Summary
The kinematics of the Regge-pole amplitude and the partialwave amplitude in the study of the scattering of particles of high spins is evolved from the spinless case through a simple differentiation procedure. In particular, the Regge-pole contribution, suitably modified to conform to the basic Mandelstam cut structure, to the scattering amplitude of arbitrary helicities is constructed. A new modified Regge-pole contribution with square-root branch point is proposed.
Riassunto
Per mezzo di un semplice procedimento di differenziazione, si sviluppa la cinematica dell’ampiezza dei poli di Regge e dell’ampiezza dell’onda parziale nello studio dello scattering delle particelle di spin elevato, partendo dal caso senza spin. In particolare, il contributo del polo di Regge all’ampiezza di scattering delle elicità arbitrarie si costruisce tenendo presenti le modifiche necessarie perchè si addattino alla struttura fondamentale del taglio di Mandelstam. Si propone un nuovo contributo modificato del polo di Regge con punto di ramificazione in radice quadrata.
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Literatur
T. W. B. Kibble:Phys. Rev.,134, 2282 (1963). We shall assume in the following that bothλ andμ are either integers or half-integers and no analytic continuation to nonphysical values of these parameters will be made.
A. Erdelyi, W. Magnus, F. Oberhettinger andF. G. Tricomi:Higher Transcendental Functions, Vol.1 (New York, 1953), p. 102.
N. N. Khuri:Phys. Rev.,130, 429 (1963).
E. Jone: Lawrence Radiation Laboratory Report UCRL-10700 (1963).
A somewhat different type of relation has been obtained byM. Gell-Mann, M. L. Goldberger, F. E. Low, E. Marx andF. Zachariasen:Phys. Rev.,133, B 145 (1964).
A. Erdélyi, W. Magnus, F. Oberhettinger andF. G. Tricomi:Higher Transcendental Functions, Vol.1 (New York, 1953), p. 102, eqs. (21), (18).
S. C. Frautschi:Regge Poles and S-Matrix Theory (New York, 1963) p. 151.
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Mohan, G. Regge-pole kinematics. Nuovo Cim 35, 284–291 (1965). https://doi.org/10.1007/BF02734839
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DOI: https://doi.org/10.1007/BF02734839