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Prog. Theor. Phys. Vol. 35 No. 4 (1966) pp. 692-704

[ Full Text PDF : FREE ACCESS (607K) ]

N/D Methods for Multichannel Scattering

Masakuni Ida

Institute of Physics, College of General Education, University of Tokyo, Komaba, Tokyo

(Received December 10, 1965)

Abstract:

Two-particle multichannel scattering is investigated in a state which has a one-particle intermediate state. The elementarity or compositeness of this particle is reflected on the asymptotic behavior of various functions. Our discussion is based on the decomposition of the partial wave scattering amplitude into its one-particle reducible and irreducible parts. The present approach, which applies a matrix N/D method to the latter part, is shown to be equivalent to Bjorken's N/D method for the full amplitude. Compositeness conditions for multichannel scattering are obtained by considering transitions from an elementary or intermediate type of solution to a composite one. Also given are some remarks on generalizing the present work so as to include three-particle states.


URL : http://ptp.ipap.jp/link?PTP/35/692/
DOI : 10.1143/PTP.35.692

[ Full Text PDF : FREE ACCESS (607K) ] Citation:

References:

  1. For earlier references see, for instance, reference 2).
  2. M. Ida, Prog. Theor. Phys. 34 (1965), 92[PTP]. This paper will be referred to as I.
  3. T. Akiba, S. Saito and F. Takagi, Nuovo Cim. 39 (1965), 316.
  4. R. Blankenbecler, M. L. Goldberger, N. N. Khuri and S. B. Treiman, Ann. of Phys. 10 (1960), 62[CrossRef].
  5. M. Ida, Phys. Rev. 135 (1964), B 499[APS].
  6. K. Kinoshita and H. Yabuki, Prog. Theor. Phys. 34 (1965), 825[PTP]; ibid. 34 (1965), 981[PTP].
  7. M. Ida, Prog. Theor. Phys. 34 (1965), 990[PTP]. This paper will be referred to as II.
  8. P. E. Kaus and F. Zachariasen, Phys. Rev. 138 (1965), B 1304[APS].
  9. J. D. Bjorken, Phys. Rev. Lett. 4 (1960), 473[APS].
    S. W. MacDowell, Phys. Rev. Lett. 6 (1961), 385[APS].
  10. T. Akiba, to be published.
  11. J. D. Bjorken and M. Nauenberg, Phys. Rev. 121 (1961), 1250[APS].
    A. W. Martin, Phys. Rev. 135 (1964), B 967[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 36 No. 1 (1966) pp. 138-147 :
    Multichannel Scattering and Equivalence between Four-Fermion and Yukawa Coupling
    Haruichi Yabuki
  2. Progress of Theoretical Physics Vol. 36 No. 4 (1966) pp. 781-798 :
    Classification of an Unstable Particle and Its Propagator
    Masayuki Uehara
  3. Progress of Theoretical Physics Vol. 38 No. 1 (1967) pp. 246-260 :
    Compositeness Condition and Propagator
    Takeshi Shirafuji
  4. Progress of Theoretical Physics Vol. 38 No. 3 (1967) pp. 705-714 :
    The Double N/D Method
    Kisei Kinoshita

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