Prog. Theor. Phys. Vol. 38 No. 3 (1967) pp. 705-714

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The Double N/D Method

— A New Approach to the Construction of the Partial-Wave Amplitude —

Kisei Kinoshita

Department of Physics, University of Tokyo, Tokyo

(Received May 2, 1967)

Abstract:

A method of obtaining the partial-wave amplitude by two steps is proposed, if the amplitude is written as T = t+r where t satisfies the unitarity relation by itself: first t is solved by the N/D method, and then r is solved with the solution of t and the left-hand discontinuity of r as inputs by using the N/D method again. It is proved that the particle pole of T appears in r, not in t.
As an interesting application, three examples are discussed: these are the addition of the modified Born term, the channel coupling effects, the effects of the small change of the left-hand discontinuity. For the last case the shifts of the mass and the coupling constant are practically the same as those derived by Dashen and Frautschi, although their derivation is very questionable.

URL : http://ptp.ipap.jp/link?PTP/38/705/
DOI : 10.1143/PTP.38.705

References:

M. Ida, Phys. Rev. 135 (1964), B499[APS].
M. Ida, Prog. Theor. Phys. 34 (1965), 92[PTP]; ibid. 35 (1966), 692[PTP].
T. Akiba, S. Saito and F. Takagi, Nuovo Cim. 39 (1965), 316.
T. Akiba, Nuovo Cim. 43 (1966), A939.
R. Dashen and S. Frautschi, Phys. Rev. 135 (1964), B1190[APS]; ibid. 137 (1965), B1318[APS].
G. F. Chew and S. Mandelstam, preprint UCRL-8728 (unpublished).
J. D. Björken, Phys. Rev. Lett. 4 (1960), 473[APS].
Y. S. Jin and S. W. MacDowell, Phys. Rev. 137 (1965), B688[APS].
See also
T. Saito, Phys. Rev. 152 (1966), 1339[APS].
N. Nakanishi, J. Math. Phys. 7 (1966), 698[CrossRef].
T. N. Truong, Phys. Rev. Lett. 17 (1966), 1102 [APS][ Errata; 18 (1967), 300[APS]].
K. Kinoshita, Prog. Theor. Phys. 38 (1967), 283[PTP].
P. Nath and G. L. Shaw, Phys. Rev. 137 (1965), B711[APS].

Citing Article(s) :

Progress of Theoretical Physics Vol. 39 No. 1 (1968) pp. 108-117 :
Effect of Hidden Channels on Low-Lying Channels

Kisei Kinoshita, Yukiko Kinoshita and Nobuyuki Murai
Progress of Theoretical Physics Vol. 41 No. 4 (1969) pp. 1046-1056 :
Dynamical Implication of the πN P₁₁ Data

Kisei Kinoshita
Progress of Theoretical Physics Vol. 42 No. 3 (1969) pp. 629-640 :
Inelastic Resonances with the Repulsive Background

Yukiko Kinoshita