Skip to main content
SpringerLink
Log in

The pion-nucleon scattering lengths from pionic deuterium

  • theoretical physics
  • Published:
The European Physical Journal C - Particles and Fields Aims and scope Submit manuscript

An Erratum to this article was published on 25 November 2005

Abstract.

We use the framework of effective field theories to discuss the determination of the S-wave \(\pi N\) scattering lengths from the recent high-precision measurements of pionic deuterium observables. The theoretical analysis proceeds in several steps. Initially, the precise value of the pion-deuteron scattering length \(a_{\pi d}\) is extracted from the data. Next, \(a_{\pi d}\) is related to the S-wave \(\pi N\) scattering lengths a + and a -. We discuss the use of this information for constraining the values of these scattering lengths in the full analysis, which also includes the input from the pionic hydrogen energy shift and width measurements, and thoroughly investigate the accuracy limits for this procedure. In this paper, we also give a detailed comparison to other effective field theory approaches, as well as to the earlier work on the subject, carried out within the potential model and multiple scattering framework.

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. D. Chatellard et al. , Nucl. Phys. A 625, 855 (1997)

    Google Scholar 

  2. P. Hauser et al. , Phys. Rev. C 58, 1869 (1998)

    ADS  Google Scholar 

  3. S. Deser, M.L. Goldberger, K. Baumann, W. Thirring, Phys. Rev. 96, 774 (1954)

    Article  ADS  Google Scholar 

  4. H.C. Schröder et al. , Eur. Phys. J. C 21, 473 (2001)

    ADS  Google Scholar 

  5. I.R. Afnan, A.W. Thomas, Phys. Rev. C 10, 109 (1974)

    Article  ADS  Google Scholar 

  6. G. Fäldt, Phys. Scripta 16, 81 (1977)

    ADS  Google Scholar 

  7. T. Mizutani, D.S. Koltun, Annals Phys. 109, 1 (1977)

    Google Scholar 

  8. A.W. Thomas, R.H. Landau, Phys. Rept. 58, 121 (1980)

    Article  ADS  Google Scholar 

  9. A. Deloff, Phys. Rev. C 64, 065205 (2001) [nucl-th/0104067]

    Article  ADS  Google Scholar 

  10. V.V. Baru, A.E. Kudryavtsev, Phys. Atom. Nucl. 60, 1475 (1997) [Yad. Fiz. 60, 1620 (1997)]; V.V. Baru, A.E. Kudryavtsev, V.E. Tarasov, Phys. Atom. Nucl. 67, 743 (2004) [Yad. Fiz. 67, 764 (2004)] [nucl-th/0301021]

    ADS  Google Scholar 

  11. T.E.O. Ericson, B. Loiseau, A.W. Thomas, Phys. Rev. C 66, 014005 (2002) [hep-ph/0009312]

    Article  ADS  Google Scholar 

  12. V. Baru, C. Hanhart, A.E. Kudryavtsev, U.-G. Meißner, Phys. Lett. B 589, 118 (2004) [nucl-th/0402027]

    ADS  Google Scholar 

  13. G. Fäldt, C. Wilkin, quant-ph/9610032; A. Boudard, G. Fäldt, C. Wilkin, Phys. Lett. B 389, 440 (1996) [nucl-th/9609032]

    ADS  Google Scholar 

  14. S. Weinberg, Phys. Lett. B 295, 114 (1992) [hep-ph/9209257]

    ADS  Google Scholar 

  15. N. Kaiser, Phys. Rev. C 65, 057001 (2002) [nucl-th/0203001]

    ADS  Google Scholar 

  16. M. Döring, E. Oset, M.J. Vicente Vacas, Phys. Rev. C 70, 045203 (2004) [nucl-th/0402086]

    ADS  Google Scholar 

  17. S.R. Beane, V. Bernard, T.-S.H. Lee, U.-G. Meißner, Phys. Rev. C 57, 424 (1998) [nucl-th/9708035]

    Article  ADS  Google Scholar 

  18. B. Borasoy, H.W. Grießhammer, Int. J. Mod. Phys. E 12, 65 (2003) [nucl-th/0105048]

    ADS  Google Scholar 

  19. S.R. Beane, M.J. Savage, Nucl. Phys. A 717, 104 (2003) [nucl-th/0204046]

    ADS  Google Scholar 

  20. S.R. Beane, V. Bernard, E. Epelbaum, U.-G. Meißner, D.R. Phillips, Nucl. Phys. A 720, 399 (2003) [hep-ph/0206219]

    ADS  Google Scholar 

  21. H. Krebs, V. Bernard, U.-G. Meißner, Ann. Phys. 316, 160 (2005) [nucl-th/0407078]

    ADS  MATH  Google Scholar 

  22. B.F. Irgaziev, B.A. Fayzullaev, hep-ph/0404203

  23. A. Gall, J. Gasser, V.E. Lyubovitskij, A. Rusetsky, Phys. Lett. B 462, 335 (1999) [hep-ph/9905309]

    ADS  Google Scholar 

  24. J. Gasser, V.E. Lyubovitskij, A. Rusetsky, Phys. Lett. B 471, 244 (1999) [hep-ph/9910438]

    ADS  Google Scholar 

  25. J. Gasser, V.E. Lyubovitskij, A. Rusetsky, A. Gall, Phys. Rev. D 64, 016008 (2001) [hep-ph/0103157]

    Article  ADS  Google Scholar 

  26. J. Schweizer, Phys. Lett. B 587, 33 (2004) [hep-ph/0401048]; Eur. Phys. J. C 36, 483 (2004) [hep-ph/0405034]

    ADS  Google Scholar 

  27. V.E. Lyubovitskij, A. Rusetsky, Phys. Lett. B 494, 9 (2000) [hep-ph/0009206]

    ADS  Google Scholar 

  28. P. Zemp, in Proceedings of HadAtom03 Workshop, 13-17 October 2003, ECT* (Trento, Italy), hep-ph/0401204; J. Gasser, P. Zemp, in preparation

