Skip to main content
SpringerLink
Log in

How (not) to renormalize integral equations with singular potentials in effective field theory

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

A Comment to this article was published on 19 April 2019

Abstract.

We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are supported by examples from effective theories with and without pions as dynamical degrees of freedom. A quantum mechanical potential with explicitly specified short- and long-range parts is considered as an “underlying fundamental theory” and the corresponding effective field theory potential is constructed. Further, the problem of the effective field theoretical renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Weinberg, Phys. Lett. B 251, 288 (1990)

    Article  ADS  Google Scholar 

  2. S. Weinberg, Nucl. Phys. B 363, 3 (1991)

    Article  ADS  Google Scholar 

  3. C. Ordonez, U. van Kolck, Phys. Lett. B 291, 459 (1992)

    Article  ADS  Google Scholar 

  4. N. Kaiser, R. Brockmann, W. Weise, Nucl. Phys. A 625, 758 (1997) arXiv:nucl-th/9706045

    Article  ADS  Google Scholar 

  5. N. Kaiser, Phys. Rev. C 61, 014003 (2000) arXiv:nucl-th/9910044

    Article  ADS  Google Scholar 

  6. P.F. Bedaque, H.W. Hammer, U. van Kolck, Nucl. Phys. A 676, 357 (2000) arXiv:nucl-th/9906032

    Article  ADS  Google Scholar 

  7. P.F. Bedaque, G. Rupak, H.W. Griesshammer, H.W. Hammer, Nucl. Phys. A 714, 589 (2003) arXiv:nucl-th/0207034

    Article  ADS  Google Scholar 

  8. H.W. Griesshammer, Nucl. Phys. A 760, 110 (2005) arXiv:nucl-th/0502039

    Article  ADS  Google Scholar 

  9. N. Kaiser, Phys. Rev. C 64, 057001 (2001) arXiv:nucl-th/0107064

    Article  ADS  Google Scholar 

  10. M.P. Valderrama, E. Ruiz Arriola, Phys. Lett. B 580, 149 (2004) arXiv:nucl-th/0306069

    Article  ADS  Google Scholar 

  11. M.P. Valderrama, E. Ruiz Arriola, Phys. Rev. C 72, 054002 (2005) arXiv:nucl-th/0504067

    Article  ADS  Google Scholar 

  12. M.P. Valderrama, E. Ruiz Arriola, Phys. Rev. C 74, 064004 (2006) arXiv:nucl-th/0507075

    Article  ADS  Google Scholar 

  13. M.C. Birse, J.A. McGovern, Phys. Rev. C 70, 054002 (2004) arXiv:nucl-th/0307050

    Article  ADS  Google Scholar 

  14. M.C. Birse, Phys. Rev. C 74, 014003 (2006) arXiv:nucl-th/0507077

    Article  ADS  Google Scholar 

  15. J.V. Steele, R.J. Furnstahl, Nucl. Phys. A 645, 439 (1999) arXiv:nucl-th/9808022

    Article  ADS  Google Scholar 

  16. M. Lutz, Nucl. Phys. A 677, 241 (2000) arXiv:nucl-th/9906028

    Article  ADS  Google Scholar 

