Cancellation of the Singularities of the Backward Unequal-Mass Regge-Pole Terms

Abstract

In terms of the contour integrals in the s plane, the Kim-Resnikoff mechanism with moving poles is studied to what extent it can be identified with that of Freedman and Wang. The method of the contour integrals is also suggested to be appropriate in under­ standing the multiple-pole theory recently given by Nakanishi. 0° Recently, Kim and Resnikoff 1 ),*) developed a method of reqUlrmg the Mandelstam analyticity for the Regge-pole term for unequal-mass particles in the' backward region (s = 0), and obtained, without introducing the daughter trajec­ tories,2)a modified Regge-pole term which is truly analytic at s = 0 and behaves asymptotically like ua(O). Furthermore, according to their result, the next largest term of the modified amplitude is proportional to which also shows up in the Freedman-Wang formulation (see Eq. (7) in refer­ ence 3)). In the latter formulation, this term results form the existence of the polar singularity of order two (<<double pole») at s = 0 in the Khuri plane, as is clear from the recent work by Nakanishi. 4 ) In the Kim-Resnikoff formulation, on the other hand, the presence of this term is connected with the implicit in­ troduction of a fixed Regge pole which probably serves as a substitute for daughter poles. There is, however, a 'criticism 5 ) on the existence of fixed Regge poles since it may contradict the miitarity condition. In this paper, we try to modify the mechanism essentially used , by Kim and Resnikoff in a plausible form which gives moving poles, and we intend to bring about a simpler understanding of the connection between the Kim-Resnikoff ,manipulation and the mechanism based on daughter poles. To this end, we will start by representing the Regge-pole term by a contour integral in the s plane, t6 the effect that the cancellation is regarded as the removal of the pinch of the integration path. We will intensionally show *) There appeared quite recently a work by Caser and Basdeyant,la) in which the technique