Nonlocal Chiral Nuclear Forces up to N5LO

  1. Entem, D. R. 1
  2. Machleidt, Ruprecht 2
  3. Nosyk, Y. 2
  1. 1 Grupo de Física Nuclear, IUFFyM, Universidad de Salamanca, Salamanca, Spain
  2. 2 Department of Physics, University of Idaho, Moscow, ID, USA
Book:
Handbook of Nuclear Physics
  1. Tanihata, I. (ed. lit.)
  2. Toki, H. (ed. lit.)
  3. Kajino, T. (ed. lit.)

Publisher: Springer

ISBN: 9789811963445 9789811963452

Year of publication: 2023

Pages: 1879-1912

Type: Book chapter

DOI: 10.1007/978-981-19-6345-2_55 GOOGLE SCHOLAR lock_openOpen access editor

Abstract

During the past two decades, chiral effective field theory (EFT) has evolved into a powerful tool to derive nuclear forces from first principles. This review is started with a pedagogical introduction, and then it is shown in detail how, governed by chiral symmetry, the long- and intermediate-range parts of the NN potential unfold order by order. The expansion proceeds up to sixth order in small momenta, where convergence is achieved. A remarkable point of chiral EFT is that it produces not only two-nucleon forces but also many-body forces on an equal footing with the two-body forces. Therefore, this review finishes with an overview of the systematic development of three- and four-nucleon forces, which play a subtle, but crucial, role in microscopic nuclear structure calculations.

