Dynamical coupled-channel approaches on a momentum lattice

  • M. Döring
  • J. Haidenbauer
  • U. -G. Meißner
  • A. Rusetsky
Regular Article - Theoretical Physics

Abstract

Dynamical coupled-channel approaches are a widely used tool in hadronic physics that allow to analyze different reactions and partial waves in a consistent way. In such approaches the basic interactions are derived within an effective Lagrangian framework and the resulting pseudo-potentials are then unitarized in a coupled-channel scattering equation. We propose a scheme that allows for a solution of the arising integral equation in discretized momentum space for periodic as well as anti-periodic boundary conditions. This permits to study finite-size effects as they appear in lattice QCD simulations. The new formalism, at this stage with a restriction to S -waves, is applied to coupled-channel models for the σ(600), f0(980), and a0(980) mesons, and also for the Λ(1405) baryon. Lattice spectra are predicted.

References

  1. 1.
    E. Klempt, J.M. Richard, Rev. Mod. Phys. 82, 1095 (2010) arXiv:0901.2055 [hep-ph].ADSCrossRefGoogle Scholar
  2. 2.
    O. Krehl, C. Hanhart, S. Krewald, J. Speth, Phys. Rev. C 62, 025207 (2000) arXiv:nucl-th/9911080.ADSCrossRefGoogle Scholar
  3. 3.
    A.M. Gasparyan, J. Haidenbauer, C. Hanhart, J. Speth, Phys. Rev. C 68, 045207 (2003) arXiv:nucl-th/0307072.ADSCrossRefGoogle Scholar
  4. 4.
    M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, Phys. Lett. B 681, 26 (2009) arXiv:0903.1781 [nucl-th].ADSCrossRefGoogle Scholar
  5. 5.
    M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, Nucl. Phys. A 829, 170 (2009) arXiv:0903.4337 [nucl-th].ADSCrossRefGoogle Scholar
  6. 6.
    M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, D. Rönchen, Nucl. Phys. A 851, 58 (2011) arXiv:1009.3781 [nucl-th].ADSCrossRefGoogle Scholar
  7. 7.
    F. Huang, M. Döring, H. Haberzettl, J. Haidenbauer, C. Hanhart, S. Krewald, U.-G. Meißner, K. Nakayama, arXiv:1110.3833 [nucl-th].
  8. 8.
    B. Juliá Díaz, T.S. Lee, A. Matsuyama, T. Sato, Phys. Rev. C 76, 065201 (2007) arXiv:0704.1615 [nucl-th].ADSCrossRefGoogle Scholar
  9. 9.
    M.W. Paris, Phys. Rev. C 79, 025208 (2009) arXiv:0802.3383 [nucl-th].ADSCrossRefGoogle Scholar
  10. 10.
    L. Tiator, S.S. Kamalov, S. Ceci, G.Y. Chen, D. Drechsel, A. Svarc, S.N. Yang, Phys. Rev. C 82, 055203 (2010) arXiv:1007.2126 [nucl-th].ADSCrossRefGoogle Scholar
  11. 11.
    S. Dürr et al., Science 322, 1224 (2008) arXiv:0906.3599 [hep-lat].ADSCrossRefGoogle Scholar
  12. 12.
    UKQCD Collaboration (C. McNeile, C. Michael), Phys. Rev. D 74, 014508 (2006) arXiv:hep-lat/0604009.ADSCrossRefGoogle Scholar
