Advertisement

Three-body scattering problem in the fixed center approximation: The case of attraction

  • Alexander E. Kudryavtsev
  • Vakhid A. GaniEmail author
  • Alexander I. Romanov
Regular Article - Theoretical Physics

Abstract.

We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous --they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors.

References

  1. 1.
    M. Kunitski et al., Science 348, 551 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    N.T. Zinner, Eur. Phys. J. D 68, 261 (2014)ADSCrossRefGoogle Scholar
  3. 3.
    Belle Collaboration (S.-K. Choi, S.L. Olsen et al.), Phys. Rev. Lett. 91, 262001 (2003)CrossRefGoogle Scholar
  4. 4.
    LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 110, 222001 (2013)CrossRefGoogle Scholar
  5. 5.
    D.M. Asner et al., Int. J. Mod. Phys. A 24, S1 (2009)CrossRefGoogle Scholar
  6. 6.
    PANDA Collaboration (M.F.M. Lutz), Physics Performance Report for PANDA: Strong Interaction Studies with Antiprotons, FAIR/PANDA/Physics Book (2009) arXiv:0903:3905 [hep-ex]Google Scholar
  7. 7.
    A.G. Drutskoy, F.-K. Guo, F.J. Llanes-Estrada, A.V. Nefediev, J.M. Torres-Rincon, Eur. Phys. J. A 49, 7 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    N. Brambilla et al., Eur. Phys. J. C 71, 1534 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    M.B. Voloshin, L.B. Okun, JETP Lett. 23, 333 (1976) (Pisma Zh. Eksp. Teor. Fiz. 23ADSGoogle Scholar
  10. 10.
    M.B. Voloshin, Phys. Lett. B 579, 316 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    N.A. Tornqvist, Phys. Lett. B 590, 209 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    V. Baru, C. Hanhart, A.A. Filin, Yu.S. Kalashnikova, A.E. Kudryavtsev, A.V. Nefediev, Phys. Rev. D 84, 074029 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    Th. Strauch et al., Eur. Phys. J. A 47, 88 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    V. Baru, C. Hanhart, M. Hoferichter, B. Kubis, A. Nogga, D.R. Phillips, Nucl. Phys. A 872, 69 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    V. Baru, C. Hanhart, M. Hoferichter, B. Kubis, A. Nogga, D.R. Phillips, Phys. Lett. B 694, 473 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    M. Mai, V. Baru, E. Epelbaum, A. Rusetsky, Phys. Rev. D 91, 054016 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    J. Gasser, V.E. Lyubovitskij, A. Rusetsky, Phys. Rep. 456, 167 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    M. Bayar, W.H. Liang, T. Uchino, C.W. Xiao, Eur. Phys. J. A 50, 67 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    W. Liang, C.W. Xiao, E. Oset, Phys. Rev. D 88, 114024 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    M. Bayar, E. Oset, Phys. Rev. C 88, 044003 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    M. Bayar, E. Oset, Nucl. Phys. A 883, 57 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    A. Martínez Torres, E.J. Garzon, E. Oset, L.R. Dai, Phys. Rev. D 83, 116002 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Ju-Jun Xie, A. Martínez Torres, E. Oset, Phys. Rev. C 83, 065207 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    G.V. Skornyakov, K.A. Ter-Martirosyan, Sov. Phys. JETP 4, 648 (1957)Google Scholar
  25. 25.
    P.F. Bedaque, H.-W. Hammer, U. van Kolck, Phys. Rev. Lett. 82, 463 (1999)ADSCrossRefGoogle Scholar
  26. 26.
    L.L. Foldy, Phys. Rev. 67, 107 (1945)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    K.A. Brückner, Phys. Rev. 89, 834 (1953)ADSCrossRefGoogle Scholar
  28. 28.
    K.A. Brückner, Phys. Rev. 90, 715 (1953)ADSCrossRefGoogle Scholar
  29. 29.
    V.M. Kolybasov, A.E. Kudryavtsev, Nucl. Phys. B 41, 510 (1972)ADSCrossRefGoogle Scholar
  30. 30.
    S. Weinberg, Phys. Lett. B 295, 114 (1992)ADSCrossRefGoogle Scholar
  31. 31.
    S.R. Beane, V. Bernard, T.-S.H. Lee, U.-G. Meißner, Phys. Rev. C 57, 424 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    S.R. Beane, V. Bernard, E. Epelbaum, U.-G. Meißner, D.R. Phillips, Nucl. Phys. A 720, 399 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    V. Baru, C. Hanhart, A.E. Kudryavtsev, U.-G. Meißner, Phys. Lett. B 589, 118 (2004)ADSCrossRefGoogle Scholar
  34. 34.
    V. Lensky, V. Baru, J. Haidenbauer, C. Hanhart, A. Kudryavtsev, U.-G. Meißner, Phys. Lett. B 648, 46 (2007)ADSCrossRefGoogle Scholar
  35. 35.
    V. Baru, J. Haidenbauer, C. Hanhart, A. Kudryavtsev, V. Lensky, U.-G. Meißner, Phys. Lett. B 659, 184 (2008)ADSCrossRefGoogle Scholar
  36. 36.
    V. Baru, E. Epelbaum, C. Hanhart, M. Hoferichter, A.E. Kudryavtsev, D.R. Phillips, Eur. Phys. J. A 48, 69 (2012)ADSCrossRefGoogle Scholar
  37. 37.
    A.E. Kudryavtsev, A.I. Romanov, V.A. Gani, Phys. At. Nucl. 76, 919 (2013) (Yad. Fiz. 76CrossRefGoogle Scholar
  38. 38.
    E. Janke, F. Emde, F. Lösch, Tafeln Höherer Funktionen, (B. G. Teubner Verlagsgesellschaft, Stuttgart, 1960)Google Scholar
  39. 39.
    G.S. Danilov, V.I. Lebedev, Sov. Phys. JETP 17, 1015 (1963) (Zh. Eksp. Teor. Fiz. 44Google Scholar
  40. 40.
    V.F. Kharchenko, Sov. J. Nucl. Phys. 16, 173 (1973) (Yad. Fiz. 16CrossRefGoogle Scholar
  41. 41.
    A.E. Kudryavtsev, in preparationGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Alexander E. Kudryavtsev
    • 1
  • Vakhid A. Gani
    • 1
    • 2
    Email author
  • Alexander I. Romanov
    • 2
  1. 1.Institute for Theoretical and Experimental PhysicsNational Research Center Kurchatov InstituteMoscowRussia
  2. 2.National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia

Personalised recommendations