Bibliographic References

  • A. Akmal, V.R. Pandharipande, D.G. Ravenhall, Phys. Rev. C 58, 1804 (1998)
  • B.R. Barrett, P. Navratil, J.P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013)
  • V. Bernard, E. Epelbaum, H. Krebs, Ulf-G. Meißner, Phys. Rev. C 77, 064004 (2008)
  • V. Bernard, E. Epelbaum, H. Krebs, Ulf-G. Meißner, Phys. Rev. C 84, 054001 (2011)
  • S. Binder, J. Langhammer, A. Calci, R. Roth, Phys. Lett. B 736, 119 (2014)
  • M.C. Birse, Phys. Rev. C 74, 014003 (2006); ibid. 76, 034002 (2007); ibid. 77, 047001 (2008); Phil. Trans. Roy. Soc. Lond. A 369, 2662 (2011)
  • R. Blankenbecler, R. Sugar, Phys. Rev. 142, 1051 (1966)
  • W.J. Briscoe, I.I. Strakovsky, R.L. Workman, SAID Partial-Wave Analysis Facility, Data Analysis Center, The George Washington University, Solution SP07 (Spring, 2007)
  • R.A. Bryan, B.L. Scott, Phys. Rev. 1964, 135, B434-B450; ibid. 1969, 177, 1435–1442
  • J. Carlson, V.R. Pandharipande, R.B. Wiringa, Nucl. Phys. A 401, 59 (1983)
  • J. Carlson, S. Gandolfi, F. Pederiva, S.C. Pieper, R. Schiavilla, K.E. Schmidt, R.B. Wiringa, Rev. Mod. Phys. 87, 1067 (2015)
  • B.D. Carlsson et al., Phys. Rev. X 6, 011019 (2016)
  • E. Caurier, P. Navratil, W.E. Ormand, J.P. Vary, Phys. Rev. C 66, 024314 (2002)
  • S. Coleman, J. Wess, B. Zumino, Phys. Rev. 177, 2239 (1969); C.G. Callan, S. Coleman, J. Wess, B. Zumino, ibid. 177, 2247 (1969). 288, 249 (2001)
  • S.A. Coon, H.K. Han, Few Body Syst. 30, 131 (2001)
  • S.A. Coon, M.D. Scadron, P.C. McNamee, B.R. Barrett, D.W.E. Blatt, B.H.J. McKeller, Nucl. Phys. A317, 242 (1979)
  • L. Coraggio, J.W. Holt, N. Itaco, R. Machleidt, F. Sammarruca, Phys. Rev. C 87, 014322 (2013)
  • L. Coraggio, J.W. Holt, N. Itaco, R. Machleidt, L.E. Marcucci, F. Sammarruca, Phys. Rev. C 89, 044321 (2014)
  • B.D. Day, Comments Nucl. Part. Phys. 11, 115 (1983)
  • C. Drischler, A. Carbone, K. Hebeler, A. Schwenk, Phys. Rev. C 94, 054307 (2016)
  • C. Drischler, K. Hebeler, A. Schwenk, Phys. Rev. Lett. 122, 042501 (2019)
  • A. Ekstrőm et al., Phys. Rev. Lett. 110, 192502 (2013)
  • A. Ekstrőm et al., Phys. Rev. C 91, 051301 (2015)
  • A. Ekstrőm, G. Hagen, T.D. Morris, T. Papenbrock, P.D. Schwartz, Phys. Rev. C 97, 024332 (2018)
  • D.R. Entem, R. Machleidt, unpublished (1993)
  • D.R. Entem, R. Machleidt, Phys. Lett. B 524, 93 (2002)
  • D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001 (2003)
  • D.R. Entem, J.A. Oller, Non-perturbative methods for NN singular interactions. [arXiv:2103.02069 [nucl-th]]
  • D.R. Entem, R. Machleidt, H. Witala, Phys. Rev. C 65, 064005 (2002)
  • D.R. Entem, N. Kaiser, R. Machleidt, Y. Nosyk, Phys. Rev. C 91, 014002 (2015)
  • D.R. Entem, N. Kaiser, R. Machleidt, Y. Nosyk, Phys. Rev. C 92, 064001 (2015)
  • D.R. Entem, R. Machleidt, Y. Nosyk, Phys. Rev. C 96, 024004 (2017)
  • E. Epelbaum, Eur. Phys. J. A34, 197 (2007)
  • E. Epelbaum, H.-W. Hammer, U.-G. Meißner, Rev. Mod. Phys. 2009, 81 (1773)
  • E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A671, 295 (2000)
  • E. Epelbaum, A. Nogga, W. Glöckle, H. Kamada, U.-G. Meißner, H. Witala, Phys. Rev. C 66, 064001 (2002)
  • E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A747, 362 (2005)
  • E. Epelbaum, H. Krebs, U.-G. Meißner, Eur. Phys. J. A51, 53 (2015a)
  • E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. Lett. 115, 122301 (2015b)
  • E. Epelbaum, J. Gegelia, U. G. Meißner, Nucl. Phys. B 925, 161 (2017)
  • E. Epelbaum, A.M. Gasparyan, J. Gegelia, U.G. Meißner, Eur. Phys. J. A 54, 186 (2018)
  • K. Erkelenz, Phys. Rep. 13C, 191–258 (1974)
  • S. Fleming, T. Mehen, I.W. Stewart, Nucl. Phys. A 677, 313 (2000)
  • J.L. Friar, D. Huber, U. van Kolck, Phys. Rev. C 59, 53 (1999)
  • J.-I. Fujita, H. Miyazawa, Prog. Theor. Phys. 17, 360 (1957)