  17. R. Higa, M.R. Robilotta, Phys. Rev. C 68, 024004 (2003) arXiv:nucl-th/0304025

    Article  ADS  Google Scholar 

  18. R. Higa, M.R. Robilotta, C.A. da Rocha, Phys. Rev. C 69, 034009 (2004) arXiv:nucl-th/0310011

    Article  ADS  Google Scholar 

  19. M.D. Cozma, O. Scholten, R.G. Timmermans, J.A. Tjon, Phys. Rev. C 75, 014006 (2007)

    Article  ADS  Google Scholar 

  20. L. Girlanda, M. Viviani, W.H. Klink, Phys. Rev. C 76, 044002 (2007) arXiv:nucl-th/0702024

    Article  ADS  Google Scholar 

  21. E. Epelbaum, U.-G. Meißner, W. Glöckle, Nucl. Phys. A 714, 535 (2003) arXiv:nucl-th/0207089

    Article  ADS  Google Scholar 

  22. E. Epelbaum et al., Phys. Rev. Lett. 86, 4787 (2001) arXiv:nucl-th/0007057

    Article  ADS  Google Scholar 

  23. E. Epelbaum et al., Phys. Rev. C 66, 064001 (2002) arXiv:nucl-th/0208023

    Article  ADS  Google Scholar 

  24. E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 637, 107 (1998) arXiv:nucl-th/9801064

    Article  ADS  Google Scholar 

  25. E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 671, 295 (2000) arXiv:nucl-th/9910064

    Article  ADS  Google Scholar 

  26. D.B. Kaplan, M.J. Savage, M.B. Wise, Nucl. Phys. B 478, 629 (1996) arXiv:nucl-th/9605002

    Article  ADS  Google Scholar 

  27. D.B. Kaplan, M.J. Savage, M.B. Wise, Phys. Lett. B 424, 390 (1998) arXiv:nucl-th/9801034

    Article  ADS  Google Scholar 

  28. D.B. Kaplan, M.J. Savage, M.B. Wise, Nucl. Phys. B 534, 329 (1998) arXiv:nucl-th/9802075

    Article  ADS  Google Scholar 

  29. T.D. Cohen, J.M. Hansen, Phys. Rev. C 59, 3047 (1999) arXiv:nucl-th/9901065

    Article  ADS  Google Scholar 

  30. S. Fleming, T. Mehen, I.W. Stewart, Nucl. Phys. A 677, 313 (2000) arXiv:nucl-th/9911001

    Article  ADS  Google Scholar 

  31. S.R. Beane, P.F. Bedaque, L. Childress, A. Kryjevski, J. McGuire, U. van Kolck, Phys. Rev. A 64, 042103 (2001) arXiv:quant-ph/0010073

    Article  ADS  Google Scholar 

  32. S.R. Beane, P.F. Bedaque, M.J. Savage, U. van Kolck, Nucl. Phys. A 700, 377 (2002) arXiv:nucl-th/0104030

    Article  ADS  Google Scholar 

  33. A. Nogga, R.G.E. Timmermans, U. van Kolck, Phys. Rev. C 72, 054006 (2005) arXiv:nucl-th/0506005

    Article  ADS  Google Scholar 

  34. G.P. Lepage, arXiv:nucl-th/9706029

  35. T.S. Park, K. Kubodera, D.P. Min, M. Rho, Nucl. Phys. A 646, 83 (1999) arXiv:nucl-th/9807054

    Article  ADS  Google Scholar 

  36. G.P. Lepage, Conference summary, in Nuclear Physics with Effective Field Theory II: Proceedings, Seattle, Washington, 25–26 Feb. 1999 (World Scientific, Singapore, 2000)