  13. 13.
    N. Mathur, A. Alexandru, Y. Chen et al., Phys. Rev. D 76, 114505 (2007) arXiv:hep-ph/0607110.ADSCrossRefGoogle Scholar
  14. 14.
    J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards, C.E. Thomas, Phys. Rev. Lett. 103, 262001 (2009) arXiv:0909.0200 [hep-ph].ADSCrossRefGoogle Scholar
  15. 15.
    J. Bulava et al., Phys. Rev. D 82, 014507 (2010) arXiv:1004.5072 [hep-lat].ADSCrossRefGoogle Scholar
  16. 16.
    BGR Collaboration (G.P. Engel, C.B. Lang, M. Limmer, D. Mohler, A. Schäfer), Phys. Rev. D 82, 034505 (2010) arXiv:1005.1748 [hep-lat].ADSCrossRefGoogle Scholar
  17. 17.
    V. Bernard, U.-G. Meißner, A. Rusetsky, Nucl. Phys. B 788, 1 (2008) arXiv:hep-lat/0702012.ADSCrossRefGoogle Scholar
  18. 18.
    V. Bernard, M. Lage, U.-G. Meißner, A. Rusetsky, JHEP 08, 024 (2008) arXiv:0806.4495 [hep-lat].ADSCrossRefGoogle Scholar
  19. 19.
    M. Lüscher, Commun. Math. Phys. 105, 153 (1986).ADSCrossRefGoogle Scholar
  20. 20.
    M. Lüscher, Nucl. Phys. B 354, 531 (1991).ADSCrossRefGoogle Scholar
  21. 21.
    CLQCD Collaboration (X. Li et al.), JHEP 06, 053 (2007) arXiv:hep-lat/0703015.Google Scholar
  22. 22.
    M. Lage, U.-G. Meißner, A. Rusetsky, Phys. Lett. B 681, 439 (2009) arXiv:0905.0069 [hep-lat].ADSCrossRefGoogle Scholar
  23. 23.
    V. Bernard, M. Lage, U.-G. Meißner, A. Rusetsky, JHEP 01, 019 (2011) arXiv:1010.6018 [hep-lat].ADSCrossRefGoogle Scholar
  24. 24.
    M. Döring, U.-G. Meißner, E. Oset, A. Rusetsky, Eur. Phys. J. A 47, 139 (2011) arXiv:1107.3988 [hep-lat].ADSCrossRefGoogle Scholar
  25. 25.
    M. Döring, U.-G. Meißner, to be published in JHEP, arXiv:1111.0616 [hep-lat].
  26. 26.
    G. Janssen, B.C. Pearce, K. Holinde, J. Speth, Phys. Rev. D 52, 2690 (1995) arXiv:nucl-th/9411021.ADSCrossRefGoogle Scholar
  27. 27.
    O. Krehl, R. Rapp, J. Speth, Phys. Lett. B 390, 23 (1997) arXiv:nucl-th/9609013.ADSCrossRefGoogle Scholar
  28. 28.
    A. Müller-Groeling, K. Holinde, J. Speth, Nucl. Phys. A 513, 557 (1990).ADSCrossRefGoogle Scholar
  29. 29.
    J. Haidenbauer, G. Krein, U.-G. Meißner, L. Tolos, Eur. Phys. J. A 47, 18 (2011) arXiv:1008.3794 [nucl-th].ADSCrossRefGoogle Scholar
  30. 30.
    R. Aaron, R.D. Amado, Phys. Rev. 150, 857 (1966).ADSCrossRefGoogle Scholar
  31. 31.
    M. Haftel, F. Tabakin, Nucl. Phys. A 158, 1 (1970).ADSCrossRefGoogle Scholar
  32. 32.
    For tabulated numbers and further references see, e.g., The On-Line Encyclopedia of Integer Sequences, http://oeis.org/A005875 for the ϑ(P) series and http://oeis.org/A008443 for the ϑ(A) series.
  33. 33.
    J.A. Oller, E. Oset, Nucl. Phys. A 620, 438 (1997) (E) 652.ADSCrossRefGoogle Scholar
  34. 34.
