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Prog. Theor. Phys. Vol. 32 No. 1 (1964) pp. 126-137

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The N/D Method and the Pion-Pion Scattering

Toshimi Adachi, Ryuji Kawamura* and Tsuneyuki Kotani*

The Tokyo Metropolitan Technical College, Sinagawa, Tokyo
*Department of Physics, Tokyo Metropolitan University, Setagaya, Tokyo

(Received March 9, 1964)

Abstract:

In most of recent calculations based on the N/D formalism, the N function is replaced by the appropriate Born terms. Thus the resulting amplitude, N/D, includes a normalization point s0. This s0, dependence is not small. If the coupled integral equations for N and D are solved, then N/D should have no s0, dependence. If the left hand singularities are approximated by a set of poles, the integral equation for N can be solved analytically. The amplitude N/D is expressed by an analytic function which does not involve s0. The relations between a resonance position (m) and its reduced width (γ2) are determined without any arbitrariness, in principle. This method is applied to the p-wave pion-pion resonance. It is shown that self-consistency can not be achieved for any reasonable values of m and γ2, if we assume the Born term due to the ρ meson exchange as the left hand cut. In order to make a bootstrap mechanism operative, such effects as to make scattering amplitudes less singular at laeger negative energies have to be taken into account. They may be substituted by introducing a phenomenological cutoff.


URL : http://ptp.ipap.jp/link?PTP/32/126/
DOI : 10.1143/PTP.32.126

[ Full Text PDF : FREE ACCESS (712K) ] Citation:

References:

  1. See, e.g., R. H. Capps, Phys. Rev. 131 (1963), 1307[APS]; ibid. 132 (1963), 2749[APS].
    A. W. Martin and K. C. Wali, Phys. Rev. 130 (1963), 2455[APS].
  2. G. F. Chew and S. Mandelstam, Phys. Rev. 119 (1960), 467[APS].
  3. G. F. Chew and S. Mandelstam, Nuovo Cim. 14 (1961), 752.
  4. F. Zachariasen, Phys. Rev. Lett. 7 (1961), 112[APS].
  5. G. F. Chew, S-Matrix Theory of Strong Interaction (W. A. Benjamin, Inc., New York, 1961), p. 52.
  6. B. Diu, J. L. Gervais and H. R. Rubinstein, Phys. Lett. 4 (1963), 280[CrossRef].
  7. S. C. Frautschi and J. D. Walecka, Phys. Rev. 120 (1960), 1486[APS].
  8. J. L. Uretsky, Phys. Rev. 123 (1961), 1459[APS].
  9. E. Abers and C. Zemach, Phys. Rev. 131 (1963), 2305[APS].
  10. F. Zachariasen and C. Zemach, Phys. Rev. 128 (1962), 849[APS].
  11. H. Kanada and K. Watanabe, Prog. Theor. Phys. 32 (1964), 254[PTP].
  12. A. P. Balázs, Phys. Rev. 128 (1962), 1939[APS].
  13. S. Okubo, Prog. Theor. Phys. 27 (1962), 949[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 32 No. 1 (1964) pp. 169-171 :
    On the Solution of the N/D Method
    Toshimi Adachi and Tsuneyuki Kotani
  2. Progress of Theoretical Physics Vol. 33 No. 6 (1965) pp. 1107-1115 :
    Variational Principles in the Coupled Channel N/D Method
    Keiji Kikkawa
  3. Progress of Theoretical Physics Vol. 40 No. 2 (1968) pp. 403-411 :
    Reggeized Short Range Potential and Resonance Width
    Michiko Imoto

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