  37. T. Frederico, V.S. Timoteo, L. Tomio, Nucl. Phys. A 653, 209 (1999) arXiv:nucl-th/9902052

    Article  ADS  Google Scholar 

  38. V.S. Timoteo, T. Frederico, A. Delfino, L. Tomio, Phys. Lett. B 621, 109 (2005) arXiv:nucl-th/0508006

    Article  ADS  Google Scholar 

  39. V.S. Timoteo, T. Frederico, A. Delfino, L. Tomio, Phys. Rev. C 83, 064005 (2011) arXiv:1006.1942 [nucl-th]

    Article  ADS  Google Scholar 

  40. C.-J. Yang, C. Elster, D.R. Phillips, Phys. Rev. C 80, 044002 (2009) arXiv:0905.4943 [nucl-th]

    Article  ADS  Google Scholar 

  41. M.C. Birse, Philos. Trans. R. Soc. London A 369, 2662 (2011) arXiv:1012.4914 [nucl-th]

    Article  ADS  MathSciNet  Google Scholar 

  42. M.P. Valderrama, Phys. Rev. C 83, 024003 (2011) arXiv:0912.0699 [nucl-th]

    Article  ADS  Google Scholar 

  43. M. Pavon Valderrama, Phys. Rev. C 84, 064002 (2011) arXiv:1108.0872 [nucl-th]

    Article  ADS  Google Scholar 

  44. B. Long, C.J. Yang, Phys. Rev. C 85, 034002 (2012) arXiv:1111.3993 [nucl-th]

    Article  ADS  Google Scholar 

  45. B. Long, U. van Kolck, Ann. Phys. 323, 1304 (2008) arXiv:0707.4325 [quant-ph]

    Article  ADS  Google Scholar 

  46. E. Epelbaum, J. Gegelia, Eur. Phys. J. A 41, 341 (2009) arXiv:0906.3822 [nucl-th]

    Article  ADS  Google Scholar 

  47. D. Djukanovic, J. Gegelia, S. Scherer, M.R. Schindler, Few Body Syst. 41, 141 (2007) arXiv:nucl-th/0609055

    Article  ADS  Google Scholar 

  48. J. Gegelia, G. Japaridze, Phys. Lett. B 517, 476 (2001) arXiv:nucl-th/0108005

    Article  ADS  Google Scholar 

  49. M.C. Birse, J.A. McGovern, K.G. Richardson, Phys. Lett. B 464, 169 (1999) arXiv:hep-ph/9807302

    Article  ADS  MathSciNet  Google Scholar 

  50. J. Gegelia, in Nonperturbative Methods in Quantum Field Theory: Proceedings (World Scientific, Singapore, 1998) pp. 30--35, arXiv:nucl-th/9802038

  51. K. Harada, H. Kubo, Nucl. Phys. B 758, 304 (2006) arXiv:nucl-th/0605004

    Article  ADS  Google Scholar 

  52. M.J. Savage, in Nuclear Physics with Effective Field Theory: Proceedings (World Scientific, Singapore, 1998) pp. 247--267, arXiv:nucl-th/9804034

  53. X.L. Ren, K.W. Li, L.S. Geng, B.W. Long, P. Ring, J. Meng, Chin. Phys. C 42, 014103 (2018) arXiv:1611.08475 [nucl-th]

    Article  ADS  Google Scholar 

  54. M. Pavón Valderrama, M. Sánchez Sánchez, C.J. Yang, B. Long, J. Carbonell, U. van Kolck, Phys. Rev. C 95, 054001 (2017) arXiv:1611.10175 [nucl-th]

    Article  ADS  Google Scholar 

  55. R. Machleidt, D.R. Entem, Phys. Rep. 503, 1 (2011) arXiv:1105.2919 [nucl-th]

    Article  ADS  Google Scholar 

  56. E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006) arXiv:nucl-th/0509032

    Article  ADS  Google Scholar 

  57. E. Epelbaum, U.-G. Meißner, Annu. Rev. Nucl. Part. Sci. 62, 159 (2012) arXiv:1201.2136 [nucl-th]

    Article  ADS  Google Scholar 

  58. P.F. Bedaque, U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002) arXiv:nucl-th/0203055

    Article  ADS  Google Scholar 

  59. E. Epelbaum, H.-W. Hammer, U.-G. Meißner, Rev. Mod. Phys. 81, 1773 (2009) arXiv:0811.1338 [nucl-th]

    Article  ADS  Google Scholar 

  60. M.C. Birse, PoS CD09, 078 (2009) arXiv:0909.4641 [nucl-th]

    Google Scholar 

  61. M.P. Valderrama, Int. J. Mod. Phys. E 25, 1641007 (2016) arXiv:1604.01332 [nucl-th]

    Article  ADS  Google Scholar 

  62. J. Gasser, H. Leutwyler, Phys. Rep. 87, 77 (1982)

    Article  ADS  Google Scholar 

  63. S. Weinberg, The Quantum Theory of Fields, Vols. 1, 2: Foundations, Modern applications (Cambridge, University Press, 1995)

  64. J.C. Collins, Renormalization. An Introduction to Renormalization, the Renormalization Group, and the Operator Product Expansion (Cambridge, University Press, 1984)