  29. U.-G. Meißner, U. Raha, A. Rusetsky, Eur. Phys. J. C 35, 349 (2004) [hep-ph/0402261]

    Article  ADS  Google Scholar 

  30. D. Sigg, A. Badertscher, P.F.A. Goudsmit, H.J. Leisi, G.C. Oades, Nucl. Phys. A 609, 310 (1996)

    ADS  Google Scholar 

  31. D. Eiras, J. Soto, Phys. Lett. B 491, 101 (2000) [hep-ph/0005066]

    ADS  Google Scholar 

  32. T.E.O. Ericson, B. Loiseau, S. Wycech, Phys. Lett. B 594, 76 (2004)

    ADS  Google Scholar 

  33. J. Bijnens, P. Talavera, JHEP 0203, 046 (2002) [hep-ph/0203049]

    ADS  Google Scholar 

  34. F. Schmidt-Kaler, D. Leibfried, M. Weitz, T.W. Hänsch, Phys. Rev. Lett. 70, 2261 (1993)

    Article  ADS  Google Scholar 

  35. U.-G. Meißner, S. Steininger, Phys. Lett. B 419, 403 (1998) [hep-ph/9709453]; G. Müller, U.-G. Meißner, Nucl. Phys. B 556, 265 (1999) [hep-ph/9903375]; N. Fettes, U.-G. Meißner, Nucl. Phys. A 693, 693 (2001) [hep-ph/0101030]

    ADS  Google Scholar 

  36. J. Gasser, M.A. Ivanov, E. Lipartia, M. Mojzis, A. Rusetsky, Eur. Phys. J. C 26, 13 (2002) [hep-ph/0206068]

    ADS  Google Scholar 

  37. U. van Kolck, UMI-94-01021; Few Body Syst. Suppl. 9, 444 (1995); E. Epelbaum, U.-G. Meißner, Phys. Lett. B 461, 287 (1999) [nucl-th/9902042]; J.L. Friar, U. van Kolck, Phys. Rev. C 60, 034006 (1999) [nucl-th/9906048]; M. Walzl, U.-G. Meißner, E. Epelbaum, Nucl. Phys. A 693, 663 (2001) [nucl-th/0010019]; E. Epelbaum, U.-G. Meißner, J.E. Palomar, Phys. Rev. C 71, 024001 (2005) [nucl-th/0407037]; J.L. Friar, G.L. Payne, U. van Kolck, Phys. Rev. C 71, 024003 (2005) [nucl-th/0408033];

    Google Scholar 

  38. D. Gotta, in Proceedings of the 8th International Workshop on Meson Production, Properties and Interaction, Krakow, Poland, 4-8 June 2004, Int. J. Mod. Phys. A 20 (2005)

  39. J.L. Friar, Few Body Syst. 22, 161 (1997) [nucl-th/9607020]

    ADS  Google Scholar 

  40. E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 747, 362 (2005) [nucl-th/0405048]

    ADS  Google Scholar 

  41. V. Bernard, N. Kaiser, U.-G. Meißner, Nucl. Phys. B 457, 147 (1995) [hep-ph/9507418]

    Article  ADS  MathSciNet  Google Scholar 

  42. E. Lipartia, V.E. Lyubovitskij, A. Rusetsky, Phys. Lett. B 533, 285 (2002) [hep-ph/0110186]

    ADS  Google Scholar 

  43. P. Büttiker et al. , in progress

  44. C. Garcia-Recio, E. Oset, L.L. Salcedo, Phys. Rev. C 37, 194 (1988); C. Garcia-Recio, J. Nieves, E. Oset, Nucl. Phys. A 547, 473 (1992)

    ADS  Google Scholar 

  45. J. Gasser, hep-ph/0412393

  46. V. Bernard, N. Kaiser, U.-G. Meißner, Nucl. Phys. A 615, 483 (1997) [hep-ph/9611253]

    ADS  MathSciNet  Google Scholar 

  47. L. Alvarez-Ruso, E. Oset, E. Hernandez, Nucl. Phys. A 633, 519 (1998) [nucl-th/9706046]

    ADS  Google Scholar 

  48. G. Ecker, J. Gasser, A. Pich, E. de Rafael, Nucl. Phys. B 321, 311 (1989)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität Bonn, Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), Nußallee 14-16, 53115, Bonn, Germany

    U.-G. Meißner, U. Raha & A. Rusetsky

  2. Forschungszentrum Jülich, Institut für Kenphysik (Theorie), 52425, Jülich, Germany

    U.-G. Meißner

Authors
  1. U.-G. Meißner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. U. Raha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Rusetsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 28 January 2005, Published online: 8 April 2005

PACS:

36.10.Gv, 12.39.Fe, 13.75.Cs, 13.75.Gx

A. Rusetsky: On leave of absence from High Energy Physics Institute, Tbilisi State University, University St. 9, 380086 Tbilisi, Georgia.

This research is part of the EU Integrated Infrastructure Initiative Hadron Physics Project under contract number RII3-CT-2004-506078. Work supported in part by DFG (SFB/TR 16, “Subnuclear Structure of Matter”).

An erratum to this article is available at http://dx.doi.org/10.1140/epjc/s2005-02444-1.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meißner, UG., Raha, U. & Rusetsky, A. The pion-nucleon scattering lengths from pionic deuterium. Eur. Phys. J. C 41, 213–232 (2005). https://doi.org/10.1140/epjc/s2005-02182-4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s2005-02182-4

Keywords

Search

Navigation