On kinematical constraints in the hadrogenesis conjecture for the baryon resonance spectrum

Regular Article - Theoretical Physics

Abstract

We consider the reaction dynamics of bosons with negative parity and spin 0 or 1 and fermions with positive parity and spin \(\tfrac{1} {2}\) or \(\tfrac{3} {2}\). Such systems are of central importance for the computation of the baryon resonance spectrum in the hadrogenesis conjecture. Based on a chiral Lagrangian the coupled-channel partial-wave scattering amplitudes have to be computed. We study the generic properties of such amplitudes. A decomposition of the various scattering amplitudes into suitable sets of invariant functions expected to satisfy Mandelstam’s dispersion-integral representation is presented. Sets are identified that are free from kinematical constraints and that can be computed efficiently in terms of a novel projection algebra. From such a representation one can deduce the analytic structure of the partial-wave amplitudes. The helicity and the conventional angular-momentum partial-wave amplitudes are kinematically constrained at the Kibble conditions. Therefore an application of a dispersion-integral representation is prohibitively cumbersome. We derive covariant partial-wave amplitudes that are free from kinematical constraints at the Kibble conditions. They correspond to specific polynomials in the 4-momenta and Dirac matrices that solve the various Bethe-Salpeter equations in the presence of short-range interactions analytically.

