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The European Physical Journal A

, Volume 32, Issue 3, pp 335–347 | Cite as

Pion-mass dependence of three-nucleon observables

  • H. -W. Hammer
  • D. R. Phillips
  • L. PlatterEmail author
Regular Article - Interdisciplinary Topics

Abstract.

We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our “pionless” EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the 1 S 0 scattering length and effective range, the deuteron binding energy, the 3 S 1 effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse 3 S 1 and 1 S 0 scattering lengths vanishing at m π crit = 197.8577 MeV. At this “critical” pion mass, the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We compute the binding energies of these states up to next-to-next-to-leading order in the pionless EFT and study the convergence pattern of the EFT in the vicinity of the critical pion mass. Furthermore, we use the pionless EFT to predict how doublet and quartet nd scattering lengths depend on m π in the region between the physical pion mass and m π = m π crit .

PACS.

12.38.Aw General properties of QCD (dynamics, confinement, etc.) 21.45.+v Few-body systems 11.10.Hi Renormalization group evolution of parameters 

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References

  1. 1.
    S.R. Beane, P.F. Bedaque, K. Orginos, M.J. Savage, Phys. Rev. Lett. 97, 012001 (2006) [arXiv:hep-lat/0602010].CrossRefADSGoogle Scholar
  2. 2.
    V. Bernard, U.-G. Meißner, Annu. Rev. Nucl. Part. Sci. 57, 33 (2007) [arXiv:hep-ph/0611231].Google Scholar
  3. 3.
    S. Weinberg, Nucl. Phys. B 363, 3 (1991)CrossRefADSGoogle Scholar
  4. 4.
    S.R. Beane, P.F. Bedaque, W.C. Haxton, D.R. Phillips, M.J. Savage, arXiv:nucl-th/0008064.Google Scholar
  5. 5.
    P.F. Bedaque, U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002) [arXiv:nucl-th/0203055].CrossRefADSGoogle Scholar
  6. 6.
    E. Epelbaum, Prog. Nucl. Part. Phys. 57, 654 (2006) [arXiv:nucl-th/0509032].CrossRefADSGoogle Scholar
  7. 7.
    A. Nogga, R.G.E. Timmermans, U. van Kolck, Phys. Rev. C 72, 054006 (2005) [arXiv:nucl-th/0506005].CrossRefADSGoogle Scholar
  8. 8.
    M.P. Valderrama, E.R. Arriola, Phys. Rev. C 74, 054001 (2006) [arXiv:nucl-th/0506047].CrossRefADSGoogle Scholar
  9. 9.
    M.C. Birse, Phys. Rev. C 74, 014003 (2006) [arXiv:nucl-th/0507077].CrossRefADSGoogle Scholar
  10. 10.
    E. Epelbaum, U.-G. Meißner, arXiv:nucl-th/0609037.Google Scholar
  11. 11.
    J. Mondejar, J. Soto, arXiv:nucl-th/0612051.Google Scholar
  12. 12.
    S.R. Beane, P.F. Bedaque, M.J. Savage, U. van Kolck, Nucl. Phys. A 700, 377 (2002) [arXiv:nucl-th/0104030].zbMATHCrossRefADSGoogle Scholar
  13. 13.
    S.R. Beane, M.J. Savage, Nucl. Phys. A 717, 91 (2003) [arXiv:nucl-th/0208021]CrossRefADSGoogle Scholar
  14. 14.
    E. Epelbaum, U.-G. Meißner, W. Glöckle, Nucl. Phys. A 714, 535 (2003) [arXiv:nucl-th/0207089].zbMATHCrossRefADSGoogle Scholar
  15. 15.
    E. Braaten, H.-W. Hammer, Phys. Rev. Lett. 91, 102002 (2003) [arXiv:nucl-th/0303038].CrossRefADSGoogle Scholar
  16. 16.
    D.B. Kaplan, M.J. Savage, M.B. Wise, Phys. Lett. B 424, 390 (1998) [arXiv:nucl-th/9801034]CrossRefADSGoogle Scholar
  17. 17.
    U. van Kolck, arXiv:hep-ph/9711222Google Scholar
  18. 18.
    P.F. Bedaque, U. van Kolck, Phys. Lett. B 428, 221 (1998) [arXiv:nucl-th/9710073]CrossRefADSGoogle Scholar
  19. 19.
    J. Gegelia, Phys. Lett. B 429, 227 (1998).CrossRefADSGoogle Scholar
  20. 20.
    M.C. Birse, J.A. McGovern, K.G. Richardson, Phys. Lett. B 464, 169 (1999) [arXiv:hep-ph/9807302].zbMATHCrossRefADSMathSciNetGoogle Scholar
  21. 21.
    J.W. Chen, G. Rupak, M.J. Savage, Nucl. Phys. A 653, 386 (1999) [arXiv:nucl-th/9902056].CrossRefADSGoogle Scholar
  22. 22.
    E. Braaten, H.-W. Hammer, Phys. Rep. 428, 259 (2006) [arXiv:cond-mat/0410417].CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    V.N. Efimov, Sov. J. Nucl. Phys. 12, 589 (1971).Google Scholar