    N. Kaiser, Eur. Phys. J. A 3, 307 (1998).ADSCrossRefGoogle Scholar
  35. 35.
    J.A. Oller, E. Oset, J.R. Pelaez, Phys. Rev. D 59, 074001 (1999) (E) 60.ADSCrossRefGoogle Scholar
  36. 36.
    U.-G. Meißner, J.A. Oller, Nucl. Phys. A 673, 311 (2000) arXiv:nucl-th/9912026.ADSCrossRefGoogle Scholar
  37. 37.
    E. Oset, A. Ramos, Nucl. Phys. A 635, 99 (1998) arXiv:nucl-th/9711022.ADSCrossRefGoogle Scholar
  38. 38.
    D. Jido, J.A. Oller, E. Oset, A. Ramos, U.-G. Meißner, Nucl. Phys. A 725, 181 (2003).ADSCrossRefGoogle Scholar
  39. 39.
    C. Garcia-Recio, M.F.M. Lutz, J. Nieves, Phys. Lett. B 582, 49 (2004) arXiv:nucl-th/0305100.ADSCrossRefGoogle Scholar
  40. 40.
  41. 41.
    H. Suganuma, K. Tsumura, N. Ishii, F. Okiharu, PoS LAT2005, 070 (2006) arXiv:hep-lat/0509121.Google Scholar
  42. 42.
    H. Suganuma, K. Tsumura, N. Ishii, F. Okiharu, Prog. Theor. Phys. Suppl. 168, 168 (2007) arXiv:0707.3309 [hep-lat].ADSCrossRefGoogle Scholar
  43. 43.
    V. Baru, J. Haidenbauer, C. Hanhart, Yu. Kalashnikova, A.E. Kudryavtsev, Phys. Lett. B 586, 53 (2004) arXiv:hep-ph/0308129.ADSCrossRefGoogle Scholar
  44. 44.
    V. Baru, J. Haidenbauer, C. Hanhart, A.E. Kudryavtsev, U.-G. Meißner, Eur. Phys. J. A 23, 523 (2005) arXiv:nucl-th/0410099.ADSCrossRefGoogle Scholar
  45. 45.
    M. Döring, Nucl. Phys. A 786, 164 (2007) arXiv:nucl-th/0701070.ADSCrossRefGoogle Scholar
  46. 46.
    M. Döring, K. Nakayama, Eur. Phys. J. A 43, 83 (2010) arXiv:0906.2949 [nucl-th].ADSCrossRefGoogle Scholar
  47. 47.
    P.C. Bruns, M. Mai, U.-G. Meißner, Phys. Lett. B 697, 254 (2011) arXiv:1012.2233 [nucl-th].ADSCrossRefGoogle Scholar
  48. 48.
    A.M. Torres, L.R. Dai, C. Koren, D. Jido, E. Oset, arXiv:1109.0396 [hep-lat].
  49. 49.
    Particle Data Group Collaboration (K. Nakamura et al.), J. Phys. G 37, 075021 (2010).ADSCrossRefGoogle Scholar
  50. 50.
    M. Albaladejo, J.A. Oller, C. Piqueras, Int. J. Mod. Phys. A 24, 581 (2009) arXiv:0804.2341 [hep-ph].ADSCrossRefGoogle Scholar
  51. 51.
    J.A. Oller, U.-G. Meißner, Phys. Lett. B 500, 263 (2001) arXiv:hep-ph/0011146.ADSCrossRefGoogle Scholar
  52. 52.
    B.J. Menadue, W. Kamleh, D.B. Leinweber, M.S. Mahbub, arXiv:1109.6716 [hep-lat].

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • M. Döring
    • 1
  • J. Haidenbauer
    • 2
    • 3
  • U. -G. Meißner
    • 1
    • 2
    • 3
  • A. Rusetsky
    • 1
  1. 1.Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical PhysicsUniversität BonnBonnGermany
  2. 2.Institute for Advanced Simulation and Jülich Center for Hadron PhysicsForschungszentrum JülichJülichGermany
  3. 3.Institut für KernphysikForschungszentrum JülichJülichGermany

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