [nucl-th]

  58. Hebeler K., Schwenk A.: Chiral three-nucleon forces and neutron matter. Phys. Rev. C 82, 014314 (2010)

    Article  ADS  Google Scholar 

  59. Fisher B.M. et al.: Proton-3He elastic scattering at low energies. Phys. Rev. C 74, 034001 (2006)

    Article  ADS  Google Scholar 

  60. Deltuva A., Fonseca A.C.: Four-body calculation of proton-3He scattering. Phys. Rev. Lett. 98, 162502 (2007)

    Article  ADS  Google Scholar 

  61. Viviani, M., Giarlanda, L., Kievsky, A., Marcucci, L.E., Rosati, S.: Proton-3He elastic scattering at low energies and the “A y Puzzle”. arXiv:1004.1306 [nucl-th]

  62. Ishikawa S., Robilotta M.R.: Two-pion exchange three-nucleon potential: \({\mathcal{O} (q^4)}\) chiral expansion. Phys. Rev. C 76, 014006 (2007)

    Article  ADS  Google Scholar 

  63. Bernard V., Epelbaum E., Krebs H., Meißner U.-G.: Subleading contributions to the chiral three-nucleon force I: long-range terms. Phys. Rev. C 77, 064004 (2008)

    Article  ADS  Google Scholar 

  64. Kaiser N.: Chiral 3π-exchange NN potentials: results for representation-invariant classes of diagrams. Phys. Rev. C 61, 014003 (2000)

    Article  ADS  Google Scholar 

  65. Kaiser N.: Chiral 3π-exchange NN potentials: results for diagrams proportional to \({g_A^4}\) and \({g_A^6}\). Phys. Rev. C 62, 024001 (2000)

    Article  ADS  Google Scholar 

  66. Kaiser N.: Chiral 3π-exchange NN potentials: results for dominant next-to-leading-order contributions. Phys. Rev. C 63, 044010 (2001)

    Article  ADS  Google Scholar 

  67. Pieper S.C. et al.: Realistic models of pion-exchange three-nucleon interactions. Phys. Rev. C 64, 014001 (2001)

    Article  ADS  Google Scholar 

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  1. Department of Physics, University of Idaho, Moscow, ID, 83844, USA

    R. Machleidt

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Machleidt, R. Nuclear Forces from Chiral EFT: The Unresolved Issues. Few-Body Syst 50, 83–89 (2011). https://doi.org/10.1007/s00601-010-0202-9

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