Renormalisation group analysis of electromagnetic couplings in the pionless effective field theory

  • A. N. Kvinikhidze
  • M. C. Birse
Open Access
Regular Article - Theoretical Physics


The Wilsonian renormalisation group is applied to a system of two nonrelativistic particles interacting via short-range forces and coupled to an external EM field. By demanding that a fully off-shell one-particle-irreducible 5-point amplitude is independent of the cutoff, a renormalisation group equation is derived for the interaction current density. This is solved to obtain the fixed point corresponding to the unitary limit. The scaling behaviour of perturbations around this point is analysed. Some of these terms are related by gauge invariance to terms in the effective-range expansion; others describe short-range physics that is not included in the two-body potential. We construct observables including the bound-state form factor and show how the scaling of the terms in the interaction current is reflected in the power counting for their contributions to observables.


  1. 1.
    S.R. Beane, P.F. Bedaque, W.C. Haxton, D.R. Phillips, M.J. Savage, in At the frontier of particle physics, edited by M. Shifman, Vol. 1 (World Scientific, Singapore, 2001) pp. 133--269Google Scholar
  2. 2.
    P.F. Bedaque, U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002)ADSCrossRefGoogle Scholar
  3. 3.
    E. Epelbaum, H.W. Hammer, U.G. Meissner, Rev. Mod. Phys. 81, 1773 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    K.G. Wilson, J.B. Kogut, Phys. Rep. 12, 75 (1974)ADSCrossRefGoogle Scholar
  5. 5.
    D.B. Kaplan, M.J. Savage, M.B. Wise, Phys. Lett. B 424, 390 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    U. van Kolck, Nucl. Phys. A 645, 273 (1999)ADSCrossRefGoogle Scholar
  7. 7.
    J. Gegelia, Phys. Lett. B 429, 227 (1998)ADSCrossRefGoogle Scholar
  8. 8.
    M.C. Birse, J.A. McGovern, K.G. Richardson, Phys. Lett. B 464, 169 (1999)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    H.A. Bethe, Phys. Rev. 76, 38 (1949)ADSCrossRefGoogle Scholar
  10. 10.
    E. Epelbaum, J. Gegelia, Eur. Phys. J. A 41, 341 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    M.C. Birse, Philos. Trans. R. Soc. Lond. A 369, 2662 (2011)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    E. Braaten, H.-W. Hammer, Phys. Rep. 428, 259 (2006)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    M.C. Birse, E. Epelbaum, J. Gegelia, Eur. Phys. J. A 52, 26 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    D.B. Kaplan, M.J. Savage, M.B. Wise, Phys. Rev. C 59, 617 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    J.W. Chen, G. Rupak, M.J. Savage, Nucl. Phys. A 653, 386 (1999)ADSCrossRefGoogle Scholar
  16. 16.
    D.W.L. Sprung, H. Wu, J. Martorell, Phys. Rev. C 42, 863 (1990)ADSCrossRefGoogle Scholar
  17. 17.
    R.K. Bhaduri, W. Leidemann, G. Orlandini, E.L. Tomusiak, Phys. Rev. C 42, 1867 (1990)ADSCrossRefGoogle Scholar
  18. 18.
    M.W. Kermode, S.A. Moszkowski, M.M. Mustafa, W. van Dijk, Phys. Rev. C 43, 416 (1991)ADSCrossRefGoogle Scholar
  19. 19.
    M. Pavón Valderrama, D.R. Phillips, Phys. Rev. Lett. 114, 082502 (2015)ADSCrossRefGoogle Scholar
  20. 20.
    A.N. Kvinikhidze, B. Blankleider, Phys. Rev. C 56, 2963 (1997)ADSCrossRefGoogle Scholar
  21. 21.
    A.N. Kvinikhidze, B. Blankleider, Phys. Rev. C 56, 2973 (1997)ADSCrossRefGoogle Scholar
  22. 22.
    A.N. Kvinikhidze, B. Blankleider, Nucl. Phys. A 631, 559C (1998)ADSCrossRefGoogle Scholar
  23. 23.
    A.N. Kvinikhidze, B. Blankleider, E. Epelbaum, C. Hanhart, M. Pavón Valderrama, Phys. Rev. C 80, 044004 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    A.N. Kvinikhidze, B. Blankleider, Phys. Rev. C 76, 064003 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    S.X. Nakamura, S.-I. Ando, Phys. Rev. C 74, 034004 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    A.J.F. Siegert, Phys. Rev. 52, 787 (1937)ADSCrossRefGoogle Scholar
  27. 27.
    J.L. Friar, S. Fallieros, Phys. Rev. C 29, 1645 (1984)ADSCrossRefGoogle Scholar
  28. 28.
    T. Barford, M.C. Birse, Phys. Rev. C 67, 064006 (2003)ADSCrossRefGoogle Scholar
  29. 29.
    D.R. Phillips, G. Rupak, M.J. Savage, Phys. Lett. B 473, 209 (2000)ADSCrossRefGoogle Scholar
  30. 30.
    S.R. Beane, M.J. Savage, Nucl. Phys. A 694, 511 (2001)ADSCrossRefGoogle Scholar
  31. 31.
    H.W. Fearing, Few Body Syst. Suppl. 12, 263 (2000)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Theoretical Physics, A. Razmadze Mathematical InstituteI. Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.Theoretical Physics Division, School of Physics and AstronomyThe University of ManchesterManchesterUK

Personalised recommendations