  65. E. Epelbaum, J. Gegelia, U.-G. Meißner, arXiv:1710.04178 [nucl-th]

  66. S.R. Beane, T.D. Cohen, D.R. Phillips, Nucl. Phys. A 632, 445 (1998) arXiv:nucl-th/9709062

    Article  ADS  Google Scholar 

  67. J. Gegelia, Phys. Lett. B 429, 227 (1998)

    Article  ADS  Google Scholar 

  68. J. Gegelia, J. Phys. G 25, 1681 (1999) arXiv:nucl-th/9805008

    Article  ADS  Google Scholar 

  69. E. Epelbaum, J. Gegelia, U.-G. Meißner, Nucl. Phys. B 925, 161 (2017) arXiv:1705.02524 [nucl-th]

    Article  ADS  Google Scholar 

  70. W. Frank, D.J. Land, R.M. Spector, Rev. Mod. Phys. 43, 36 (1971)

    Article  ADS  Google Scholar 

  71. E. Epelbaum, H. Krebs, U.-G. Meißner, Eur. Phys. J. A 51, 53 (2015) arXiv:1412.0142 [nucl-th]

    Article  ADS  Google Scholar 

  72. J. Gegelia, S. Scherer, Int. J. Mod. Phys. A 21, 1079 (2006) arXiv:nucl-th/0403052

    Article  ADS  Google Scholar 

  73. E. Epelbaum, U.-G. Meißner, Few Body Syst. 54, 2175 (2013) arXiv:nucl-th/0609037

    Article  ADS  Google Scholar 

  74. E. Epelbaum, A.M. Gasparyan, J. Gegelia, H. Krebs, Eur. Phys. J. A 51, 71 (2015) arXiv:1501.01191 [nucl-th]

    Article  ADS  Google Scholar 

  75. P.F. Bedaque, H.W. Hammer, U. van Kolck, Nucl. Phys. A 646, 444 (1999) arXiv:nucl-th/9811046

    Article  ADS  Google Scholar 

  76. G.V. Skornyakov, Ter-Martirosyan, Sov. Phys. JETP 4, 648 (1957) Zh. Eksp. Teor. Fiz. 31

    Google Scholar 

  77. G.S. Danilov, Sov. Phys. JETP 13, 349 (1961)

    Google Scholar 

  78. P.F. Bedaque, H.W. Hammer, U. van Kolck, Phys. Rev. Lett. 82, 463 (1999) arXiv:nucl-th/9809025

    Article  ADS  Google Scholar 

  79. E. Epelbaum, J. Gegelia, U.-G. Meißner, D.L. Yao, Eur. Phys. J. A 53, 98 (2017) arXiv:1611.06040 [nucl-th]

    Article  ADS  Google Scholar 

  80. S. Moroz, S. Floerchinger, R. Schmidt, C. Wetterich, Phys. Rev. A 79, 042705 (2009) arXiv:0812.0528 [cond-mat.stat-mech]

    Article  ADS  Google Scholar 

  81. K. Harada, H. Kubo, I. Yoshimoto, Phys. Rev. D 87, 085006 (2013) arXiv:1208.0719 [hep-th]

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik II, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, 44780, Bochum, Germany

    E. Epelbaum & A. M. Gasparyan

  2. Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218, Moscow, Russia

    A. M. Gasparyan

  3. Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425, Jülich, Germany

    J. Gegelia & Ulf-G. Meißner

  4. Tbilisi State University, 0186, Tbilisi, Georgia

    J. Gegelia

  5. Helmholtz Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany

    Ulf-G. Meißner

Authors
  1. E. Epelbaum
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Gasparyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Gegelia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ulf-G. Meißner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Gegelia.

Additional information

Communicated by V. Somà

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Epelbaum, E., Gasparyan, A.M., Gegelia, J. et al. How (not) to renormalize integral equations with singular potentials in effective field theory. Eur. Phys. J. A 54, 186 (2018). https://doi.org/10.1140/epja/i2018-12632-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/i2018-12632-1

Search

Navigation