References

  1. 1.
    M.F.M. Lutz, E.E. Kolomeitsev, Found. Phys. 31, 1671 (2001).CrossRefGoogle Scholar
  2. 2.
    M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A 700, 193 (2002).ADSCrossRefGoogle Scholar
  3. 3.
    M.F.M. Lutz, G. Wolf, B. Friman, Nucl. Phys. A 706, 431 (2002).ADSCrossRefGoogle Scholar
  4. 4.
    M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A 730, 392 (2004).ADSCrossRefGoogle Scholar
  5. 5.
    E.E. Kolomeitsev, M.F.M. Lutz, Phys. Lett. B 585, 243 (2004).ADSCrossRefGoogle Scholar
  6. 6.
    M.F.M. Lutz, E.E. Kolomeitsev, C.L. Korpa, Prog. Theor. Phys. Suppl. 156, 51 (2004).ADSCrossRefGoogle Scholar
  7. 7.
    M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A 755, 29 (2005).ADSCrossRefGoogle Scholar
  8. 8.
    Matthias F.M. Lutz, Madeleine Soyeur, Nucl. Phys. A 813, 14 (2008).ADSCrossRefGoogle Scholar
  9. 9.
    M.F.M. Lutz, S. Leupold, Nucl. Phys. A 813, 96 (2008).ADSCrossRefGoogle Scholar
  10. 10.
    C. Terschlüsen, S. Leupold, M.F.M. Lutz, Eur. Phys. J. A 48, 190 (2012).ADSCrossRefGoogle Scholar
  11. 11.
    Norbert Kaiser, P.B. Siegel, W. Weise, Phys. Lett. B 362, 23 (1995).ADSCrossRefGoogle Scholar
  12. 12.
    C. Garcia-Recio, M.F.M. Lutz, J. Nieves, Phys. Lett. B 582, 49 (2004).ADSCrossRefGoogle Scholar
  13. 13.
    M.F.M. Lutz, C. Garcia-Recio, E.E. Kolomeitsev, J. Nieves, Nucl. Phys. A 754, 212 (2005).ADSCrossRefGoogle Scholar
  14. 14.
    C. Ordonez, L. Ray, U. van Kolck, Phys. Rev. C 53, 2086 (1996).ADSCrossRefGoogle Scholar
  15. 15.
    Matthias Lutz, Nucl. Phys. A 677, 241 (2000).CrossRefGoogle Scholar
  16. 16.
    Evgeny Epelbaum, Hans-Werner Hammer, Ulf-G. Meissner, Rev. Mod. Phys. 81, 1773 (2009).ADSCrossRefGoogle Scholar
  17. 17.
    A.M. Gasparyan, M.F.M. Lutz, E. Epelbaum, Eur. Phys. J. A 49, 115 (2013).ADSCrossRefGoogle Scholar
  18. 18.
    O. Romanets, L. Tolos, C. Garcia-Recio, J. Nieves, L.L. Salcedo et al., Phys. Rev. D 85, 114032 (2012).ADSCrossRefGoogle Scholar
  19. 19.
    M.F.M. Lutz, A. Semke, Phys. Rev. D 83, 034008 (2011).ADSCrossRefGoogle Scholar
  20. 20.
    M.F.M. Lutz, D. Samart, A. Semke, Phys. Rev. D 84, 096015 (2011).ADSCrossRefGoogle Scholar
  21. 21.
    M.F.M. Lutz, D. Samart, Y. Yan, Combined large-Nc and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons, arXiv:1402.6427 (2014).
  22. 22.
    A. Gasparyan, M.F.M. Lutz, Nucl. Phys. A 848, 126 (2010).ADSCrossRefGoogle Scholar
  23. 23.
    I.V. Danilkin, A.M. Gasparyan, M.F.M. Lutz, Phys. Lett. B 697, 147 (2011).ADSCrossRefGoogle Scholar
  24. 24.
    A.M. Gasparyan, M.F.M. Lutz, B. Pasquini, Nucl. Phys. A 866, 79 (2011).ADSCrossRefGoogle Scholar
  25. 25.
    I.V. Danilkin, L.I.R. Gil, M.F.M. Lutz, Phys. Lett. B 703, 504 (2011).ADSCrossRefGoogle Scholar
  26. 26.
    I.V. Danilkin, M.F.M. Lutz, S. Leupold, C. Terschlusen, Eur. Phys. J. C 73, 2358 (2013).ADSCrossRefGoogle Scholar
  27. 27.
    Porter W. Johnson, Robert Lee Warnock, J. Math. Phys. 22, 385 (1981).ADSCrossRefMathSciNetGoogle Scholar
  28. 28.
    L.D. Landau, Nucl. Phys. 13, 181 (1959).CrossRefMATHGoogle Scholar
  29. 29.
    M. Jacob, G.C. Wick, Ann. Phys. 7, 404 (1959).ADSCrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    G.F. Chew, M.L. Goldberger, F.E. Low, Yoichiro Nambu, Phys. Rev. 106, 1345 (1957).ADSCrossRefMATHMathSciNetGoogle Scholar
  31. 31.
    Noboru Nakanishi, J. Math. Phys. 3, 1139 (1962).ADSCrossRefGoogle Scholar
  32. 32.
    Frits A. Berends, A. Donnachie, D.L. Weaver, Nucl. Phys. B 4, 1 (1967).ADSCrossRefGoogle Scholar
  33. 33.
    M.F.M. Lutz, C.L. Korpa, Nucl. Phys. A 700, 309 (2002).ADSCrossRefGoogle Scholar
  34. 34.
    M.F.M. Lutz, C.L. Korpa, M. Moller, Nucl. Phys. A 808, 124 (2008).ADSCrossRefGoogle Scholar
  35. 35.
    C.L. Korpa, M.F.M. Lutz, F. Riek, Phys. Rev. C 80, 024901 (2009).ADSCrossRefGoogle Scholar
  36. 36.
    M.F.M. Lutz, I. Vidana, Eur. Phys. J. A 48, 124 (2012).ADSCrossRefGoogle Scholar
  37. 37.
    S. Stoica, M.F.M. Lutz, O. Scholten, Phys. Rev. D 84, 125001 (2011).ADSCrossRefGoogle Scholar
  38. 38.
    Juan Nieves, Enrique Ruiz Arriola, Nucl. Phys. A 679, 57 (2000).ADSCrossRefGoogle Scholar
  39. 39.
    James Stutsman Ball, Phys. Rev. 124, 2014 (1961).CrossRefMATHMathSciNetGoogle Scholar
  40. 40.
    Asim O. Barut, Ivan Muzinich, David N. Williams, Phys. Rev. 130, 442 (1963).ADSCrossRefMATHMathSciNetGoogle Scholar
  41. 41.
    Yasuo Hara, Phys. Rev. 136, B507 (1964).CrossRefGoogle Scholar
  42. 42.
    J.D. Jackson, G.E. Hite, Phys. Rev. 169, 1248 (1968).ADSCrossRefGoogle Scholar
  43. 43.
    Ling-Lie Chau Wang, Phys. Rev. 142, 1187 (1966).ADSCrossRefGoogle Scholar
  44. 44.
    Jerrold Franklin, Phys. Rev. 170, 1606 (1968).CrossRefGoogle Scholar
  45. 45.
    M.D. Scadron, H.F. Jones, Phys. Rev. 173, 1734 (1968).ADSCrossRefGoogle Scholar
  46. 46.
    G. Cohen-Tannoudji, A. Morel, H. Navelet, Ann. Phys. 46, 239 (1968).ADSCrossRefGoogle Scholar
  47. 47.
    William A. Bardeen, W.K. Tung, Phys. Rev. 173, 1423 (1968).ADSCrossRefGoogle Scholar
  48. 48.
    S.W. MacDowell, Phys. Rev. 116, 774 (1959).ADSCrossRefMATHMathSciNetGoogle Scholar
  49. 49.
    F.F.K. Cheung, Fei Shian Chen-Cheung, Phys. Rev. D 5, 970 (1972).ADSCrossRefGoogle Scholar
  50. 50.
    S. Mandelstam, Phys. Rev. 112, 1344 (1958).ADSCrossRefMathSciNetGoogle Scholar
  51. 51.
    J. Nieves, E. Ruiz Arriola, Phys. Rev. D 64, 116008 (2001).ADSCrossRefGoogle Scholar
  52. 52.
    Peter C. Bruns, Maxim Mai, Ulf G. Meissner, Phys. Lett. B 697, 254 (2011).ADSCrossRefGoogle Scholar
  53. 53.
    William R. Frazer, Jose R. Fulco, Phys. Rev. 119, 1420 (1960).ADSCrossRefMATHMathSciNetGoogle Scholar
  54. 54.
    Yu-Chien Liu, I.J. Mcgee, Phys. Rev. D 3, 183 (1971).ADSCrossRefGoogle Scholar
  55. 55.
    T.W.B. Kibble, Phys. Rev. 117, 1159 (1960).ADSCrossRefMATHMathSciNetGoogle Scholar
  56. 56.
    A. Semke, M.F.M. Lutz, Nucl. Phys. A 778, 153 (2006).ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.GSI Helmholtzzentrum für Schwerionenforschung GmbHDarmstadtGermany

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