  • R.J. Furnstahl, D.R. Phillips, S. Wesolowski, J. Phys. G 42, 034028 (2015)
  • J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984); Nucl. Phys. B250, 465 (1985)
  • J. Gasser, M.E. Sainio, A. Švarc, Nucl. Phys. B307, 779 (1986)
  • A. Gezerlis, I. Tews, E. Epelbaum, M. Freunek, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. C 90, 054323 (2014)
  • L. Girlanda, A. Kievsky, M. Viviani, Phys. Rev. C 84, 014001 (2011) [erratum: Phys. Rev. C 102(1), 019903 (2020)]
  • L. Girlanda, A. Kievsky, M. Viviani, L.E. Marcucci, Phys. Rev. C 99, 054003 (2019)
  • J. Golak et al., Eur. Phys. J. A 50, 177 (2014)
  • H. Hagen, M. Hjorth-Jensen, G.R. Jansen, R. Machleidt, T. Papenbrock, Phys. Rev. Lett. 108, 242501 (2012a)
  • H. Hagen, M. Hjorth-Jensen, G.R. Jansen, R. Machleidt, T. Papenbrock, Phys. Rev. Lett. 109, 032502 (2012b)
  • G. Hagen, T. Papenbrock, M. Hjorth-Jensen, D. J. Dean, Rept. Prog. Phys. 77, 096302 (2014a)
  • G. Hagen, T. Papenbrock, A. Ekstrőm, K.A. Wendt, G. Baardsen, S. Gandolfi, M. Hjorth-Jensen, C.J. Horowitz, Phys. Rev. C 89, 014319 (2014b)
  • G. Hagen, G.R. Jansen, T. Papenbrock, Phys. Rev. Lett. 117, 172501 (2016)
  • H.W. Hammer, S. König, U. van Kolck, Rev. Mod. Phys. 92, 025004 (2020)
  • K. Hebeler, A. Schwenk, Phys. Rev. C 82, 014314 (2010)
  • K. Hebeler, S.K. Bogner, R.J. Furnstahl, A. Nogga, A. Schwenk, Phys. Rev. C 83, 031301(R) (2011)
  • H. Hergert, S.K. Bogner, S. Binder, A. Calci, J. Langhammer, R. Roth, A. Schwenk, Phys. Rev. C 87, 034307 (2013)
  • K. Hebeler, H. Krebs, E. Epelbaum, J. Golak, R. Skibinski, Phys. Rev. C 91, 044001 (2015)
  • H. Hergert, S.K. Bogner, T.D. Morris, A. Schwenk, K. Tsukiyama, Phys. Rep. 621, 165 (2016)
  • M. Hoferichter, J. Ruiz de Elvira, B. Kubis, U.-G. Meißner, Phys. Rev. Lett. 115, 192301 (2015); Phys. Rep. 625, 1 (2016)
  • K. Holinde, R. Machleidt, Nucl. Phys. A247, 495–520 (1975); ibid. A256, 479–496 (1976)
  • J. Hoppe, C. Drischler, K. Hebeler, A. Schwenk, J. Simonis, Phys. Rev. C 100, 024318 (2019)
  • T. Hüther, K. Vobig, K. Hebeler, R. Machleidt, R. Roth, Phys. Lett. B 808, 135651 (2020)
  • U.D. Jentschura, A. Matveev, C.G. Parthey, J. Alnis, R. Pohl, Th. Udem, N. Kolachevsky, T.W. Ha̋nsch, Phys. Rev. A 83, 042505 (2011)
  • S. Kőnig, H.W. Grießhammer, H.-W. Hammer, U. van Kolck, Phys. Rev. Lett. 118, 202501 (2017)
  • N. Kaiser, Phys. Rev. C 61, 014003 (2000a)
  • N. Kaiser, Phys. Rev. C 62, 024001 (2000b)
  • N. Kaiser, Eur. Phys. J. A 48, 135 (2012)
  • N. Kaiser, R. Milkus, Phys. Rev. C 92, 064001 (2015)
  • N. Kaiser, R. Milkus, Eur. Phys. J. A 52, 4 (2016)
  • N. Kaiser, R. Brockmann, W. Weise, Nucl. Phys. A625, 758 (1997)
  • D.B. Kaplan, M. Savage, M.B. Wise, Nucl. Phys. B478, 629 (1996); Phys. Lett. B424, 390 (1998); Nucl. Phys. B534, 329 (1998)
  • A. Kievsky, M. Viviani, L. Girlanda, L.E. Marcucci, Phys. Rev. C 81, 044003 (2010)
  • T. Krűger, I. Tews, K Hebeler, A. Schwenk, Phys. Rev. C 88, 025802 (2013)
  • H. Krebs, A. Gasparyan, E. Epelbaum, Phys. Rev. C 85, 054006 (2012)
  • H. Krebs, A. Gasparyan, E. Epelbaum, Phys. Rev. C 87, 054007 (2013)
  • M. Lacombe, B. Loiseau, J.M. Richard, R. Vinh Mau, J. Côté, P. Pires, R. de Tourreil, Phys. Rev. C 21, 861–873 (1980)
  • V. Lapoux, V. Somà, C. Barbieri, H. Hergert, J.D. Holt, S.R. Stroberg, Phys. Rev. Lett. 117, 052501 (2016)
  • G.P. Lepage, How to Renormalize the Schrödinger Equation (1977). arXiv:nucl-th/9706029
  • D. Lonardoni, A. Lovato, S.C. Pieper, R.B. Wiringa, Phys. Rev. C 96(2), 024326 (2017)
  • B. Long, Int. J. Mod. Phys. E 25, 1641006 (2016)
  • B. Long, C. Yang, Phys. Rev. C 86, 024001 (2012)
  • R. Machleidt, K. Holinde, Ch. Elster, Phys. Rep. 149, 1–89 (1987)
  • R. Machleidt, Adv. Nucl. Phys. 19, 189–376 (1989)
  • R. Machleidt, Phys. Rev. C 63, 024001 (2001)