  24. 24.
    V.N. Efimov, Sov. J. Nucl. Phys. 29, 546 (1979).Google Scholar
  25. 25.
    K.G. Wilson, Phys. Rev. D 3, 1818 (1971).CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    V. Efimov, Nucl. Phys. A 362, 45 (1981).CrossRefADSGoogle Scholar
  27. 27.
    P.F. Bedaque, H.-W. Hammer, U. van Kolck, Nucl. Phys. A 676, 357 (2000) [arXiv:nucl-th/9906032].CrossRefADSGoogle Scholar
  28. 28.
    V. Efimov, E.G. Tkachenko, Phys. Lett. B 157, 108 (1985).CrossRefADSGoogle Scholar
  29. 29.
    H.-W. Hammer, T. Mehen, Phys. Lett. B 516, 353 (2001) [arXiv:nucl-th/0105072].CrossRefADSGoogle Scholar
  30. 30.
    P.F. Bedaque, G. Rupak, H.W. Grießhammer, H.-W. Hammer, Nucl. Phys. A 714, 589 (2003) [arXiv:nucl-th/0207034]. zbMATHCrossRefADSGoogle Scholar
  31. 31.
    L. Platter, D.R. Phillips, Few-Body Syst. 40, 35 (2006) [arXiv:cond-mat/0604255].CrossRefGoogle Scholar
  32. 32.
    L. Platter, Phys. Rev. C 74, 037001 (2006) [arXiv:nucl-th/0606006].CrossRefADSGoogle Scholar
  33. 33.
    H.W. Grießhammer, Nucl. Phys. A 760, 110 (2005) [arXiv:nucl-th/0502039].CrossRefADSGoogle Scholar
  34. 34.
    E. Epelbaum, H.-W. Hammer, U.-G. Meißner, A. Nogga, Eur. Phys. J. C 48, 169 (2006) [arXiv:hep-ph/0602225].CrossRefADSGoogle Scholar
  35. 35.
    U. van Kolck, Phys. Rev. C 49, 2932 (1994).CrossRefADSGoogle Scholar
  36. 36.
    E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 671, 295 (2000) [arXiv:nucl-th/9910064].CrossRefADSGoogle Scholar
  37. 37.
    M.R. Schindler, D. Djukanovic, J. Gegelia, S. Scherer, arXiv:hep-ph/0612164.Google Scholar
  38. 38.
    P. Büttiker, U.-G. Meißner, Nucl. Phys. A 668, 97 (2000) [arXiv:hep-ph/9908247].CrossRefADSGoogle Scholar
  39. 39.
    E. Matsinos, arXiv:hep-ph/9807395.Google Scholar
  40. 40.
    R.A. Arndt, W.J. Briscoe, I.I. Strakovsky, R.L. Workman, Phys. Rev. C 74, 045205 (2006) [arXiv:nucl-th/0605082].CrossRefADSGoogle Scholar
  41. 41.
    D.B. Kaplan, M.J. Savage, M.B. Wise, Nucl. Phys. B 478, 629 (1996) [arXiv:nucl-th/9605002].CrossRefADSGoogle Scholar
  42. 42.
    C. Ordonez, L. Ray, U. van Kolck, Phys. Rev. C 53, 2086 (1996) [arXiv:hep-ph/9511380].CrossRefADSGoogle Scholar
  43. 43.
    N. Kaiser, R. Brockmann, W. Weise, Nucl. Phys. A 625, 758 (1997) [arXiv:nucl-th/9706045].CrossRefADSGoogle Scholar
  44. 44.
    E. Epelbaum, private communication (2006).Google Scholar
  45. 45.
    H.-W. Hammer, T. Mehen, Nucl. Phys. A 690, 535 (2001) [arXiv:nucl-th/0011024].zbMATHCrossRefADSGoogle Scholar
  46. 46.
    I.R. Afnan, D.R. Phillips, Phys. Rev. C 69, 034010 (2004) [arXiv:nucl-th/0312021].CrossRefADSGoogle Scholar
  47. 47.
    P.F. Bedaque, H.-W. Hammer, U. van Kolck, Phys. Rev. Lett. 82, 463 (1999) [arXiv:nucl-th/9809025]CrossRefADSGoogle Scholar
  48. 48.
    Th. Mehen, I.W. Stewart, M.B. Wise, Phys. Rev. Lett. 83, 931 (1999) [arXiv:hep-ph/9902370].CrossRefADSGoogle Scholar
  49. 49.
    A. Nogga, private communication (2007).Google Scholar
  50. 50.
    G.V. Skorniakov, K.A. Ter-Martirosian, Sov. Phys. JETP 4, 648 (1957) (J. Exp. Theor. Phys. (U.S.S.R.) 31, 775 (1956)).MathSciNetGoogle Scholar
  51. 51.
    H.W. Grießhammer, Nucl. Phys. A 744, 192 (2004) [arXiv:nucl-th/0404073].CrossRefADSGoogle Scholar
  52. 52.
    V. Efimov, Phys. Rev. C 44, 2303 (1991).CrossRefADSGoogle Scholar
  53. 53.
    W. Dilg, L. Koester, W. Nistler, Phys. Lett. B 36, 208 (1971).CrossRefADSGoogle Scholar
  54. 54.
    T. Kraemer, M. Mark, P. Waldburger, J.G. Danzl, C. Chin, B. Engeser, A.D. Lange, K. Pilch, A. Jaakkola, H.-C. Nägerl, R. Grimm, Nature 440, 315 (2006).CrossRefADSGoogle Scholar
  55. 55.
    K.G. Wilson, Nucl. Phys. Proc. Suppl. 140, 3 (2005) [arXiv:hep-lat/0412043].CrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag 2007

Authors and Affiliations

  1. 1.Helmholtz-Institut für Strahlen- und Kernphysik (Theorie)Universität BonnBonnGermany
  2. 2.Department of Physics and AstronomyOhio UniversityAthensUSA

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