  • R. Machleidt, D.R. Entem, Phys Reports 503, 1 (2011)
  • R. Machleidt, F. Sammarruca, Phys. Scr. 91, 083007 (2016)
  • R. Machleidt, F. Sammarruca, Eur. Phys. J. A 56, 95 (2020)
  • L.E. Marcucci, A. Kievsky, S. Rosati, R. Schiavilla, M. Viviani, Phys. Rev. Lett. 108, 052502 (2012)
  • E. Marji et al., Phys. Rev. C 88, 054002 (2013)
  • T.D. Morris, J. Simonis, S.R. Stroberg, C. Stumpf, G. Hagen, J.D. Holt, G.R. Jansen, T. Papenbrock, R. Roth, A. Schwenk, Phys. Rev. Lett. 120, 152503 (2018)
  • R. Navarro Pérez, J.E. Amaro, E. Ruiz Arriola, Phys. Rev. C 91, 054002 (2015), and references to the comprehensive work by the Granada group therein
  • P. Navratil, Few Body Syst. 41, 117 (2007)
  • P. Navratil, V.G. Gueorguiev, J.P. Vary, W.E. Ormand, A. Nogga, Phys. Rev. Lett. 99, 042501 (2007)
  • P. Navratil, R. Roth, S. Quaglioni, Phys. Rev. C 82, 034609 (2010)
  • A. Nogga, R.G.E. Timmermans, U. van Kolck, Phys. Rev. C 72, 054006 (2005)
  • A. Nogga, P. Navratil, B.R. Barrett, J.P. Vary, Phys. Rev. C 73, 064002 (2006)
  • C. Ordóñez, L. Ray, U. van Kolck, Phys. Rev. C 53, 2086 (1996)
  • M. Pavon Valderrama, Phys. Rev. C 84, 064002 (2011)
  • M. Pavon Valderrama, M. Sanchez Sanchez, C.J. Yang, B. Long, J. Carbonell, U. van Kolck, Phys. Rev. C 95, 054001 (2017)
  • M. Piarulli, L. Girlanda, R. Schiavilla, R. Navarro Pérez, J.E. Amaro, E. Ruiz Arriola, Phys. Rev. C 91, 024003 (2015)
  • M. Piarulli, L. Girlanda, R. Schiavilla, A. Kievsky, A. Lovato, L.E. Marcucci, Steven C. Pieper, M. Viviani, R.B. Wiringa, Phys. Rev. C 94, 054007 (2016)
  • P. Reinert, H. Krebs, E. Epelbaum, Eur. Phys. J. A 54, 86 (2018)
  • V.G.J. Stoks, R.A.M. Klomp, M.C.M. Rentmeester, J.J. de Swart, Phys. Rev. C 48, 792 (1993)
  • R. Roth, J. Langhammer, A. Calci, S. Binder, P. Navratil, Phys. Rev. Lett. 107, 072501 (2011)
  • R. Roth, S. Binder, K. Vobig, A. Calci, J. Langhammer, P. Navratil, Phys. Rev. Lett. 109, 052501 (2012)
  • D. Rozpedzik, J. Golak, R. Skibinski, H. Witala, W. Glöckle, E. Epelbaum, A. Nogga, H. Kamada, Acta Phys. Polon. B37, 2889 (2006); arXiv:nucl-th/0606017
  • F. Sammarruca, R. Millerson, Phys. Rev. C 102, 034313 (2020)
  • F. Sammarruca, L.E. Marcucci, L. Coraggio, J.W. Holt, N. Itaco, R. Machleidt, arXiv:1807.06640 [nucl-th]
  • F. Sammarruca, B. Chen, L. Coraggio, N. Itaco, R. Machleidt, Phys. Rev. C 86, 054317 (2012)
  • F. Sammarruca, L. Coraggio, J.W. Holt, N. Itaco, R. Machleidt, L.E. Marcucci, Phys. Rev. C 91, 054311 (2015)
  • S. Scherer, Adv. Nucl. Phys. 27, 277 (2003)
  • J. Simonis, K. Hebeler, J.D. Holt, J. Menendez, A. Schwenk, Phys. Rev. C 93, 011302 (2016)
  • J. Simonis, S.R. Stroberg, K. Hebeler, J.D. Holt, A. Schwenk, Phys. Rev. C 96, 014303 (2017)
  • V. Somà, A. Cipollone, C. Barbieri, P. Navratil, T. Duget, Phys. Rev. C 89, 061301(R) (2014)
  • V. Somà, P. Navrátil, F. Raimondi, C. Barbieri, T. Duguet, Phys. Rev. C 101, 014318 (2020)
  • M.P. Valderrama, Scattering amplitudes versus potentials in nuclear effective field theory: is there a potential compromise? arXiv:1902.08172 [nucl-th]
  • M.P. Valderrama, Phys. Rev. C 83, 024003 (2011)
  • M.P. Valderrama, Int. J. Mod. Phys. E 25, 1641007 (2016)
  • U. van Kolck, Phys. Rev. C 49, 2932 (1994)
  • U. van Kolck, Front. Phys. 8, 79 (2020)
  • R. Vinh Mau, in Mesons in Nuclei, Vol. I, ed. by M. Rho, D.H. Wilkinson (North-Holland, Amsterdam, 1979), pp. 151–196
  • M. Viviani, L. Girlanda, A. Kievsky, L.E. Marcucci, Phys. Rev. Lett. 111, 172302 (2013)
  • S. Weinberg, Physica 96A, 327 (1979)
  • S. Weinberg, Phys. Lett. B251, 288 (1990)
  • S. Weinberg, Nucl. Phys. B363, 3 (1991)
  • S. Weinberg, Phys. Lett. B 295, 114 (1992)
  • H. Yukawa, Proc. Phys. Math. Soc. Jpn. 17, 48–57 (1935)
  • P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020)